in \"points to\" pull ? */\r\n let int_points_to_pull_start = next_int_point_num;\r\n let int_points_to_pull_num = intPointsPoolCount(int_points, int_points_to_pull_start, cur_face);\r\n\r\n\r\n let edge_from = int_point_current.edge_after;\r\n let edge_to = int_point_next.edge_before;\r\n\r\n if ((edge_from.bv === INSIDE$1 && edge_to.bv === INSIDE$1 && op === BOOLEAN_UNION) ||\r\n (edge_from.bv === OUTSIDE$1 && edge_to.bv === OUTSIDE$1 && op === BOOLEAN_INTERSECT) ||\r\n ((edge_from.bv === OUTSIDE$1 || edge_to.bv === OUTSIDE$1) && op === BOOLEAN_SUBTRACT && !is_res_polygon) ||\r\n ((edge_from.bv === INSIDE$1 || edge_to.bv === INSIDE$1) && op === BOOLEAN_SUBTRACT && is_res_polygon) ||\r\n (edge_from.bv === BOUNDARY$1 && edge_to.bv === BOUNDARY$1 && (edge_from.overlap & OVERLAP_SAME$1) && is_res_polygon) ||\r\n (edge_from.bv === BOUNDARY$1 && edge_to.bv === BOUNDARY$1 && (edge_from.overlap & OVERLAP_OPPOSITE$1))) {\r\n\r\n polygon.removeChain(cur_face, edge_from, edge_to);\r\n\r\n /* update all points in \"points from\" pull */\r\n for (let k = int_points_from_pull_start; k < int_points_from_pull_start + int_points_from_pull_num; k++) {\r\n int_points[k].edge_after = undefined;\r\n }\r\n\r\n /* update all points in \"points to\" pull */\r\n for (let k = int_points_to_pull_start; k < int_points_to_pull_start + int_points_to_pull_num; k++) {\r\n int_points[k].edge_before = undefined;\r\n }\r\n }\r\n\r\n /* skip to the last point in \"points from\" group */\r\n i += int_points_from_pull_num - 1;\r\n }\r\n}\r\nfunction copyWrkToRes(res_polygon, wrk_polygon, op, int_points)\r\n{\r\n for (let face of wrk_polygon.faces) {\r\n for (let edge of face) {\r\n res_polygon.edges.add(edge);\r\n }\r\n // If union - add face from wrk_polygon that is not intersected with res_polygon\r\n if ( /*(op === BOOLEAN_UNION || op == BOOLEAN_SUBTRACT) &&*/\r\n int_points.find((ip) => (ip.face === face)) === undefined) {\r\n res_polygon.addFace(face.first, face.last);\r\n }\r\n }\r\n}\r\n\r\nfunction swapLinks(res_polygon, wrk_polygon, intersections)\r\n{\r\n if (intersections.int_points1.length === 0) return;\r\n\r\n for (let i = 0; i < intersections.int_points1.length; i++) {\r\n let int_point1 = intersections.int_points1[i];\r\n let int_point2 = intersections.int_points2[i];\r\n\r\n // Simple case - find continuation on the other polygon\r\n\r\n // Process edge from res_polygon\r\n if (int_point1.edge_before !== undefined && int_point1.edge_after === undefined) { // swap need\r\n if (int_point2.edge_before === undefined && int_point2.edge_after !== undefined) { // simple case\r\n // Connect edges\r\n int_point1.edge_before.next = int_point2.edge_after;\r\n int_point2.edge_after.prev = int_point1.edge_before;\r\n\r\n // Fill in missed links in intersection points\r\n int_point1.edge_after = int_point2.edge_after;\r\n int_point2.edge_before = int_point1.edge_before;\r\n }\r\n }\r\n // Process edge from wrk_polygon\r\n if (int_point2.edge_before !== undefined && int_point2.edge_after === undefined) { // swap need\r\n if (int_point1.edge_before === undefined && int_point1.edge_after !== undefined) { // simple case\r\n // Connect edges\r\n int_point2.edge_before.next = int_point1.edge_after;\r\n int_point1.edge_after.prev = int_point2.edge_before;\r\n\r\n // Complete missed links\r\n int_point2.edge_after = int_point1.edge_after;\r\n int_point1.edge_before = int_point2.edge_before;\r\n }\r\n }\r\n\r\n // Continuation not found - complex case\r\n // Continuation will be found on the same polygon.\r\n // It happens when intersection point is actually touching point\r\n // Polygon1\r\n if (int_point1.edge_before !== undefined && int_point1.edge_after === undefined) { // still swap need\r\n for (let int_point of intersections.int_points1_sorted) {\r\n if (int_point === int_point1) continue; // skip same\r\n if (int_point.edge_before === undefined && int_point.edge_after !== undefined) {\r\n if (int_point.pt.equalTo(int_point1.pt)) {\r\n // Connect edges\r\n int_point1.edge_before.next = int_point.edge_after;\r\n int_point.edge_after.prev = int_point1.edge_before;\r\n\r\n // Complete missed links\r\n int_point1.edge_after = int_point.edge_after;\r\n int_point.edge_before = int_point1.edge_before;\r\n }\r\n }\r\n }\r\n }\r\n // Polygon2\r\n if (int_point2.edge_before !== undefined && int_point2.edge_after === undefined) { // still swap need\r\n for (let int_point of intersections.int_points2_sorted) {\r\n if (int_point === int_point2) continue; // skip same\r\n if (int_point.edge_before === undefined && int_point.edge_after !== undefined) {\r\n if (int_point.pt.equalTo(int_point2.pt)) {\r\n // Connect edges\r\n int_point2.edge_before.next = int_point.edge_after;\r\n int_point.edge_after.prev = int_point2.edge_before;\r\n\r\n // Complete missed links\r\n int_point2.edge_after = int_point.edge_after;\r\n int_point.edge_before = int_point2.edge_before;\r\n }\r\n }\r\n }\r\n }\r\n }\r\n // Sanity check that no dead ends left\r\n}\r\n\r\nfunction removeOldFaces(polygon, int_points)\r\n{\r\n for (let int_point of int_points) {\r\n polygon.faces.delete(int_point.face);\r\n int_point.face = undefined;\r\n if (int_point.edge_before)\r\n int_point.edge_before.face = undefined;\r\n if (int_point.edge_after)\r\n int_point.edge_after.face = undefined;\r\n }\r\n}\r\n\r\nfunction restoreFaces(polygon, int_points, other_int_points)\r\n{\r\n // For each intersection point - create new face\r\n for (let int_point of int_points) {\r\n if (int_point.edge_before === undefined || int_point.edge_after === undefined) // completely deleted\r\n continue;\r\n if (int_point.face) // already restored\r\n continue;\r\n\r\n if (int_point.edge_after.face || int_point.edge_before.face) // Face already created. Possible case in duplicated intersection points\r\n continue;\r\n\r\n let first = int_point.edge_after; // face start\r\n let last = int_point.edge_before; // face end;\r\n\r\n LinkedList.testInfiniteLoop(first); // check and throw error if infinite loop found\r\n\r\n let face = polygon.addFace(first, last);\r\n\r\n // Mark intersection points from the newly create face\r\n // to avoid multiple creation of the same face\r\n // Face was assigned to each edge of new face in addFace function\r\n for (let int_point_tmp of int_points) {\r\n if (int_point_tmp.edge_before && int_point_tmp.edge_after &&\r\n int_point_tmp.edge_before.face === face && int_point_tmp.edge_after.face === face) {\r\n int_point_tmp.face = face;\r\n }\r\n }\r\n // Mark other intersection points as well\r\n for (let int_point_tmp of other_int_points) {\r\n if (int_point_tmp.edge_before && int_point_tmp.edge_after &&\r\n int_point_tmp.edge_before.face === face && int_point_tmp.edge_after.face === face) {\r\n int_point_tmp.face = face;\r\n }\r\n }\r\n }\r\n}\r\n\r\nfunction removeNotRelevantNotIntersectedFaces(polygon, notIntersectedFaces, op, is_res_polygon)\r\n{\r\n for (let face of notIntersectedFaces) {\r\n let rel = face.first.bv;\r\n if (op === BOOLEAN_UNION && rel === INSIDE$1 ||\r\n op === BOOLEAN_SUBTRACT && rel === INSIDE$1 && is_res_polygon ||\r\n op === BOOLEAN_SUBTRACT && rel === OUTSIDE$1 && !is_res_polygon ||\r\n op === BOOLEAN_INTERSECT && rel === OUTSIDE$1) {\r\n\r\n polygon.deleteFace(face);\r\n }\r\n }\r\n}\r\n\r\nvar BooleanOperations = /*#__PURE__*/Object.freeze({\r\n BOOLEAN_UNION: BOOLEAN_UNION,\r\n BOOLEAN_INTERSECT: BOOLEAN_INTERSECT,\r\n BOOLEAN_SUBTRACT: BOOLEAN_SUBTRACT,\r\n unify: unify,\r\n subtract: subtract,\r\n intersect: intersect,\r\n innerClip: innerClip,\r\n outerClip: outerClip,\r\n calculateIntersections: calculateIntersections,\r\n removeNotRelevantChains: removeNotRelevantChains,\r\n removeOldFaces: removeOldFaces,\r\n restoreFaces: restoreFaces\r\n});\r\n\r\n/*\r\n Dimensionally extended 9-intersected model\r\n See https://en.wikipedia.org/wiki/DE-9IM for more details\r\n */\r\n// const DISJOINT = RegExp('FF.FF....');\r\nconst EQUAL = RegExp('T.F..FFF.|T.F...F..');\r\nconst INTERSECT = RegExp('T........|.T.......|...T.....|....T....');\r\nconst TOUCH = RegExp('FT.......|F..T.....|F...T....');\r\nconst INSIDE$2 = RegExp('T.F..F...');\r\nconst COVERED = RegExp('T.F..F...|.TF..F...|..FT.F...|..F.TF...');\r\n\r\nclass DE9IM {\r\n /**\r\n * Create new instance of DE9IM matrix\r\n */\r\n constructor() {\r\n /**\r\n * Array representing 3x3 intersection matrix\r\n * @type {Shape[]}\r\n */\r\n this.m = new Array(9).fill(undefined);\r\n }\r\n\r\n /**\r\n * Get Interior To Interior intersection\r\n * @returns {Shape[] | undefined}\r\n */\r\n get I2I() {\r\n return this.m[0];\r\n }\r\n\r\n /**\r\n * Set Interior To Interior intersection\r\n * @param geom\r\n */\r\n set I2I(geom) {\r\n this.m[0] = geom;\r\n }\r\n\r\n /**\r\n * Get Interior To Boundary intersection\r\n * @returns {Shape[] | undefined}\r\n */\r\n get I2B() {\r\n return this.m[1];\r\n }\r\n\r\n /**\r\n * Set Interior to Boundary intersection\r\n * @param geomc\r\n */\r\n set I2B(geom) {\r\n this.m[1] = geom;\r\n }\r\n\r\n /**\r\n * Get Interior To Exterior intersection\r\n * @returns {Shape[] | undefined}\r\n */\r\n get I2E() {\r\n return this.m[2];\r\n }\r\n\r\n /**\r\n * Set Interior to Exterior intersection\r\n * @param geom\r\n */\r\n set I2E(geom) {\r\n this.m[2] = geom;\r\n }\r\n\r\n /**\r\n * Get Boundary To Interior intersection\r\n * @returns {Shape[] | undefined}\r\n */\r\n get B2I() {\r\n return this.m[3];\r\n }\r\n\r\n /**\r\n * Set Boundary to Interior intersection\r\n * @param geom\r\n */\r\n set B2I(geom) {\r\n this.m[3] = geom;\r\n }\r\n\r\n /**\r\n * Get Boundary To Boundary intersection\r\n * @returns {Shape[] | undefined}\r\n */\r\n get B2B() {\r\n return this.m[4];\r\n }\r\n\r\n /**\r\n * Set Boundary to Boundary intersection\r\n * @param geom\r\n */\r\n set B2B(geom) {\r\n this.m[4] = geom;\r\n }\r\n\r\n /**\r\n * Get Boundary To Exterior intersection\r\n * @returns {Shape[] | undefined}\r\n */\r\n get B2E() {\r\n return this.m[5];\r\n }\r\n\r\n /**\r\n * Set Boundary to Exterior intersection\r\n * @param geom\r\n */\r\n set B2E(geom) {\r\n this.m[5] = geom;\r\n }\r\n\r\n /**\r\n * Get Exterior To Interior intersection\r\n * @returns {Shape[] | undefined}\r\n */\r\n get E2I() {\r\n return this.m[6];\r\n }\r\n\r\n /**\r\n * Set Exterior to Interior intersection\r\n * @param geom\r\n */\r\n set E2I(geom) {\r\n this.m[6] = geom;\r\n }\r\n\r\n /**\r\n * Get Exterior To Boundary intersection\r\n * @returns {Shape[] | undefined}\r\n */\r\n get E2B() {\r\n return this.m[7];\r\n }\r\n\r\n /**\r\n * Set Exterior to Boundary intersection\r\n * @param geom\r\n */\r\n set E2B(geom) {\r\n this.m[7] = geom;\r\n }\r\n\r\n /**\r\n * Get Exterior to Exterior intersection\r\n * @returns {Shape[] | undefined}\r\n */\r\n get E2E() {\r\n return this.m[8];\r\n }\r\n\r\n /**\r\n * Set Exterior to Exterior intersection\r\n * @param geom\r\n */\r\n set E2E(geom) {\r\n this.m[8] = geom;\r\n }\r\n\r\n /**\r\n * Return de9im matrix as string where
\r\n * - intersection is 'T'
\r\n * - not intersected is 'F'
\r\n * - not relevant is '*'
\r\n * For example, string 'FF**FF****' means 'DISJOINT'\r\n * @returns {string}\r\n */\r\n toString() {\r\n return this.m.map( e => {\r\n if (e instanceof Array && e.length > 0) {\r\n return 'T'\r\n }\r\n else if (e instanceof Array && e.length === 0) {\r\n return 'F'\r\n }\r\n else {\r\n return '*'\r\n }\r\n }).join(\"\")\r\n }\r\n\r\n equal() {\r\n return EQUAL.test(this.toString());\r\n }\r\n\r\n intersect() {\r\n return INTERSECT.test(this.toString());\r\n }\r\n\r\n touch() {\r\n return TOUCH.test(this.toString());\r\n }\r\n\r\n inside() {\r\n return INSIDE$2.test(this.toString());\r\n }\r\n\r\n covered() {\r\n return COVERED.test(this.toString());\r\n }\r\n}\r\n\r\n/**\r\n * Intersection\r\n *\r\n * */\r\n\r\nfunction intersectLine2Line(line1, line2) {\r\n let ip = [];\r\n\r\n let [A1, B1, C1] = line1.standard;\r\n let [A2, B2, C2] = line2.standard;\r\n\r\n /* Cramer's rule */\r\n let det = A1 * B2 - B1 * A2;\r\n let detX = C1 * B2 - B1 * C2;\r\n let detY = A1 * C2 - C1 * A2;\r\n\r\n if (!Flatten.Utils.EQ_0(det)) {\r\n let x, y;\r\n\r\n if (B1 === 0) { // vertical line x = C1/A1, where A1 == +1 or -1\r\n x = C1/A1;\r\n y = detY / det;\r\n }\r\n else if (B2 === 0) { // vertical line x = C2/A2, where A2 = +1 or -1\r\n x = C2/A2;\r\n y = detY / det;\r\n }\r\n else if (A1 === 0) { // horizontal line y = C1/B1, where B1 = +1 or -1\r\n x = detX / det;\r\n y = C1/B1;\r\n }\r\n else if (A2 === 0) { // horizontal line y = C2/B2, where B2 = +1 or -1\r\n x = detX / det;\r\n y = C2/B2;\r\n }\r\n else {\r\n x = detX / det;\r\n y = detY / det;\r\n }\r\n\r\n ip.push(new Flatten.Point(x, y));\r\n }\r\n\r\n return ip;\r\n}\r\n\r\nfunction intersectLine2Circle(line, circle) {\r\n let ip = [];\r\n let prj = circle.pc.projectionOn(line); // projection of circle center on line\r\n let dist = circle.pc.distanceTo(prj)[0]; // distance from circle center to projection\r\n\r\n if (Flatten.Utils.EQ(dist, circle.r)) { // line tangent to circle - return single intersection point\r\n ip.push(prj);\r\n } else if (Flatten.Utils.LT(dist, circle.r)) { // return two intersection points\r\n let delta = Math.sqrt(circle.r * circle.r - dist * dist);\r\n let v_trans, pt;\r\n\r\n v_trans = line.norm.rotate90CCW().multiply(delta);\r\n pt = prj.translate(v_trans);\r\n ip.push(pt);\r\n\r\n v_trans = line.norm.rotate90CW().multiply(delta);\r\n pt = prj.translate(v_trans);\r\n ip.push(pt);\r\n }\r\n return ip;\r\n}\r\n\r\nfunction intersectLine2Box(line, box) {\r\n let ips = [];\r\n for (let seg of box.toSegments()) {\r\n let ips_tmp = intersectSegment2Line(seg, line);\r\n for (let pt of ips_tmp) {\r\n if (!ptInIntPoints(pt, ips)) {\r\n ips.push(pt);\r\n }\r\n }\r\n }\r\n return ips;\r\n}\r\n\r\nfunction intersectLine2Arc(line, arc) {\r\n let ip = [];\r\n\r\n if (intersectLine2Box(line, arc.box).length === 0) {\r\n return ip;\r\n }\r\n\r\n let circle = new Flatten.Circle(arc.pc, arc.r);\r\n let ip_tmp = intersectLine2Circle(line, circle);\r\n for (let pt of ip_tmp) {\r\n if (pt.on(arc)) {\r\n ip.push(pt);\r\n }\r\n }\r\n\r\n return ip;\r\n}\r\n\r\nfunction intersectSegment2Line(seg, line) {\r\n let ip = [];\r\n\r\n // Boundary cases\r\n if (seg.ps.on(line)) {\r\n ip.push(seg.ps);\r\n }\r\n // If both ends lay on line, return two intersection points\r\n if (seg.pe.on(line) && !seg.isZeroLength()) {\r\n ip.push(seg.pe);\r\n }\r\n\r\n if (ip.length > 0) {\r\n return ip; // done, intersection found\r\n }\r\n\r\n // If zero-length segment and nothing found, return no intersections\r\n if (seg.isZeroLength()) {\r\n return ip;\r\n }\r\n\r\n // Not a boundary case, check if both points are on the same side and\r\n // hence there is no intersection\r\n if (seg.ps.leftTo(line) && seg.pe.leftTo(line) ||\r\n !seg.ps.leftTo(line) && !seg.pe.leftTo(line)) {\r\n return ip;\r\n }\r\n\r\n // Calculate intersection between lines\r\n let line1 = new Flatten.Line(seg.ps, seg.pe);\r\n return intersectLine2Line(line1, line);\r\n}\r\n\r\nfunction intersectSegment2Segment(seg1, seg2) {\r\n let ip = [];\r\n\r\n // quick reject\r\n if (seg1.box.not_intersect(seg2.box)) {\r\n return ip;\r\n }\r\n\r\n // Special case of seg1 zero length\r\n if (seg1.isZeroLength()) {\r\n if (seg1.ps.on(seg2)) {\r\n ip.push(seg1.ps);\r\n }\r\n return ip;\r\n }\r\n\r\n // Special case of seg2 zero length\r\n if (seg2.isZeroLength()) {\r\n if (seg2.ps.on(seg1)) {\r\n ip.push(seg2.ps);\r\n }\r\n return ip;\r\n }\r\n\r\n // Neither seg1 nor seg2 is zero length\r\n let line1 = new Flatten.Line(seg1.ps, seg1.pe);\r\n let line2 = new Flatten.Line(seg2.ps, seg2.pe);\r\n\r\n // Check overlapping between segments in case of incidence\r\n // If segments touching, add one point. If overlapping, add two points\r\n if (line1.incidentTo(line2)) {\r\n if (seg1.ps.on(seg2)) {\r\n ip.push(seg1.ps);\r\n }\r\n if (seg1.pe.on(seg2)) {\r\n ip.push(seg1.pe);\r\n }\r\n if (seg2.ps.on(seg1) && !seg2.ps.equalTo(seg1.ps) && !seg2.ps.equalTo(seg1.pe)) {\r\n ip.push(seg2.ps);\r\n }\r\n if (seg2.pe.on(seg1) && !seg2.pe.equalTo(seg1.ps) && !seg2.pe.equalTo(seg1.pe)) {\r\n ip.push(seg2.pe);\r\n }\r\n } else { /* not incident - parallel or intersect */\r\n // Calculate intersection between lines\r\n let new_ip = intersectLine2Line(line1, line2);\r\n if (new_ip.length > 0 && new_ip[0].on(seg1) && new_ip[0].on(seg2)) {\r\n ip.push(new_ip[0]);\r\n }\r\n\r\n // Fix missing intersection\r\n // const tol = 10*Flatten.DP_TOL;\r\n // if (ip.length === 0 && new_ip.length > 0 && (new_ip[0].distanceTo(seg1)[0] < tol || new_ip[0].distanceTo(seg2)[0] < tol) ) {\r\n // if (seg1.start.distanceTo(seg2)[0] < tol) {\r\n // ip.push(new_ip[0]);\r\n // }\r\n // else if (seg1.end.distanceTo(seg2)[0] < tol) {\r\n // ip.push(new_ip[0]);\r\n // }\r\n // else if (seg2.start.distanceTo(seg1)[0] < tol) {\r\n // ip.push(new_ip[0]);\r\n // }\r\n // else if (seg2.end.distanceTo(seg1)[0] < tol) {\r\n // ip.push(new_ip[0]);\r\n // }\r\n // }\r\n }\r\n\r\n return ip;\r\n}\r\n\r\nfunction intersectSegment2Circle(segment, circle) {\r\n let ips = [];\r\n\r\n if (segment.box.not_intersect(circle.box)) {\r\n return ips;\r\n }\r\n\r\n // Special case of zero length segment\r\n if (segment.isZeroLength()) {\r\n let [dist, shortest_segment] = segment.ps.distanceTo(circle.pc);\r\n if (Flatten.Utils.EQ(dist, circle.r)) {\r\n ips.push(segment.ps);\r\n }\r\n return ips;\r\n }\r\n\r\n // Non zero-length segment\r\n let line = new Flatten.Line(segment.ps, segment.pe);\r\n\r\n let ips_tmp = intersectLine2Circle(line, circle);\r\n\r\n for (let ip of ips_tmp) {\r\n if (ip.on(segment)) {\r\n ips.push(ip);\r\n }\r\n }\r\n\r\n return ips;\r\n}\r\n\r\nfunction intersectSegment2Arc(segment, arc) {\r\n let ip = [];\r\n\r\n if (segment.box.not_intersect(arc.box)) {\r\n return ip;\r\n }\r\n\r\n // Special case of zero-length segment\r\n if (segment.isZeroLength()) {\r\n if (segment.ps.on(arc)) {\r\n ip.push(segment.ps);\r\n }\r\n return ip;\r\n }\r\n\r\n // Non-zero length segment\r\n let line = new Flatten.Line(segment.ps, segment.pe);\r\n let circle = new Flatten.Circle(arc.pc, arc.r);\r\n\r\n let ip_tmp = intersectLine2Circle(line, circle);\r\n\r\n for (let pt of ip_tmp) {\r\n if (pt.on(segment) && pt.on(arc)) {\r\n ip.push(pt);\r\n }\r\n }\r\n return ip;\r\n\r\n}\r\n\r\nfunction intersectSegment2Box(segment, box) {\r\n let ips = [];\r\n for (let seg of box.toSegments()) {\r\n let ips_tmp = intersectSegment2Segment(seg, segment);\r\n for (let ip of ips_tmp) {\r\n ips.push(ip);\r\n }\r\n }\r\n return ips;\r\n}\r\n\r\nfunction intersectCircle2Circle(circle1, circle2) {\r\n let ip = [];\r\n\r\n if (circle1.box.not_intersect(circle2.box)) {\r\n return ip;\r\n }\r\n\r\n let vec = new Flatten.Vector(circle1.pc, circle2.pc);\r\n\r\n let r1 = circle1.r;\r\n let r2 = circle2.r;\r\n\r\n // Degenerated circle\r\n if (Flatten.Utils.EQ_0(r1) || Flatten.Utils.EQ_0(r2))\r\n return ip;\r\n\r\n // In case of equal circles return one leftmost point\r\n if (Flatten.Utils.EQ_0(vec.x) && Flatten.Utils.EQ_0(vec.y) && Flatten.Utils.EQ(r1, r2)) {\r\n ip.push(circle1.pc.translate(-r1, 0));\r\n return ip;\r\n }\r\n\r\n let dist = circle1.pc.distanceTo(circle2.pc)[0];\r\n\r\n if (Flatten.Utils.GT(dist, r1 + r2)) // circles too far, no intersections\r\n return ip;\r\n\r\n if (Flatten.Utils.LT(dist, Math.abs(r1 - r2))) // one circle is contained within another, no intersections\r\n return ip;\r\n\r\n // Normalize vector.\r\n vec.x /= dist;\r\n vec.y /= dist;\r\n\r\n let pt;\r\n\r\n // Case of touching from outside or from inside - single intersection point\r\n // TODO: check this specifically not sure if correct\r\n if (Flatten.Utils.EQ(dist, r1 + r2) || Flatten.Utils.EQ(dist, Math.abs(r1 - r2))) {\r\n pt = circle1.pc.translate(r1 * vec.x, r1 * vec.y);\r\n ip.push(pt);\r\n return ip;\r\n }\r\n\r\n // Case of two intersection points\r\n\r\n // Distance from first center to center of common chord:\r\n // a = (r1^2 - r2^2 + d^2) / 2d\r\n // Separate for better accuracy\r\n let a = (r1 * r1) / (2 * dist) - (r2 * r2) / (2 * dist) + dist / 2;\r\n\r\n let mid_pt = circle1.pc.translate(a * vec.x, a * vec.y);\r\n let h = Math.sqrt(r1 * r1 - a * a);\r\n // let norm;\r\n\r\n // norm = vec.rotate90CCW().multiply(h);\r\n pt = mid_pt.translate(vec.rotate90CCW().multiply(h));\r\n ip.push(pt);\r\n\r\n // norm = vec.rotate90CW();\r\n pt = mid_pt.translate(vec.rotate90CW().multiply(h));\r\n ip.push(pt);\r\n\r\n return ip;\r\n}\r\n\r\nfunction intersectCircle2Box(circle, box) {\r\n let ips = [];\r\n for (let seg of box.toSegments()) {\r\n let ips_tmp = intersectSegment2Circle(seg, circle);\r\n for (let ip of ips_tmp) {\r\n ips.push(ip);\r\n }\r\n }\r\n return ips;\r\n}\r\n\r\nfunction intersectArc2Arc(arc1, arc2) {\r\n var ip = [];\r\n\r\n if (arc1.box.not_intersect(arc2.box)) {\r\n return ip;\r\n }\r\n\r\n // Special case: overlapping arcs\r\n // May return up to 4 intersection points\r\n if (arc1.pc.equalTo(arc2.pc) && Flatten.Utils.EQ(arc1.r, arc2.r)) {\r\n let pt;\r\n\r\n pt = arc1.start;\r\n if (pt.on(arc2))\r\n ip.push(pt);\r\n\r\n pt = arc1.end;\r\n if (pt.on(arc2))\r\n ip.push(pt);\r\n\r\n pt = arc2.start;\r\n if (pt.on(arc1)) ip.push(pt);\r\n\r\n pt = arc2.end;\r\n if (pt.on(arc1)) ip.push(pt);\r\n\r\n return ip;\r\n }\r\n\r\n // Common case\r\n let circle1 = new Flatten.Circle(arc1.pc, arc1.r);\r\n let circle2 = new Flatten.Circle(arc2.pc, arc2.r);\r\n let ip_tmp = circle1.intersect(circle2);\r\n for (let pt of ip_tmp) {\r\n if (pt.on(arc1) && pt.on(arc2)) {\r\n ip.push(pt);\r\n }\r\n }\r\n return ip;\r\n}\r\n\r\nfunction intersectArc2Circle(arc, circle) {\r\n let ip = [];\r\n\r\n if (arc.box.not_intersect(circle.box)) {\r\n return ip;\r\n }\r\n\r\n // Case when arc center incident to circle center\r\n // Return arc's end points as 2 intersection points\r\n if (circle.pc.equalTo(arc.pc) && Flatten.Utils.EQ(circle.r, arc.r)) {\r\n ip.push(arc.start);\r\n ip.push(arc.end);\r\n return ip;\r\n }\r\n\r\n // Common case\r\n let circle1 = circle;\r\n let circle2 = new Flatten.Circle(arc.pc, arc.r);\r\n let ip_tmp = intersectCircle2Circle(circle1, circle2);\r\n for (let pt of ip_tmp) {\r\n if (pt.on(arc)) {\r\n ip.push(pt);\r\n }\r\n }\r\n return ip;\r\n}\r\n\r\nfunction intersectArc2Box(arc, box) {\r\n let ips = [];\r\n for (let seg of box.toSegments()) {\r\n let ips_tmp = intersectSegment2Arc(seg, arc);\r\n for (let ip of ips_tmp) {\r\n ips.push(ip);\r\n }\r\n }\r\n return ips;\r\n}\r\n\r\nfunction intersectEdge2Segment(edge, segment) {\r\n return edge.isSegment() ? intersectSegment2Segment(edge.shape, segment) : intersectSegment2Arc(segment, edge.shape);\r\n}\r\n\r\nfunction intersectEdge2Arc(edge, arc) {\r\n return edge.isSegment() ? intersectSegment2Arc(edge.shape, arc) : intersectArc2Arc(edge.shape, arc);\r\n}\r\n\r\nfunction intersectEdge2Line(edge, line) {\r\n return edge.isSegment() ? intersectSegment2Line(edge.shape, line) : intersectLine2Arc(line, edge.shape);\r\n}\r\n\r\nfunction intersectEdge2Circle(edge, circle) {\r\n return edge.isSegment() ? intersectSegment2Circle(edge.shape, circle) : intersectArc2Circle(edge.shape, circle);\r\n}\r\n\r\nfunction intersectSegment2Polygon(segment, polygon) {\r\n let ip = [];\r\n\r\n for (let edge of polygon.edges) {\r\n for (let pt of intersectEdge2Segment(edge, segment)) {\r\n ip.push(pt);\r\n }\r\n }\r\n\r\n return ip;\r\n}\r\n\r\nfunction intersectArc2Polygon(arc, polygon) {\r\n let ip = [];\r\n\r\n for (let edge of polygon.edges) {\r\n for (let pt of intersectEdge2Arc(edge, arc)) {\r\n ip.push(pt);\r\n }\r\n }\r\n\r\n return ip;\r\n}\r\n\r\nfunction intersectLine2Polygon(line, polygon) {\r\n let ip = [];\r\n\r\n if (polygon.isEmpty()) {\r\n return ip;\r\n }\r\n\r\n for (let edge of polygon.edges) {\r\n for (let pt of intersectEdge2Line(edge, line)) {\r\n if (!ptInIntPoints(pt, ip)) {\r\n ip.push(pt);\r\n }\r\n }\r\n }\r\n\r\n return line.sortPoints(ip);\r\n}\r\n\r\nfunction intersectCircle2Polygon(circle, polygon) {\r\n let ip = [];\r\n\r\n if (polygon.isEmpty()) {\r\n return ip;\r\n }\r\n\r\n for (let edge of polygon.edges) {\r\n for (let pt of intersectEdge2Circle(edge, circle)) {\r\n ip.push(pt);\r\n }\r\n }\r\n\r\n return ip;\r\n}\r\n\r\nfunction intersectEdge2Edge(edge1, edge2) {\r\n const shape1 = edge1.shape;\r\n const shape2 = edge2.shape;\r\n return edge1.isSegment() ?\r\n (edge2.isSegment() ? intersectSegment2Segment(shape1, shape2) : intersectSegment2Arc(shape1, shape2)) :\r\n (edge2.isSegment() ? intersectSegment2Arc(shape2, shape1) : intersectArc2Arc(shape1, shape2));\r\n}\r\n\r\nfunction intersectEdge2Polygon(edge, polygon) {\r\n let ip = [];\r\n\r\n if (polygon.isEmpty() || edge.shape.box.not_intersect(polygon.box)) {\r\n return ip;\r\n }\r\n\r\n let resp_edges = polygon.edges.search(edge.shape.box);\r\n\r\n for (let resp_edge of resp_edges) {\r\n for (let pt of intersectEdge2Edge(edge, resp_edge)) {\r\n ip.push(pt);\r\n }\r\n }\r\n\r\n return ip;\r\n}\r\n\r\nfunction intersectPolygon2Polygon(polygon1, polygon2) {\r\n let ip = [];\r\n\r\n if (polygon1.isEmpty() || polygon2.isEmpty()) {\r\n return ip;\r\n }\r\n\r\n if (polygon1.box.not_intersect(polygon2.box)) {\r\n return ip;\r\n }\r\n\r\n for (let edge1 of polygon1.edges) {\r\n for (let pt of intersectEdge2Polygon(edge1, polygon2)) {\r\n ip.push(pt);\r\n }\r\n }\r\n\r\n return ip;\r\n}\r\n\r\nfunction intersectShape2Polygon(shape, polygon) {\r\n if (shape instanceof Flatten.Line) {\r\n return intersectLine2Polygon(shape, polygon);\r\n }\r\n else if (shape instanceof Flatten.Segment) {\r\n return intersectSegment2Polygon(shape, polygon);\r\n }\r\n else if (shape instanceof Flatten.Arc) {\r\n return intersectArc2Polygon(shape, polygon);\r\n }\r\n else {\r\n return [];\r\n }\r\n}\r\n\r\nfunction ptInIntPoints(new_pt, ip) {\r\n return ip.some( pt => pt.equalTo(new_pt) )\r\n}\r\n\r\n/**\r\n * Class Multiline represent connected path of [edges]{@link Flatten.Edge}, where each edge may be\r\n * [segment]{@link Flatten.Segment}, [arc]{@link Flatten.Arc}, [line]{@link Flatten.Line} or [ray]{@link Flatten.Ray}\r\n */\r\nclass Multiline extends LinkedList {\r\n constructor(...args) {\r\n super();\r\n\r\n if (args.length === 0) {\r\n return;\r\n }\r\n\r\n if (args.length == 1) {\r\n if (args[0] instanceof Array) {\r\n let shapes = args[0];\r\n if (shapes.length == 0)\r\n return;\r\n\r\n // TODO: more strict validation:\r\n // there may be only one line\r\n // only first and last may be rays\r\n let validShapes = shapes.every((shape) => {\r\n return shape instanceof Flatten.Segment ||\r\n shape instanceof Flatten.Arc ||\r\n shape instanceof Flatten.Ray ||\r\n shape instanceof Flatten.Line\r\n });\r\n\r\n for (let shape of shapes) {\r\n let edge = new Flatten.Edge(shape);\r\n this.append(edge);\r\n }\r\n }\r\n }\r\n }\r\n\r\n /**\r\n * (Getter) Return array of edges\r\n * @returns {Edge[]}\r\n */\r\n get edges() {\r\n return [...this];\r\n }\r\n\r\n /**\r\n * (Getter) Return bounding box of the multiline\r\n * @returns {Box}\r\n */\r\n get box() {\r\n return this.edges.reduce( (acc,edge) => acc = acc.merge(edge.box), new Flatten.Box() );\r\n }\r\n\r\n /**\r\n * (Getter) Returns array of vertices\r\n * @returns {Point[]}\r\n */\r\n get vertices() {\r\n let v = this.edges.map(edge => edge.start);\r\n v.push(this.last.end);\r\n return v;\r\n }\r\n\r\n /**\r\n * Return new cloned instance of Multiline\r\n * @returns {Multiline}\r\n */\r\n clone() {\r\n return new Multiline(this.toShapes());\r\n }\r\n\r\n /**\r\n * Split edge and add new vertex, return new edge inserted\r\n * @param {Point} pt - point on edge that will be added as new vertex\r\n * @param {Edge} edge - edge to split\r\n * @returns {Edge}\r\n */\r\n addVertex(pt, edge) {\r\n let shapes = edge.shape.split(pt);\r\n // if (shapes.length < 2) return;\r\n\r\n if (shapes[0] === null) // point incident to edge start vertex, return previous edge\r\n return edge.prev;\r\n\r\n if (shapes[1] === null) // point incident to edge end vertex, return edge itself\r\n return edge;\r\n\r\n let newEdge = new Flatten.Edge(shapes[0]);\r\n let edgeBefore = edge.prev;\r\n\r\n /* Insert first split edge into linked list after edgeBefore */\r\n this.insert(newEdge, edgeBefore); // edge.face ?\r\n\r\n // Update edge shape with second split edge keeping links\r\n edge.shape = shapes[1];\r\n\r\n return newEdge;\r\n }\r\n\r\n /**\r\n * Split edges of multiline with intersection points and return mutated multiline\r\n * @param {Point[]} ip - array of points to be added as new vertices\r\n * @returns {Multiline}\r\n */\r\n split(ip) {\r\n for (let pt of ip) {\r\n let edge = this.findEdgeByPoint(pt);\r\n this.addVertex(pt, edge);\r\n }\r\n return this;\r\n }\r\n\r\n /**\r\n * Returns edge which contains given point\r\n * @param {Point} pt\r\n * @returns {Edge}\r\n */\r\n findEdgeByPoint(pt) {\r\n let edgeFound;\r\n for (let edge of this) {\r\n if (edge.shape.contains(pt)) {\r\n edgeFound = edge;\r\n break;\r\n }\r\n }\r\n return edgeFound;\r\n }\r\n\r\n /**\r\n * Returns new multiline translated by vector vec\r\n * @param {Vector} vec\r\n * @returns {Multiline}\r\n */\r\n translate(vec) {\r\n return new Multiline(this.edges.map( edge => edge.shape.translate(vec)));\r\n }\r\n\r\n /**\r\n * Return new multiline rotated by given angle around given point\r\n * If point omitted, rotate around origin (0,0)\r\n * Positive value of angle defines rotation counter clockwise, negative - clockwise\r\n * @param {number} angle - rotation angle in radians\r\n * @param {Point} center - rotation center, default is (0,0)\r\n * @returns {Multiline} - new rotated polygon\r\n */\r\n rotate(angle = 0, center = new Flatten.Point()) {\r\n return new Multiline(this.edges.map( edge => edge.shape.rotate(angle, center) ));\r\n }\r\n\r\n /**\r\n * Return new multiline transformed using affine transformation matrix\r\n * Method does not support unbounded shapes\r\n * @param {Matrix} matrix - affine transformation matrix\r\n * @returns {Multiline} - new multiline\r\n */\r\n transform(matrix = new Flatten.Matrix()) {\r\n return new Multiline(this.edges.map( edge => edge.shape.transform(matrix)));\r\n }\r\n\r\n /**\r\n * Transform multiline into array of shapes\r\n * @returns {Shape[]}\r\n */\r\n toShapes() {\r\n return this.edges.map(edge => edge.shape.clone())\r\n }\r\n\r\n /**\r\n * This method returns an object that defines how data will be\r\n * serialized when called JSON.stringify() method\r\n * @returns {Object}\r\n */\r\n toJSON() {\r\n return this.edges.map(edge => edge.toJSON());\r\n }\r\n\r\n /**\r\n * Return string to draw multiline in svg\r\n * @param attrs - an object with attributes for svg path element,\r\n * like \"stroke\", \"strokeWidth\", \"fill\", \"fillRule\", \"fillOpacity\"\r\n * Defaults are stroke:\"black\", strokeWidth:\"1\", fill:\"lightcyan\", fillRule:\"evenodd\", fillOpacity: \"1\"\r\n * TODO: support semi-infinite Ray and infinite Line\r\n * @returns {string}\r\n */\r\n svg(attrs = {}) {\r\n let {stroke, strokeWidth, fill, fillRule, fillOpacity, id, className} = attrs;\r\n let id_str = (id && id.length > 0) ? `id=\"${id}\"` : \"\";\r\n let class_str = (className && className.length > 0) ? `class=\"${className}\"` : \"\";\r\n\r\n let svgStr = `\\n\\n`;\r\n\r\n return svgStr;\r\n }\r\n}\r\n\r\nFlatten.Multiline = Multiline;\r\n\r\n/**\r\n * Shortcut function to create multiline\r\n * @param args\r\n */\r\nconst multiline = (...args) => new Flatten.Multiline(...args);\r\nFlatten.multiline = multiline;\r\n\r\n/**\r\n * @module RayShoot\r\n */\r\n/**\r\n * Implements ray shooting algorithm. Returns relation between point and polygon: inside, outside or boundary\r\n * @param {Polygon} polygon - polygon to test\r\n * @param {Point} point - point to test\r\n * @returns {INSIDE|OUTSIDE|BOUNDARY}\r\n */\r\nfunction ray_shoot(polygon, point) {\r\n let contains = undefined;\r\n\r\n // 1. Quick reject\r\n // if (polygon.box.not_intersect(point.box)) {\r\n // return Flatten.OUTSIDE;\r\n // }\r\n\r\n let ray = new Flatten.Ray(point);\r\n let line = new Flatten.Line(ray.pt, ray.norm);\r\n\r\n // 2. Locate relevant edges of the polygon\r\n const searchBox = new Flatten.Box(\r\n ray.box.xmin-Flatten.DP_TOL, ray.box.ymin-Flatten.DP_TOL,\r\n ray.box.xmax, ray.box.ymax+Flatten.DP_TOL\r\n );\r\n\r\n if (polygon.box.not_intersect(searchBox)) {\r\n return Flatten.OUTSIDE;\r\n }\r\n\r\n let resp_edges = polygon.edges.search(searchBox);\r\n\r\n if (resp_edges.length == 0) {\r\n return Flatten.OUTSIDE;\r\n }\r\n\r\n // 2.5 Check if boundary\r\n for (let edge of resp_edges) {\r\n if (edge.shape.contains(point)) {\r\n return Flatten.BOUNDARY;\r\n }\r\n }\r\n\r\n // 3. Calculate intersections\r\n let intersections = [];\r\n for (let edge of resp_edges) {\r\n for (let ip of ray.intersect(edge.shape)) {\r\n\r\n // If intersection is equal to query point then point lays on boundary\r\n if (ip.equalTo(point)) {\r\n return Flatten.BOUNDARY;\r\n }\r\n\r\n intersections.push({\r\n pt: ip,\r\n edge: edge\r\n });\r\n }\r\n }\r\n\r\n // 4. Sort intersection in x-ascending order\r\n intersections.sort((i1, i2) => {\r\n if (LT(i1.pt.x, i2.pt.x)) {\r\n return -1;\r\n }\r\n if (GT(i1.pt.x, i2.pt.x)) {\r\n return 1;\r\n }\r\n return 0;\r\n });\r\n\r\n // 5. Count real intersections, exclude touching\r\n let counter = 0;\r\n\r\n for (let i = 0; i < intersections.length; i++) {\r\n let intersection = intersections[i];\r\n if (intersection.pt.equalTo(intersection.edge.shape.start)) {\r\n /* skip same point between same edges if already counted */\r\n if (i > 0 && intersection.pt.equalTo(intersections[i - 1].pt) &&\r\n intersection.edge.prev === intersections[i - 1].edge) {\r\n continue;\r\n }\r\n let prev_edge = intersection.edge.prev;\r\n while (EQ_0(prev_edge.length)) {\r\n prev_edge = prev_edge.prev;\r\n }\r\n let prev_tangent = prev_edge.shape.tangentInEnd();\r\n let prev_point = intersection.pt.translate(prev_tangent);\r\n\r\n let cur_tangent = intersection.edge.shape.tangentInStart();\r\n let cur_point = intersection.pt.translate(cur_tangent);\r\n\r\n let prev_on_the_left = prev_point.leftTo(line);\r\n let cur_on_the_left = cur_point.leftTo(line);\r\n\r\n if ((prev_on_the_left && !cur_on_the_left) || (!prev_on_the_left && cur_on_the_left)) {\r\n counter++;\r\n }\r\n } else if (intersection.pt.equalTo(intersection.edge.shape.end)) {\r\n /* skip same point between same edges if already counted */\r\n if (i > 0 && intersection.pt.equalTo(intersections[i - 1].pt) &&\r\n intersection.edge.next === intersections[i - 1].edge) {\r\n continue;\r\n }\r\n let next_edge = intersection.edge.next;\r\n while (EQ_0(next_edge.length)) {\r\n next_edge = next_edge.next;\r\n }\r\n let next_tangent = next_edge.shape.tangentInStart();\r\n let next_point = intersection.pt.translate(next_tangent);\r\n\r\n let cur_tangent = intersection.edge.shape.tangentInEnd();\r\n let cur_point = intersection.pt.translate(cur_tangent);\r\n\r\n let next_on_the_left = next_point.leftTo(line);\r\n let cur_on_the_left = cur_point.leftTo(line);\r\n\r\n if ((next_on_the_left && !cur_on_the_left) || (!next_on_the_left && cur_on_the_left)) {\r\n counter++;\r\n }\r\n } else { /* intersection point is not a coincident with a vertex */\r\n if (intersection.edge.shape instanceof Flatten.Segment) {\r\n counter++;\r\n } else {\r\n /* Check if ray does not touch the curve in the extremal (top or bottom) point */\r\n let box = intersection.edge.shape.box;\r\n if (!(EQ(intersection.pt.y, box.ymin) ||\r\n EQ(intersection.pt.y, box.ymax))) {\r\n counter++;\r\n }\r\n }\r\n }\r\n }\r\n\r\n // 6. Odd or even?\r\n contains = counter % 2 == 1 ? INSIDE : OUTSIDE;\r\n\r\n return contains;\r\n}\r\n\r\n/*\r\n Calculate relationship between two shapes and return result in the form of\r\n Dimensionally Extended nine-Intersection Matrix (https://en.wikipedia.org/wiki/DE-9IM)\r\n */\r\n\r\n/**\r\n * Returns true if shapes are topologically equal: their interiors intersect and\r\n * no part of the interior or boundary of one geometry intersects the exterior of the other\r\n * @param shape1\r\n * @param shape2\r\n * @returns {boolean}\r\n */\r\nfunction equal(shape1, shape2) {\r\n return relate(shape1, shape2).equal();\r\n}\r\n\r\n/**\r\n * Returns true if shapes have at least one point in common, same as \"not disjoint\"\r\n * @param shape1\r\n * @param shape2\r\n * @returns {boolean}\r\n */\r\nfunction intersect$1(shape1, shape2) {\r\n return relate(shape1, shape2).intersect();\r\n}\r\n\r\n/**\r\n * Returns true if shapes have at least one point in common, but their interiors do not intersect\r\n * @param shape1\r\n * @param shape2\r\n * @returns {boolean}\r\n */\r\nfunction touch(shape1, shape2) {\r\n return relate(shape1, shape2).touch();\r\n}\r\n\r\n/**\r\n * Returns true if shapes have no points in common neither in interior nor in boundary\r\n * @param shape1\r\n * @param shape2\r\n * @returns {boolean}\r\n */\r\nfunction disjoint(shape1, shape2) {\r\n return !intersect$1(shape1, shape2);\r\n}\r\n\r\n/**\r\n * Returns true shape1 lies in the interior of shape2\r\n * @param shape1\r\n * @param shape2\r\n * @returns {boolean}\r\n */\r\nfunction inside(shape1, shape2) {\r\n return relate(shape1, shape2).inside();\r\n}\r\n\r\n/**\r\n * Returns true if every point in shape1 lies in the interior or on the boundary of shape2\r\n * @param shape1\r\n * @param shape2\r\n * @returns {boolean}\r\n */\r\nfunction covered(shape1, shape2) {\r\n return relate(shape1, shape2).covered();\r\n}\r\n\r\n/**\r\n * Returns true shape1's interior contains shape2
\r\n * Same as inside(shape2, shape1)\r\n * @param shape1\r\n * @param shape2\r\n * @returns {boolean}\r\n */\r\nfunction contain(shape1, shape2) {\r\n return inside(shape2, shape1);\r\n}\r\n\r\n/**\r\n * Returns true shape1's cover shape2, same as shape2 covered by shape1\r\n * @param shape1\r\n * @param shape2\r\n * @returns {boolean}\r\n */\r\nfunction cover(shape1, shape2) {\r\n return covered(shape2, shape1);\r\n}\r\n\r\n/**\r\n * Returns relation between two shapes as intersection 3x3 matrix, where each\r\n * element contains relevant intersection as array of shapes.\r\n * If there is no intersection, element contains empty array\r\n * If intersection is irrelevant it left undefined. (For example, intersection\r\n * between two exteriors is usually irrelevant)\r\n * @param shape1\r\n * @param shape2\r\n * @returns {DE9IM}\r\n */\r\nfunction relate(shape1, shape2) {\r\n if (shape1 instanceof Flatten.Line && shape2 instanceof Flatten.Line) {\r\n return relateLine2Line(shape1, shape2);\r\n }\r\n else if (shape1 instanceof Flatten.Line && shape2 instanceof Flatten.Circle) {\r\n return relateLine2Circle(shape1, shape2);\r\n }\r\n else if (shape1 instanceof Flatten.Line && shape2 instanceof Flatten.Box) {\r\n return relateLine2Box(shape1, shape2);\r\n }\r\n else if ( shape1 instanceof Flatten.Line && shape2 instanceof Flatten.Polygon) {\r\n return relateLine2Polygon(shape1, shape2);\r\n }\r\n else if ( (shape1 instanceof Flatten.Segment || shape1 instanceof Flatten.Arc) && shape2 instanceof Flatten.Polygon) {\r\n return relateShape2Polygon(shape1, shape2);\r\n }\r\n else if ( (shape1 instanceof Flatten.Segment || shape1 instanceof Flatten.Arc) &&\r\n (shape2 instanceof Flatten.Circle || shape2 instanceof Flatten.Box) ) {\r\n return relateShape2Polygon(shape1, new Flatten.Polygon(shape2));\r\n }\r\n else if (shape1 instanceof Flatten.Polygon && shape2 instanceof Flatten.Polygon) {\r\n return relatePolygon2Polygon(shape1, shape2);\r\n }\r\n else if ((shape1 instanceof Flatten.Circle || shape1 instanceof Flatten.Box) &&\r\n (shape2 instanceof Flatten.Circle || shape2 instanceof Flatten.Box)) {\r\n return relatePolygon2Polygon(new Flatten.Polygon(shape1), new Flatten.Polygon(shape2));\r\n }\r\n else if ((shape1 instanceof Flatten.Circle || shape1 instanceof Flatten.Box) && shape2 instanceof Flatten.Polygon) {\r\n return relatePolygon2Polygon(new Flatten.Polygon(shape1), shape2);\r\n }\r\n else if (shape1 instanceof Flatten.Polygon && (shape2 instanceof Flatten.Circle || shape2 instanceof Flatten.Box)) {\r\n return relatePolygon2Polygon(shape1, new Flatten.Polygon(shape2));\r\n }\r\n}\r\n\r\nfunction relateLine2Line(line1, line2) {\r\n let denim = new DE9IM();\r\n let ip = intersectLine2Line(line1, line2);\r\n if (ip.length === 0) { // parallel or equal ?\r\n if (line1.contains(line2.pt) && line2.contains(line1.pt)) {\r\n denim.I2I = [line1]; // equal 'T.F...F..' - no boundary\r\n denim.I2E = [];\r\n denim.E2I = [];\r\n }\r\n else { // parallel - disjoint 'FFTFF*T**'\r\n denim.I2I = [];\r\n denim.I2E = [line1];\r\n denim.E2I = [line2];\r\n }\r\n }\r\n else { // intersect 'T********'\r\n denim.I2I = ip;\r\n denim.I2E = line1.split(ip);\r\n denim.E2I = line2.split(ip);\r\n }\r\n return denim;\r\n}\r\n\r\nfunction relateLine2Circle(line,circle) {\r\n let denim = new DE9IM();\r\n let ip = intersectLine2Circle(line, circle);\r\n if (ip.length === 0) {\r\n denim.I2I = [];\r\n denim.I2B = [];\r\n denim.I2E = [line];\r\n denim.E2I = [circle];\r\n }\r\n else if (ip.length === 1) {\r\n denim.I2I = [];\r\n denim.I2B = ip;\r\n denim.I2E = line.split(ip);\r\n\r\n denim.E2I = [circle];\r\n }\r\n else { // ip.length == 2\r\n let multiline = new Multiline([line]);\r\n let ip_sorted = line.sortPoints(ip);\r\n multiline.split(ip_sorted);\r\n let splitShapes = multiline.toShapes();\r\n\r\n denim.I2I = [splitShapes[1]];\r\n denim.I2B = ip_sorted;\r\n denim.I2E = [splitShapes[0], splitShapes[2]];\r\n\r\n denim.E2I = new Flatten.Polygon([circle.toArc()]).cut(multiline);\r\n }\r\n\r\n return denim;\r\n}\r\n\r\nfunction relateLine2Box(line, box) {\r\n let denim = new DE9IM();\r\n let ip = intersectLine2Box(line, box);\r\n if (ip.length === 0) {\r\n denim.I2I = [];\r\n denim.I2B = [];\r\n denim.I2E = [line];\r\n\r\n denim.E2I = [box];\r\n }\r\n else if (ip.length === 1) {\r\n denim.I2I = [];\r\n denim.I2B = ip;\r\n denim.I2E = line.split(ip);\r\n\r\n denim.E2I = [box];\r\n }\r\n else { // ip.length == 2\r\n let multiline = new Multiline([line]);\r\n let ip_sorted = line.sortPoints(ip);\r\n multiline.split(ip_sorted);\r\n let splitShapes = multiline.toShapes();\r\n\r\n /* Are two intersection points on the same segment of the box boundary ? */\r\n if (box.toSegments().some( segment => segment.contains(ip[0]) && segment.contains(ip[1]) )) {\r\n denim.I2I = []; // case of touching\r\n denim.I2B = [splitShapes[1]];\r\n denim.I2E = [splitShapes[0], splitShapes[2]];\r\n\r\n denim.E2I = [box];\r\n }\r\n else { // case of intersection\r\n denim.I2I = [splitShapes[1]]; // [segment(ip[0], ip[1])];\r\n denim.I2B = ip_sorted;\r\n denim.I2E = [splitShapes[0], splitShapes[2]];\r\n\r\n denim.E2I = new Flatten.Polygon(box.toSegments()).cut(multiline);\r\n }\r\n }\r\n return denim;\r\n}\r\n\r\nfunction relateLine2Polygon(line, polygon) {\r\n let denim = new DE9IM();\r\n let ip = intersectLine2Polygon(line, polygon);\r\n let multiline = new Multiline([line]);\r\n let ip_sorted = ip.length > 0 ? ip.slice() : line.sortPoints(ip);\r\n\r\n multiline.split(ip_sorted);\r\n\r\n [...multiline].forEach(edge => edge.setInclusion(polygon));\r\n\r\n denim.I2I = [...multiline].filter(edge => edge.bv === Flatten.INSIDE).map(edge => edge.shape);\r\n denim.I2B = [...multiline].slice(1).map( (edge) => edge.bv === Flatten.BOUNDARY ? edge.shape : edge.shape.start );\r\n denim.I2E = [...multiline].filter(edge => edge.bv === Flatten.OUTSIDE).map(edge => edge.shape);\r\n\r\n denim.E2I = polygon.cut(multiline);\r\n\r\n return denim;\r\n}\r\n\r\nfunction relateShape2Polygon(shape, polygon) {\r\n let denim = new DE9IM();\r\n let ip = intersectShape2Polygon(shape, polygon);\r\n let ip_sorted = ip.length > 0 ? ip.slice() : shape.sortPoints(ip);\r\n\r\n let multiline = new Multiline([shape]);\r\n multiline.split(ip_sorted);\r\n\r\n [...multiline].forEach(edge => edge.setInclusion(polygon));\r\n\r\n denim.I2I = [...multiline].filter(edge => edge.bv === Flatten.INSIDE).map(edge => edge.shape);\r\n denim.I2B = [...multiline].slice(1).map( (edge) => edge.bv === Flatten.BOUNDARY ? edge.shape : edge.shape.start );\r\n denim.I2E = [...multiline].filter(edge => edge.bv === Flatten.OUTSIDE).map(edge => edge.shape);\r\n\r\n\r\n denim.B2I = [];\r\n denim.B2B = [];\r\n denim.B2E = [];\r\n for (let pt of [shape.start, shape.end]) {\r\n switch (ray_shoot(polygon, pt)) {\r\n case Flatten.INSIDE:\r\n denim.B2I.push(pt);\r\n break;\r\n case Flatten.BOUNDARY:\r\n denim.B2B.push(pt);\r\n break;\r\n case Flatten.OUTSIDE:\r\n denim.B2E.push(pt);\r\n break;\r\n default:\r\n break;\r\n }\r\n }\r\n\r\n // denim.E2I TODO: calculate, not clear what is expected result\r\n\r\n return denim;\r\n}\r\n\r\nfunction relatePolygon2Polygon(polygon1, polygon2) {\r\n let denim = new DE9IM();\r\n\r\n let [ip_sorted1, ip_sorted2] = calculateIntersections(polygon1, polygon2);\r\n let boolean_intersection = intersect(polygon1, polygon2);\r\n let boolean_difference1 = subtract(polygon1, polygon2);\r\n let boolean_difference2 = subtract(polygon2, polygon1);\r\n let [inner_clip_shapes1, inner_clip_shapes2] = innerClip(polygon1, polygon2);\r\n let outer_clip_shapes1 = outerClip(polygon1, polygon2);\r\n let outer_clip_shapes2 = outerClip(polygon2, polygon1);\r\n\r\n denim.I2I = boolean_intersection.isEmpty() ? [] : [boolean_intersection];\r\n denim.I2B = inner_clip_shapes2;\r\n denim.I2E = boolean_difference1.isEmpty() ? [] : [boolean_difference1];\r\n\r\n denim.B2I = inner_clip_shapes1;\r\n denim.B2B = ip_sorted1;\r\n denim.B2E = outer_clip_shapes1;\r\n\r\n denim.E2I = boolean_difference2.isEmpty() ? [] : [boolean_difference2];\r\n denim.E2B = outer_clip_shapes2;\r\n // denim.E2E not relevant meanwhile\r\n\r\n return denim;\r\n}\r\n\r\nvar Relations = /*#__PURE__*/Object.freeze({\r\n equal: equal,\r\n intersect: intersect$1,\r\n touch: touch,\r\n disjoint: disjoint,\r\n inside: inside,\r\n covered: covered,\r\n contain: contain,\r\n cover: cover,\r\n relate: relate\r\n});\r\n\r\n/**\r\n * Class representing an affine transformation 3x3 matrix:\r\n * \r\n * [ a c tx\r\n * A = b d ty\r\n * 0 0 1 ]\r\n * \r\n * If parameters omitted, construct identity matrix a = 1, d = 1\r\n * @param {number} a - position(0,0) sx*cos(alpha)\r\n * @param {number} b - position (0,1) sx*sin(alpha)\r\n * @param {number} c - position (1,0) -sy*sin(alpha)\r\n * @param {number} d - position (1,1) sy*cos(alpha)\r\n * @param {number} tx - position (2,0) translation by x\r\n * @param {number} ty - position (2,1) translation by y\r\n */\r\n constructor(a = 1, b = 0, c = 0, d = 1, tx = 0, ty = 0) {\r\n this.a = a;\r\n this.b = b;\r\n this.c = c;\r\n this.d = d;\r\n this.tx = tx;\r\n this.ty = ty;\r\n }\r\n\r\n /**\r\n * Return new cloned instance of matrix\r\n * @return {Matrix}\r\n **/\r\n clone() {\r\n return new Matrix(this.a, this.b, this.c, this.d, this.tx, this.ty);\r\n };\r\n\r\n /**\r\n * Transform vector [x,y] using transformation matrix.
\r\n * Vector [x,y] is an abstract array[2] of numbers and not a FlattenJS object
\r\n * The result is also an abstract vector [x',y'] = A * [x,y]:\r\n * \r\n * [x' [ ax + by + tx\r\n * y' = cx + dy + ty\r\n * 1] 1 ]\r\n * \r\n * @param {number[]} vector - array[2] of numbers\r\n * @returns {number[]} transformation result - array[2] of numbers\r\n */\r\n transform(vector) {\r\n return [\r\n vector[0] * this.a + vector[1] * this.c + this.tx,\r\n vector[0] * this.b + vector[1] * this.d + this.ty\r\n ]\r\n };\r\n\r\n /**\r\n * Returns result of multiplication of this matrix by other matrix\r\n * @param {Matrix} other_matrix - matrix to multiply by\r\n * @returns {Matrix}\r\n */\r\n multiply(other_matrix) {\r\n return new Matrix(\r\n this.a * other_matrix.a + this.c * other_matrix.b,\r\n this.b * other_matrix.a + this.d * other_matrix.b,\r\n this.a * other_matrix.c + this.c * other_matrix.d,\r\n this.b * other_matrix.c + this.d * other_matrix.d,\r\n this.a * other_matrix.tx + this.c * other_matrix.ty + this.tx,\r\n this.b * other_matrix.tx + this.d * other_matrix.ty + this.ty\r\n )\r\n };\r\n\r\n /**\r\n * Return new matrix as a result of multiplication of the current matrix\r\n * by the matrix(1,0,0,1,tx,ty)\r\n * @param {number} tx - translation by x\r\n * @param {number} ty - translation by y\r\n * @returns {Matrix}\r\n */\r\n translate(...args) {\r\n let tx, ty;\r\n if (args.length == 1 && (args[0] instanceof Flatten.Vector)) {\r\n tx = args[0].x;\r\n ty = args[0].y;\r\n } else if (args.length == 2 && typeof (args[0]) == \"number\" && typeof (args[1]) == \"number\") {\r\n tx = args[0];\r\n ty = args[1];\r\n } else {\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n return this.multiply(new Matrix(1, 0, 0, 1, tx, ty))\r\n };\r\n\r\n /**\r\n * Return new matrix as a result of multiplication of the current matrix\r\n * by the matrix that defines rotation by given angle (in radians) around\r\n * point (0,0) in counter clockwise direction\r\n * @param {number} angle - angle in radians\r\n * @returns {Matrix}\r\n */\r\n rotate(angle) {\r\n let cos = Math.cos(angle);\r\n let sin = Math.sin(angle);\r\n return this.multiply(new Matrix(cos, sin, -sin, cos, 0, 0));\r\n };\r\n\r\n /**\r\n * Return new matrix as a result of multiplication of the current matrix\r\n * by the matrix (sx,0,0,sy,0,0) that defines scaling\r\n * @param {number} sx\r\n * @param {number} sy\r\n * @returns {Matrix}\r\n */\r\n scale(sx, sy) {\r\n return this.multiply(new Matrix(sx, 0, 0, sy, 0, 0));\r\n };\r\n\r\n /**\r\n * Returns true if two matrix are equal parameter by parameter\r\n * @param {Matrix} matrix - other matrix\r\n * @returns {boolean} true if equal, false otherwise\r\n */\r\n equalTo(matrix) {\r\n if (!Flatten.Utils.EQ(this.tx, matrix.tx)) return false;\r\n if (!Flatten.Utils.EQ(this.ty, matrix.ty)) return false;\r\n if (!Flatten.Utils.EQ(this.a, matrix.a)) return false;\r\n if (!Flatten.Utils.EQ(this.b, matrix.b)) return false;\r\n if (!Flatten.Utils.EQ(this.c, matrix.c)) return false;\r\n if (!Flatten.Utils.EQ(this.d, matrix.d)) return false;\r\n return true;\r\n };\r\n}\r\nFlatten.Matrix = Matrix;\r\n/**\r\n * Function to create matrix equivalent to \"new\" constructor\r\n * @param args\r\n */\r\nconst matrix = (...args) => new Flatten.Matrix(...args);\r\nFlatten.matrix = matrix;\r\n\r\n/**\r\n * Created by Alex Bol on 4/1/2017.\r\n */\r\n\r\n/**\r\n * Interval is a pair of numbers or a pair of any comparable objects on which may be defined predicates\r\n * *equal*, *less* and method *max(p1, p1)* that returns maximum in a pair.\r\n * When interval is an object rather than pair of numbers, this object should have properties *low*, *high*, *max*\r\n * and implement methods *less_than(), equal_to(), intersect(), not_intersect(), clone(), output()*.\r\n * Two static methods *comparable_max(), comparable_less_than()* define how to compare values in pair.
\r\n * This interface is described in typescript definition file *index.d.ts*\r\n *\r\n * Axis aligned rectangle is an example of such interval.\r\n * We may look at rectangle as an interval between its low left and top right corners.\r\n * See **Box** class in [flatten-js](https://github.com/alexbol99/flatten-js) library as the example\r\n * of Interval interface implementation\r\n * @type {Interval}\r\n */\r\nconst Interval = class Interval {\r\n /**\r\n * Accept two comparable values and creates new instance of interval\r\n * Predicate Interval.comparable_less(low, high) supposed to return true on these values\r\n * @param low\r\n * @param high\r\n */\r\n constructor(low, high) {\r\n this.low = low;\r\n this.high = high;\r\n }\r\n\r\n /**\r\n * Clone interval\r\n * @returns {Interval}\r\n */\r\n clone() {\r\n return new Interval(this.low, this.high);\r\n }\r\n\r\n /**\r\n * Propery max returns clone of this interval\r\n * @returns {Interval}\r\n */\r\n get max() {\r\n return this.clone(); // this.high;\r\n }\r\n\r\n /**\r\n * Predicate returns true is this interval less than other interval\r\n * @param other_interval\r\n * @returns {boolean}\r\n */\r\n less_than(other_interval) {\r\n return this.low < other_interval.low ||\r\n this.low == other_interval.low && this.high < other_interval.high;\r\n }\r\n\r\n /**\r\n * Predicate returns true is this interval equals to other interval\r\n * @param other_interval\r\n * @returns {boolean}\r\n */\r\n equal_to(other_interval) {\r\n return this.low == other_interval.low && this.high == other_interval.high;\r\n }\r\n\r\n /**\r\n * Predicate returns true if this interval intersects other interval\r\n * @param other_interval\r\n * @returns {boolean}\r\n */\r\n intersect(other_interval) {\r\n return !this.not_intersect(other_interval);\r\n }\r\n\r\n /**\r\n * Predicate returns true if this interval does not intersect other interval\r\n * @param other_interval\r\n * @returns {boolean}\r\n */\r\n not_intersect(other_interval) {\r\n return (this.high < other_interval.low || other_interval.high < this.low);\r\n }\r\n\r\n /**\r\n * Returns new interval merged with other interval\r\n * @param {Interval} interval - Other interval to merge with\r\n * @returns {Interval}\r\n */\r\n merge(other_interval) {\r\n return new Interval(\r\n this.low === undefined ? other_interval.low : Math.min(this.low, other_interval.low),\r\n this.high === undefined ? other_interval.high : Math.max(this.high, other_interval.high)\r\n );\r\n }\r\n\r\n /**\r\n * Returns how key should return\r\n */\r\n output() {\r\n return [this.low, this.high];\r\n }\r\n\r\n /**\r\n * Function returns maximum between two comparable values\r\n * @param interval1\r\n * @param interval2\r\n * @returns {Interval}\r\n */\r\n static comparable_max(interval1, interval2) {\r\n return interval1.merge(interval2);\r\n }\r\n\r\n /**\r\n * Predicate returns true if first value less than second value\r\n * @param val1\r\n * @param val2\r\n * @returns {boolean}\r\n */\r\n static comparable_less_than(val1, val2 ) {\r\n return val1 < val2;\r\n }\r\n};\r\n\r\n/**\r\n * Created by Alex Bol on 3/28/2017.\r\n */\r\n\r\n// module.exports = {\r\n// RB_TREE_COLOR_RED: 0,\r\n// RB_TREE_COLOR_BLACK: 1\r\n// };\r\n\r\nconst RB_TREE_COLOR_RED = 0;\r\nconst RB_TREE_COLOR_BLACK = 1;\r\n\r\n/**\r\n * Created by Alex Bol on 4/1/2017.\r\n */\r\n\r\nclass Node {\r\n constructor(key = undefined, value = undefined,\r\n left = null, right = null, parent = null, color = RB_TREE_COLOR_BLACK) {\r\n this.left = left; // reference to left child node\r\n this.right = right; // reference to right child node\r\n this.parent = parent; // reference to parent node\r\n this.color = color;\r\n\r\n this.item = {key: key, value: value}; // key is supposed to be instance of Interval\r\n\r\n /* If not, this should by an array of two numbers */\r\n if (key && key instanceof Array && key.length == 2) {\r\n if (!Number.isNaN(key[0]) && !Number.isNaN(key[1])) {\r\n this.item.key = new Interval(Math.min(key[0], key[1]), Math.max(key[0], key[1]));\r\n }\r\n }\r\n\r\n this.max = this.item.key ? this.item.key.max : undefined;\r\n }\r\n\r\n isNil() {\r\n return (this.item.key === undefined && this.item.value === undefined &&\r\n this.left === null && this.right === null && this.color === RB_TREE_COLOR_BLACK);\r\n }\r\n\r\n less_than(other_node) {\r\n // if tree stores only keys\r\n if (this.item.value === this.item.key && other_node.item.value === other_node.item.key) {\r\n return this.item.key.less_than(other_node.item.key);\r\n }\r\n else { // if tree stores keys and values\r\n let value_less_than = this.item.value && other_node.item.value && this.item.value.less_than ? this.item.value.less_than(other_node.item.value) :\r\n this.item.value < other_node.item.value;\r\n return this.item.key.less_than(other_node.item.key) ||\r\n this.item.key.equal_to((other_node.item.key)) && value_less_than;\r\n }\r\n\r\n // if (this.item.value && other_node.item.value) {\r\n // let item_less_than = this.item.value.less_than ? this.item.value.less_than(other_node.item.value) :\r\n // this.item.value < other_node.item.value;\r\n // return this.item.key.less_than(other_node.item.key) ||\r\n // this.item.key.equal_to((other_node.item.key)) && item_less_than;\r\n // }\r\n // else {\r\n // return this.item.key.less_than(other_node.item.key);\r\n // }\r\n }\r\n\r\n equal_to(other_node) {\r\n // if tree stores only keys\r\n if (this.item.value === this.item.key && other_node.item.value === other_node.item.key) {\r\n return this.item.key.equal_to(other_node.item.key);\r\n }\r\n else { // if tree stores keys and values\r\n let value_equal = this.item.value && other_node.item.value && this.item.value.equal_to ? this.item.value.equal_to(other_node.item.value) :\r\n this.item.value == other_node.item.value;\r\n return this.item.key.equal_to(other_node.item.key) && value_equal;\r\n }\r\n\r\n // let value_equal = true;\r\n // if (this.item.value && other_node.item.value) {\r\n // value_equal = this.item.value.equal_to ? this.item.value.equal_to(other_node.item.value) :\r\n // this.item.value == other_node.item.value;\r\n // }\r\n // return this.item.key.equal_to(other_node.item.key) && value_equal;\r\n }\r\n\r\n intersect(other_node) {\r\n return this.item.key.intersect(other_node.item.key);\r\n }\r\n\r\n copy_data(other_node) {\r\n this.item.key = other_node.item.key;\r\n this.item.value = other_node.item.value;\r\n }\r\n\r\n update_max() {\r\n // use key (Interval) max property instead of key.high\r\n this.max = this.item.key ? this.item.key.max : undefined;\r\n if (this.right && this.right.max) {\r\n const comparable_max = this.item.key.constructor.comparable_max; // static method\r\n this.max = comparable_max(this.max, this.right.max);\r\n }\r\n if (this.left && this.left.max) {\r\n const comparable_max = this.item.key.constructor.comparable_max; // static method\r\n this.max = comparable_max(this.max, this.left.max);\r\n }\r\n }\r\n\r\n // Other_node does not intersect any node of left subtree, if this.left.max < other_node.item.key.low\r\n not_intersect_left_subtree(search_node) {\r\n const comparable_less_than = this.item.key.constructor.comparable_less_than; // static method\r\n let high = this.left.max.high !== undefined ? this.left.max.high : this.left.max;\r\n return comparable_less_than(high, search_node.item.key.low);\r\n }\r\n\r\n // Other_node does not intersect right subtree if other_node.item.key.high < this.right.key.low\r\n not_intersect_right_subtree(search_node) {\r\n const comparable_less_than = this.item.key.constructor.comparable_less_than; // static method\r\n let low = this.right.max.low !== undefined ? this.right.max.low : this.right.item.key.low;\r\n return comparable_less_than(search_node.item.key.high, low);\r\n }\r\n}\r\n\r\n/**\r\n * Created by Alex Bol on 3/31/2017.\r\n */\r\n\r\n// const nil_node = new Node();\r\n\r\n/**\r\n * Implementation of interval binary search tree
\r\n * Interval tree stores items which are couples of {key:interval, value: value}
\r\n * Interval is an object with high and low properties or simply pair [low,high] of numeric values
\r\n * @type {IntervalTree}\r\n */\r\nclass IntervalTree {\r\n /**\r\n * Construct new empty instance of IntervalTree\r\n */\r\n constructor() {\r\n this.root = null;\r\n this.nil_node = new Node();\r\n }\r\n\r\n /**\r\n * Returns number of items stored in the interval tree\r\n * @returns {number}\r\n */\r\n get size() {\r\n let count = 0;\r\n this.tree_walk(this.root, () => count++);\r\n return count;\r\n }\r\n\r\n /**\r\n * Returns array of sorted keys in the ascending order\r\n * @returns {Array}\r\n */\r\n get keys() {\r\n let res = [];\r\n this.tree_walk(this.root, (node) => res.push(\r\n node.item.key.output ? node.item.key.output() : node.item.key\r\n ));\r\n return res;\r\n }\r\n\r\n /**\r\n * Return array of values in the ascending keys order\r\n * @returns {Array}\r\n */\r\n get values() {\r\n let res = [];\r\n this.tree_walk(this.root, (node) => res.push(node.item.value));\r\n return res;\r\n }\r\n\r\n /**\r\n * Returns array of items ( pairs) in the ascended keys order\r\n * @returns {Array}\r\n */\r\n get items() {\r\n let res = [];\r\n this.tree_walk(this.root, (node) => res.push({\r\n key: node.item.key.output ? node.item.key.output() : node.item.key,\r\n value: node.item.value\r\n }));\r\n return res;\r\n }\r\n\r\n /**\r\n * Returns true if tree is empty\r\n * @returns {boolean}\r\n */\r\n isEmpty() {\r\n return (this.root == null || this.root == this.nil_node);\r\n }\r\n\r\n /**\r\n * Clear tree\r\n */\r\n clear() {\r\n this.root = null;\r\n }\r\n\r\n /**\r\n * Insert new item into interval tree\r\n * @param {Interval} key - interval object or array of two numbers [low, high]\r\n * @param {any} value - value representing any object (optional)\r\n * @returns {Node} returns reference to inserted node as an object {key:interval, value: value}\r\n */\r\n insert(key, value = key) {\r\n if (key === undefined) return;\r\n let insert_node = new Node(key, value, this.nil_node, this.nil_node, null, RB_TREE_COLOR_RED);\r\n this.tree_insert(insert_node);\r\n this.recalc_max(insert_node);\r\n return insert_node;\r\n }\r\n\r\n /**\r\n * Returns true if item {key,value} exist in the tree\r\n * @param {Interval} key - interval correspondent to keys stored in the tree\r\n * @param {any} value - value object to be checked\r\n * @returns {boolean} true if item {key, value} exist in the tree, false otherwise\r\n */\r\n exist(key, value = key) {\r\n let search_node = new Node(key, value);\r\n return this.tree_search(this.root, search_node) ? true : false;\r\n }\r\n\r\n /**\r\n * Remove entry {key, value} from the tree\r\n * @param {Interval} key - interval correspondent to keys stored in the tree\r\n * @param {any} value - value object\r\n * @returns {boolean} true if item {key, value} deleted, false if not found\r\n */\r\n remove(key, value = key) {\r\n let search_node = new Node(key, value);\r\n let delete_node = this.tree_search(this.root, search_node);\r\n if (delete_node) {\r\n this.tree_delete(delete_node);\r\n }\r\n return delete_node;\r\n }\r\n\r\n /**\r\n * Returns array of entry values which keys intersect with given interval
\r\n * If no values stored in the tree, returns array of keys which intersect given interval\r\n * @param {Interval} interval - search interval, or tuple [low, high]\r\n * @param outputMapperFn(value,key) - optional function that maps (value, key) to custom output\r\n * @returns {Array}\r\n */\r\n search(interval, outputMapperFn = (value, key) => value === key ? key.output() : value) {\r\n let search_node = new Node(interval);\r\n let resp_nodes = [];\r\n this.tree_search_interval(this.root, search_node, resp_nodes);\r\n return resp_nodes.map(node => outputMapperFn(node.item.value, node.item.key))\r\n }\r\n\r\n /**\r\n * Returns true if intersection between given and any interval stored in the tree found\r\n * @param {Interval} interval - search interval or tuple [low, high]\r\n * @returns {boolean}\r\n */\r\n intersect_any(interval) {\r\n let search_node = new Node(interval);\r\n let found = this.tree_find_any_interval(this.root, search_node);\r\n return found;\r\n }\r\n\r\n /**\r\n * Tree visitor. For each node implement a callback function.
\r\n * Method calls a callback function with two parameters (key, value)\r\n * @param visitor(key,value) - function to be called for each tree item\r\n */\r\n forEach(visitor) {\r\n this.tree_walk(this.root, (node) => visitor(node.item.key, node.item.value));\r\n }\r\n\r\n /** Value Mapper. Walk through every node and map node value to another value\r\n * @param callback(value,key) - function to be called for each tree item\r\n */\r\n map(callback) {\r\n const tree = new IntervalTree();\r\n this.tree_walk(this.root, (node) => tree.insert(node.item.key, callback(node.item.value, node.item.key)));\r\n return tree;\r\n }\r\n\r\n recalc_max(node) {\r\n let node_current = node;\r\n while (node_current.parent != null) {\r\n node_current.parent.update_max();\r\n node_current = node_current.parent;\r\n }\r\n }\r\n\r\n tree_insert(insert_node) {\r\n let current_node = this.root;\r\n let parent_node = null;\r\n\r\n if (this.root == null || this.root == this.nil_node) {\r\n this.root = insert_node;\r\n }\r\n else {\r\n while (current_node != this.nil_node) {\r\n parent_node = current_node;\r\n if (insert_node.less_than(current_node)) {\r\n current_node = current_node.left;\r\n }\r\n else {\r\n current_node = current_node.right;\r\n }\r\n }\r\n\r\n insert_node.parent = parent_node;\r\n\r\n if (insert_node.less_than(parent_node)) {\r\n parent_node.left = insert_node;\r\n }\r\n else {\r\n parent_node.right = insert_node;\r\n }\r\n }\r\n\r\n this.insert_fixup(insert_node);\r\n }\r\n\r\n// After insertion insert_node may have red-colored parent, and this is a single possible violation\r\n// Go upwords to the root and re-color until violation will be resolved\r\n insert_fixup(insert_node) {\r\n let current_node;\r\n let uncle_node;\r\n\r\n current_node = insert_node;\r\n while (current_node != this.root && current_node.parent.color == RB_TREE_COLOR_RED) {\r\n if (current_node.parent == current_node.parent.parent.left) { // parent is left child of grandfather\r\n uncle_node = current_node.parent.parent.right; // right brother of parent\r\n if (uncle_node.color == RB_TREE_COLOR_RED) { // Case 1. Uncle is red\r\n // re-color father and uncle into black\r\n current_node.parent.color = RB_TREE_COLOR_BLACK;\r\n uncle_node.color = RB_TREE_COLOR_BLACK;\r\n current_node.parent.parent.color = RB_TREE_COLOR_RED;\r\n current_node = current_node.parent.parent;\r\n }\r\n else { // Case 2 & 3. Uncle is black\r\n if (current_node == current_node.parent.right) { // Case 2. Current if right child\r\n // This case is transformed into Case 3.\r\n current_node = current_node.parent;\r\n this.rotate_left(current_node);\r\n }\r\n current_node.parent.color = RB_TREE_COLOR_BLACK; // Case 3. Current is left child.\r\n // Re-color father and grandfather, rotate grandfather right\r\n current_node.parent.parent.color = RB_TREE_COLOR_RED;\r\n this.rotate_right(current_node.parent.parent);\r\n }\r\n }\r\n else { // parent is right child of grandfather\r\n uncle_node = current_node.parent.parent.left; // left brother of parent\r\n if (uncle_node.color == RB_TREE_COLOR_RED) { // Case 4. Uncle is red\r\n // re-color father and uncle into black\r\n current_node.parent.color = RB_TREE_COLOR_BLACK;\r\n uncle_node.color = RB_TREE_COLOR_BLACK;\r\n current_node.parent.parent.color = RB_TREE_COLOR_RED;\r\n current_node = current_node.parent.parent;\r\n }\r\n else {\r\n if (current_node == current_node.parent.left) { // Case 5. Current is left child\r\n // Transform into case 6\r\n current_node = current_node.parent;\r\n this.rotate_right(current_node);\r\n }\r\n current_node.parent.color = RB_TREE_COLOR_BLACK; // Case 6. Current is right child.\r\n // Re-color father and grandfather, rotate grandfather left\r\n current_node.parent.parent.color = RB_TREE_COLOR_RED;\r\n this.rotate_left(current_node.parent.parent);\r\n }\r\n }\r\n }\r\n\r\n this.root.color = RB_TREE_COLOR_BLACK;\r\n }\r\n\r\n tree_delete(delete_node) {\r\n let cut_node; // node to be cut - either delete_node or successor_node (\"y\" from 14.4)\r\n let fix_node; // node to fix rb tree property (\"x\" from 14.4)\r\n\r\n if (delete_node.left == this.nil_node || delete_node.right == this.nil_node) { // delete_node has less then 2 children\r\n cut_node = delete_node;\r\n }\r\n else { // delete_node has 2 children\r\n cut_node = this.tree_successor(delete_node);\r\n }\r\n\r\n // fix_node if single child of cut_node\r\n if (cut_node.left != this.nil_node) {\r\n fix_node = cut_node.left;\r\n }\r\n else {\r\n fix_node = cut_node.right;\r\n }\r\n\r\n // remove cut_node from parent\r\n /*if (fix_node != this.nil_node) {*/\r\n fix_node.parent = cut_node.parent;\r\n /*}*/\r\n\r\n if (cut_node == this.root) {\r\n this.root = fix_node;\r\n }\r\n else {\r\n if (cut_node == cut_node.parent.left) {\r\n cut_node.parent.left = fix_node;\r\n }\r\n else {\r\n cut_node.parent.right = fix_node;\r\n }\r\n cut_node.parent.update_max(); // update max property of the parent\r\n }\r\n\r\n this.recalc_max(fix_node); // update max property upward from fix_node to root\r\n\r\n // COPY DATA !!!\r\n // Delete_node becomes cut_node, it means that we cannot hold reference\r\n // to node in outer structure and we will have to delete by key, additional search need\r\n if (cut_node != delete_node) {\r\n delete_node.copy_data(cut_node);\r\n delete_node.update_max(); // update max property of the cut node at the new place\r\n this.recalc_max(delete_node); // update max property upward from delete_node to root\r\n }\r\n\r\n if (/*fix_node != this.nil_node && */cut_node.color == RB_TREE_COLOR_BLACK) {\r\n this.delete_fixup(fix_node);\r\n }\r\n }\r\n\r\n delete_fixup(fix_node) {\r\n let current_node = fix_node;\r\n let brother_node;\r\n\r\n while (current_node != this.root && current_node.parent != null && current_node.color == RB_TREE_COLOR_BLACK) {\r\n if (current_node == current_node.parent.left) { // fix node is left child\r\n brother_node = current_node.parent.right;\r\n if (brother_node.color == RB_TREE_COLOR_RED) { // Case 1. Brother is red\r\n brother_node.color = RB_TREE_COLOR_BLACK; // re-color brother\r\n current_node.parent.color = RB_TREE_COLOR_RED; // re-color father\r\n this.rotate_left(current_node.parent);\r\n brother_node = current_node.parent.right; // update brother\r\n }\r\n // Derive to cases 2..4: brother is black\r\n if (brother_node.left.color == RB_TREE_COLOR_BLACK &&\r\n brother_node.right.color == RB_TREE_COLOR_BLACK) { // case 2: both nephews black\r\n brother_node.color = RB_TREE_COLOR_RED; // re-color brother\r\n current_node = current_node.parent; // continue iteration\r\n }\r\n else {\r\n if (brother_node.right.color == RB_TREE_COLOR_BLACK) { // case 3: left nephew red, right nephew black\r\n brother_node.color = RB_TREE_COLOR_RED; // re-color brother\r\n brother_node.left.color = RB_TREE_COLOR_BLACK; // re-color nephew\r\n this.rotate_right(brother_node);\r\n brother_node = current_node.parent.right; // update brother\r\n // Derive to case 4: left nephew black, right nephew red\r\n }\r\n // case 4: left nephew black, right nephew red\r\n brother_node.color = current_node.parent.color;\r\n current_node.parent.color = RB_TREE_COLOR_BLACK;\r\n brother_node.right.color = RB_TREE_COLOR_BLACK;\r\n this.rotate_left(current_node.parent);\r\n current_node = this.root; // exit from loop\r\n }\r\n }\r\n else { // fix node is right child\r\n brother_node = current_node.parent.left;\r\n if (brother_node.color == RB_TREE_COLOR_RED) { // Case 1. Brother is red\r\n brother_node.color = RB_TREE_COLOR_BLACK; // re-color brother\r\n current_node.parent.color = RB_TREE_COLOR_RED; // re-color father\r\n this.rotate_right(current_node.parent);\r\n brother_node = current_node.parent.left; // update brother\r\n }\r\n // Go to cases 2..4\r\n if (brother_node.left.color == RB_TREE_COLOR_BLACK &&\r\n brother_node.right.color == RB_TREE_COLOR_BLACK) { // case 2\r\n brother_node.color = RB_TREE_COLOR_RED; // re-color brother\r\n current_node = current_node.parent; // continue iteration\r\n }\r\n else {\r\n if (brother_node.left.color == RB_TREE_COLOR_BLACK) { // case 3: right nephew red, left nephew black\r\n brother_node.color = RB_TREE_COLOR_RED; // re-color brother\r\n brother_node.right.color = RB_TREE_COLOR_BLACK; // re-color nephew\r\n this.rotate_left(brother_node);\r\n brother_node = current_node.parent.left; // update brother\r\n // Derive to case 4: right nephew black, left nephew red\r\n }\r\n // case 4: right nephew black, left nephew red\r\n brother_node.color = current_node.parent.color;\r\n current_node.parent.color = RB_TREE_COLOR_BLACK;\r\n brother_node.left.color = RB_TREE_COLOR_BLACK;\r\n this.rotate_right(current_node.parent);\r\n current_node = this.root; // force exit from loop\r\n }\r\n }\r\n }\r\n\r\n current_node.color = RB_TREE_COLOR_BLACK;\r\n }\r\n\r\n tree_search(node, search_node) {\r\n if (node == null || node == this.nil_node)\r\n return undefined;\r\n\r\n if (search_node.equal_to(node)) {\r\n return node;\r\n }\r\n if (search_node.less_than(node)) {\r\n return this.tree_search(node.left, search_node);\r\n }\r\n else {\r\n return this.tree_search(node.right, search_node);\r\n }\r\n }\r\n\r\n // Original search_interval method; container res support push() insertion\r\n // Search all intervals intersecting given one\r\n tree_search_interval(node, search_node, res) {\r\n if (node != null && node != this.nil_node) {\r\n // if (node->left != this.nil_node && node->left->max >= low) {\r\n if (node.left != this.nil_node && !node.not_intersect_left_subtree(search_node)) {\r\n this.tree_search_interval(node.left, search_node, res);\r\n }\r\n // if (low <= node->high && node->low <= high) {\r\n if (node.intersect(search_node)) {\r\n res.push(node);\r\n }\r\n // if (node->right != this.nil_node && node->low <= high) {\r\n if (node.right != this.nil_node && !node.not_intersect_right_subtree(search_node)) {\r\n this.tree_search_interval(node.right, search_node, res);\r\n }\r\n }\r\n }\r\n\r\n tree_find_any_interval(node, search_node) {\r\n let found = false;\r\n if (node != null && node != this.nil_node) {\r\n // if (node->left != this.nil_node && node->left->max >= low) {\r\n if (node.left != this.nil_node && !node.not_intersect_left_subtree(search_node)) {\r\n found = this.tree_find_any_interval(node.left, search_node);\r\n }\r\n // if (low <= node->high && node->low <= high) {\r\n if (!found) {\r\n found = node.intersect(search_node);\r\n }\r\n // if (node->right != this.nil_node && node->low <= high) {\r\n if (!found && node.right != this.nil_node && !node.not_intersect_right_subtree(search_node)) {\r\n found = this.tree_find_any_interval(node.right, search_node);\r\n }\r\n }\r\n return found;\r\n }\r\n\r\n local_minimum(node) {\r\n let node_min = node;\r\n while (node_min.left != null && node_min.left != this.nil_node) {\r\n node_min = node_min.left;\r\n }\r\n return node_min;\r\n }\r\n\r\n // not in use\r\n local_maximum(node) {\r\n let node_max = node;\r\n while (node_max.right != null && node_max.right != this.nil_node) {\r\n node_max = node_max.right;\r\n }\r\n return node_max;\r\n }\r\n\r\n tree_successor(node) {\r\n let node_successor;\r\n let current_node;\r\n let parent_node;\r\n\r\n if (node.right != this.nil_node) {\r\n node_successor = this.local_minimum(node.right);\r\n }\r\n else {\r\n current_node = node;\r\n parent_node = node.parent;\r\n while (parent_node != null && parent_node.right == current_node) {\r\n current_node = parent_node;\r\n parent_node = parent_node.parent;\r\n }\r\n node_successor = parent_node;\r\n }\r\n return node_successor;\r\n }\r\n\r\n // | right-rotate(T,y) |\r\n // y ---------------. x\r\n // / \\ / \\\r\n // x c left-rotate(T,x) a y\r\n // / \\ <--------------- / \\\r\n // a b b c\r\n\r\n rotate_left(x) {\r\n let y = x.right;\r\n\r\n x.right = y.left; // b goes to x.right\r\n\r\n if (y.left != this.nil_node) {\r\n y.left.parent = x; // x becomes parent of b\r\n }\r\n y.parent = x.parent; // move parent\r\n\r\n if (x == this.root) {\r\n this.root = y; // y becomes root\r\n }\r\n else { // y becomes child of x.parent\r\n if (x == x.parent.left) {\r\n x.parent.left = y;\r\n }\r\n else {\r\n x.parent.right = y;\r\n }\r\n }\r\n y.left = x; // x becomes left child of y\r\n x.parent = y; // and y becomes parent of x\r\n\r\n if (x != null && x != this.nil_node) {\r\n x.update_max();\r\n }\r\n\r\n y = x.parent;\r\n if (y != null && y != this.nil_node) {\r\n y.update_max();\r\n }\r\n }\r\n\r\n rotate_right(y) {\r\n let x = y.left;\r\n\r\n y.left = x.right; // b goes to y.left\r\n\r\n if (x.right != this.nil_node) {\r\n x.right.parent = y; // y becomes parent of b\r\n }\r\n x.parent = y.parent; // move parent\r\n\r\n if (y == this.root) { // x becomes root\r\n this.root = x;\r\n }\r\n else { // y becomes child of x.parent\r\n if (y == y.parent.left) {\r\n y.parent.left = x;\r\n }\r\n else {\r\n y.parent.right = x;\r\n }\r\n }\r\n x.right = y; // y becomes right child of x\r\n y.parent = x; // and x becomes parent of y\r\n\r\n if (y != null && y != this.nil_node) {\r\n y.update_max();\r\n }\r\n\r\n x = y.parent;\r\n if (x != null && x != this.nil_node) {\r\n x.update_max();\r\n }\r\n }\r\n\r\n tree_walk(node, action) {\r\n if (node != null && node != this.nil_node) {\r\n this.tree_walk(node.left, action);\r\n // arr.push(node.toArray());\r\n action(node);\r\n this.tree_walk(node.right, action);\r\n }\r\n }\r\n\r\n /* Return true if all red nodes have exactly two black child nodes */\r\n testRedBlackProperty() {\r\n let res = true;\r\n this.tree_walk(this.root, function (node) {\r\n if (node.color == RB_TREE_COLOR_RED) {\r\n if (!(node.left.color == RB_TREE_COLOR_BLACK && node.right.color == RB_TREE_COLOR_BLACK)) {\r\n res = false;\r\n }\r\n }\r\n });\r\n return res;\r\n }\r\n\r\n /* Throw error if not every path from root to bottom has same black height */\r\n testBlackHeightProperty(node) {\r\n let height = 0;\r\n let heightLeft = 0;\r\n let heightRight = 0;\r\n if (node.color == RB_TREE_COLOR_BLACK) {\r\n height++;\r\n }\r\n if (node.left != this.nil_node) {\r\n heightLeft = this.testBlackHeightProperty(node.left);\r\n }\r\n else {\r\n heightLeft = 1;\r\n }\r\n if (node.right != this.nil_node) {\r\n heightRight = this.testBlackHeightProperty(node.right);\r\n }\r\n else {\r\n heightRight = 1;\r\n }\r\n if (heightLeft != heightRight) {\r\n throw new Error('Red-black height property violated');\r\n }\r\n height += heightLeft;\r\n return height;\r\n };\r\n}\r\n\r\n/**\r\n * Created by Alex Bol on 3/12/2017.\r\n */\r\n\r\n/**\r\n * Class representing a planar set - a generic container with ability to keep and retrieve shapes and\r\n * perform spatial queries. Planar set is an extension of Set container, so it supports\r\n * Set properties and methods\r\n */\r\nclass PlanarSet extends Set {\r\n /**\r\n * Create new instance of PlanarSet\r\n * @param shapes - array or set of geometric objects to store in planar set\r\n * Each object should have a box property\r\n */\r\n constructor(shapes) {\r\n super(shapes);\r\n this.index = new IntervalTree();\r\n this.forEach(shape => this.index.insert(shape));\r\n }\r\n\r\n /**\r\n * Add new shape to planar set and to its spatial index.
\r\n * If shape already exist, it will not be added again.\r\n * This happens with no error, it is possible to use size property to check if\r\n * a shape was actually added.
\r\n * Method returns planar set object updated and may be chained\r\n * @param {Shape} shape - shape to be added, should have valid box property\r\n * @returns {PlanarSet}\r\n */\r\n add(shape) {\r\n let size = this.size;\r\n super.add(shape);\r\n // size not changed - item not added, probably trying to add same item twice\r\n if (this.size > size) {\r\n let node = this.index.insert(shape.box, shape);\r\n }\r\n return this; // in accordance to Set.add interface\r\n }\r\n\r\n /**\r\n * Delete shape from planar set. Returns true if shape was actually deleted, false otherwise\r\n * @param {Shape} shape - shape to be deleted\r\n * @returns {boolean}\r\n */\r\n delete(shape) {\r\n let deleted = super.delete(shape);\r\n if (deleted) {\r\n this.index.remove(shape.box, shape);\r\n }\r\n return deleted;\r\n }\r\n\r\n /**\r\n * Clear planar set\r\n */\r\n clear() {\r\n super.clear();\r\n this.index = new IntervalTree();\r\n }\r\n\r\n /**\r\n * 2d range search in planar set.
\r\n * Returns array of all shapes in planar set which bounding box is intersected with query box\r\n * @param {Box} box - query box\r\n * @returns {Shapes[]}\r\n */\r\n search(box) {\r\n let resp = this.index.search(box);\r\n return resp;\r\n }\r\n\r\n /**\r\n * Point location test. Returns array of shapes which contains given point\r\n * @param {Point} point - query point\r\n * @returns {Array}\r\n */\r\n hit(point) {\r\n let box = new Flatten.Box(point.x - 1, point.y - 1, point.x + 1, point.y + 1);\r\n let resp = this.index.search(box);\r\n return resp.filter((shape) => point.on(shape));\r\n }\r\n\r\n /**\r\n * Returns svg string to draw all shapes in planar set\r\n * @returns {String}\r\n */\r\n svg() {\r\n let svgcontent = [...this].reduce((acc, shape) => acc + shape.svg(), \"\");\r\n return svgcontent;\r\n }\r\n}\r\n\r\nFlatten.PlanarSet = PlanarSet;\r\n\r\n/**\r\n * Created by Alex Bol on 2/18/2017.\r\n */\r\n\r\n/**\r\n *\r\n * Class representing a point\r\n * @type {Point}\r\n */\r\nclass Point {\r\n /**\r\n * Point may be constructed by two numbers, or by array of two numbers\r\n * @param {number} x - x-coordinate (float number)\r\n * @param {number} y - y-coordinate (float number)\r\n */\r\n constructor(...args) {\r\n /**\r\n * x-coordinate (float number)\r\n * @type {number}\r\n */\r\n this.x = 0;\r\n /**\r\n * y-coordinate (float number)\r\n * @type {number}\r\n */\r\n this.y = 0;\r\n\r\n if (args.length === 0) {\r\n return;\r\n }\r\n\r\n if (args.length === 1 && args[0] instanceof Array && args[0].length === 2) {\r\n let arr = args[0];\r\n if (typeof (arr[0]) == \"number\" && typeof (arr[1]) == \"number\") {\r\n this.x = arr[0];\r\n this.y = arr[1];\r\n return;\r\n }\r\n }\r\n\r\n if (args.length === 1 && args[0] instanceof Object && args[0].name === \"point\") {\r\n let {x, y} = args[0];\r\n this.x = x;\r\n this.y = y;\r\n return;\r\n }\r\n\r\n if (args.length === 2) {\r\n if (typeof (args[0]) == \"number\" && typeof (args[1]) == \"number\") {\r\n this.x = args[0];\r\n this.y = args[1];\r\n return;\r\n }\r\n }\r\n\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n\r\n }\r\n\r\n /**\r\n * Returns bounding box of a point\r\n * @returns {Box}\r\n */\r\n get box() {\r\n return new Flatten.Box(this.x, this.y, this.x, this.y);\r\n }\r\n\r\n /**\r\n * Return new cloned instance of point\r\n * @returns {Point}\r\n */\r\n clone() {\r\n return new Flatten.Point(this.x, this.y);\r\n }\r\n\r\n get vertices() {\r\n return [this.clone()];\r\n }\r\n\r\n /**\r\n * Returns true if points are equal up to [Flatten.Utils.DP_TOL]{@link DP_TOL} tolerance\r\n * @param {Point} pt Query point\r\n * @returns {boolean}\r\n */\r\n equalTo(pt) {\r\n return Flatten.Utils.EQ(this.x, pt.x) && Flatten.Utils.EQ(this.y, pt.y);\r\n }\r\n\r\n /**\r\n * Defines predicate \"less than\" between points. Returns true if the point is less than query points, false otherwise
\r\n * By definition point1 < point2 if {point1.y < point2.y || point1.y == point2.y && point1.x < point2.x
\r\n * Numeric values compared with [Flatten.Utils.DP_TOL]{@link DP_TOL} tolerance\r\n * @param {Point} pt Query point\r\n * @returns {boolean}\r\n */\r\n lessThan(pt) {\r\n if (Flatten.Utils.LT(this.y, pt.y))\r\n return true;\r\n if (Flatten.Utils.EQ(this.y, pt.y) && Flatten.Utils.LT(this.x, pt.x))\r\n return true;\r\n return false;\r\n }\r\n\r\n /**\r\n * Returns new point rotated by given angle around given center point.\r\n * If center point is omitted, rotates around zero point (0,0).\r\n * Positive value of angle defines rotation in counter clockwise direction,\r\n * negative angle defines rotation in clockwise clockwise direction\r\n * @param {number} angle - angle in radians\r\n * @param {Point} [center=(0,0)] center\r\n * @returns {Point}\r\n */\r\n rotate(angle, center = {x: 0, y: 0}) {\r\n var x_rot = center.x + (this.x - center.x) * Math.cos(angle) - (this.y - center.y) * Math.sin(angle);\r\n var y_rot = center.y + (this.x - center.x) * Math.sin(angle) + (this.y - center.y) * Math.cos(angle);\r\n\r\n return new Flatten.Point(x_rot, y_rot);\r\n }\r\n\r\n /**\r\n * Returns new point translated by given vector.\r\n * Translation vector may by also defined by a pair of numbers.\r\n * @param {Vector} vector - Translation vector defined as Flatten.Vector or\r\n * @param {number|number} - Translation vector defined as pair of numbers\r\n * @returns {Point}\r\n */\r\n translate(...args) {\r\n if (args.length == 1 &&\r\n (args[0] instanceof Flatten.Vector || !isNaN(args[0].x) && !isNaN(args[0].y))) {\r\n return new Flatten.Point(this.x + args[0].x, this.y + args[0].y);\r\n }\r\n\r\n if (args.length == 2 && typeof (args[0]) == \"number\" && typeof (args[1]) == \"number\") {\r\n return new Flatten.Point(this.x + args[0], this.y + args[1]);\r\n }\r\n\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n\r\n /**\r\n * Return new point transformed by affine transformation matrix m\r\n * @param {Matrix} m - affine transformation matrix (a,b,c,d,tx,ty)\r\n * @returns {Point}\r\n */\r\n transform(m) {\r\n // let [x,y] = m.transform([this.x,this.y]);\r\n return new Flatten.Point(m.transform([this.x, this.y]))\r\n }\r\n\r\n /**\r\n * Returns projection point on given line\r\n * @param {Line} line Line this point be projected on\r\n * @returns {Point}\r\n */\r\n projectionOn(line) {\r\n if (this.equalTo(line.pt)) // this point equal to line anchor point\r\n return this.clone();\r\n\r\n let vec = new Flatten.Vector(this, line.pt);\r\n if (Flatten.Utils.EQ_0(vec.cross(line.norm))) // vector to point from anchor point collinear to normal vector\r\n return line.pt.clone();\r\n\r\n let dist = vec.dot(line.norm); // signed distance\r\n let proj_vec = line.norm.multiply(dist);\r\n return this.translate(proj_vec);\r\n }\r\n\r\n /**\r\n * Returns true if point belongs to the \"left\" semi-plane, which means, point belongs to the same semi plane where line normal vector points to\r\n * Return false if point belongs to the \"right\" semi-plane or to the line itself\r\n * @param {Line} line Query line\r\n * @returns {boolean}\r\n */\r\n leftTo(line) {\r\n let vec = new Flatten.Vector(line.pt, this);\r\n let onLeftSemiPlane = Flatten.Utils.GT(vec.dot(line.norm), 0);\r\n return onLeftSemiPlane;\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment from point to shape and return as array [distance, shortest segment]\r\n * @param {Shape} shape Shape of the one of supported types Point, Line, Circle, Segment, Arc, Polygon or Planar Set\r\n * @returns {number} distance from point to shape\r\n * @returns {Segment} shortest segment between point and shape (started at point, ended at shape)\r\n */\r\n distanceTo(shape) {\r\n if (shape instanceof Point) {\r\n let dx = shape.x - this.x;\r\n let dy = shape.y - this.y;\r\n return [Math.sqrt(dx * dx + dy * dy), new Flatten.Segment(this, shape)];\r\n }\r\n\r\n if (shape instanceof Flatten.Line) {\r\n return Flatten.Distance.point2line(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n return Flatten.Distance.point2circle(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n return Flatten.Distance.point2segment(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n // let [dist, ...rest] = Distance.point2arc(this, shape);\r\n // return dist;\r\n return Flatten.Distance.point2arc(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Polygon) {\r\n // let [dist, ...rest] = Distance.point2polygon(this, shape);\r\n // return dist;\r\n return Flatten.Distance.point2polygon(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.PlanarSet) {\r\n return Flatten.Distance.shape2planarSet(this, shape);\r\n }\r\n }\r\n\r\n /**\r\n * Returns true if point is on a shape, false otherwise\r\n * @param {Shape} shape Shape of the one of supported types Point, Line, Circle, Segment, Arc, Polygon\r\n * @returns {boolean}\r\n */\r\n on(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n return this.equalTo(shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Line) {\r\n return shape.contains(this);\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n return shape.contains(this);\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n return shape.contains(this);\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n return shape.contains(this);\r\n }\r\n\r\n if (shape instanceof Flatten.Polygon) {\r\n return shape.contains(this);\r\n }\r\n }\r\n\r\n /**\r\n * This method returns an object that defines how data will be\r\n * serialized when called JSON.stringify() method\r\n * @returns {Object}\r\n */\r\n toJSON() {\r\n return Object.assign({}, this, {name: \"point\"});\r\n }\r\n\r\n /**\r\n * Return string to draw point in svg as circle with radius \"r\"
\r\n * Accept any valid attributes of svg elements as svg object\r\n * Defaults attribues are:
\r\n * {\r\n * r:\"3\",\r\n * stroke:\"black\",\r\n * strokeWidth:\"1\",\r\n * fill:\"red\"\r\n * }\r\n * @param {Object} attrs - Any valid attributes of svg circle element, like \"r\", \"stroke\", \"strokeWidth\", \"fill\"\r\n * @returns {String}\r\n */\r\n svg(attrs = {}) {\r\n let {r, stroke, strokeWidth, fill, id, className} = attrs;\r\n // let rest_str = Object.keys(rest).reduce( (acc, key) => acc += ` ${key}=\"${rest[key]}\"`, \"\");\r\n let id_str = (id && id.length > 0) ? `id=\"${id}\"` : \"\";\r\n let class_str = (className && className.length > 0) ? `class=\"${className}\"` : \"\";\r\n return `\\n`;\r\n }\r\n\r\n}\r\nFlatten.Point = Point;\r\n/**\r\n * Function to create point equivalent to \"new\" constructor\r\n * @param args\r\n */\r\nconst point = (...args) => new Flatten.Point(...args);\r\nFlatten.point = point;\r\n\r\n// export {Point};\r\n\r\n/**\r\n * Created by Alex Bol on 2/19/2017.\r\n */\r\n\r\n/**\r\n * Class representing a vector\r\n * @type {Vector}\r\n */\r\nclass Vector {\r\n /**\r\n * Vector may be constructed by two points, or by two float numbers,\r\n * or by array of two numbers\r\n * @param {Point} ps - start point\r\n * @param {Point} pe - end point\r\n */\r\n constructor(...args) {\r\n /**\r\n * x-coordinate of a vector (float number)\r\n * @type {number}\r\n */\r\n this.x = 0;\r\n /**\r\n * y-coordinate of a vector (float number)\r\n * @type {number}\r\n */\r\n this.y = 0;\r\n\r\n /* return zero vector */\r\n if (args.length === 0) {\r\n return;\r\n }\r\n\r\n if (args.length === 1 && args[0] instanceof Array && args[0].length === 2) {\r\n let arr = args[0];\r\n if (typeof (arr[0]) == \"number\" && typeof (arr[1]) == \"number\") {\r\n this.x = arr[0];\r\n this.y = arr[1];\r\n return;\r\n }\r\n }\r\n\r\n if (args.length === 1 && args[0] instanceof Object && args[0].name === \"vector\") {\r\n let {x, y} = args[0];\r\n this.x = x;\r\n this.y = y;\r\n return;\r\n }\r\n\r\n if (args.length === 2) {\r\n let a1 = args[0];\r\n let a2 = args[1];\r\n\r\n if (typeof (a1) == \"number\" && typeof (a2) == \"number\") {\r\n this.x = a1;\r\n this.y = a2;\r\n return;\r\n }\r\n\r\n if (a1 instanceof Flatten.Point && a2 instanceof Flatten.Point) {\r\n this.x = a2.x - a1.x;\r\n this.y = a2.y - a1.y;\r\n return;\r\n }\r\n\r\n }\r\n\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n\r\n /**\r\n * Method clone returns new instance of Vector\r\n * @returns {Vector}\r\n */\r\n clone() {\r\n return new Flatten.Vector(this.x, this.y);\r\n }\r\n\r\n /**\r\n * Slope of the vector in radians from 0 to 2PI\r\n * @returns {number}\r\n */\r\n get slope() {\r\n let angle = Math.atan2(this.y, this.x);\r\n if (angle < 0) angle = 2 * Math.PI + angle;\r\n return angle;\r\n }\r\n\r\n /**\r\n * Length of vector\r\n * @returns {number}\r\n */\r\n get length() {\r\n return Math.sqrt(this.dot(this));\r\n }\r\n\r\n /**\r\n * Returns true if vectors are equal up to [DP_TOL]{@link http://localhost:63342/flatten-js/docs/global.html#DP_TOL}\r\n * tolerance\r\n * @param {Vector} v\r\n * @returns {boolean}\r\n */\r\n equalTo(v) {\r\n return Flatten.Utils.EQ(this.x, v.x) && Flatten.Utils.EQ(this.y, v.y);\r\n }\r\n\r\n /**\r\n * Returns new vector multiplied by scalar\r\n * @param {number} scalar\r\n * @returns {Vector}\r\n */\r\n multiply(scalar) {\r\n return (new Flatten.Vector(scalar * this.x, scalar * this.y));\r\n }\r\n\r\n /**\r\n * Returns scalar product (dot product) of two vectors
\r\n * dot_product = (this * v)\r\n * @param {Vector} v Other vector\r\n * @returns {number}\r\n */\r\n dot(v) {\r\n return (this.x * v.x + this.y * v.y);\r\n }\r\n\r\n /**\r\n * Returns vector product (cross product) of two vectors
\r\n * cross_product = (this x v)\r\n * @param {Vector} v Other vector\r\n * @returns {number}\r\n */\r\n cross(v) {\r\n return (this.x * v.y - this.y * v.x);\r\n }\r\n\r\n /**\r\n * Returns unit vector.
\r\n * Throw error if given vector has zero length\r\n * @returns {Vector}\r\n */\r\n normalize() {\r\n if (!Flatten.Utils.EQ_0(this.length)) {\r\n return (new Flatten.Vector(this.x / this.length, this.y / this.length));\r\n }\r\n throw Flatten.Errors.ZERO_DIVISION;\r\n }\r\n\r\n /**\r\n * Returns new vector rotated by given angle,\r\n * positive angle defines rotation in counter clockwise direction,\r\n * negative - in clockwise direction\r\n * @param {number} angle - Angle in radians\r\n * @returns {Vector}\r\n */\r\n rotate(angle) {\r\n let point = new Flatten.Point(this.x, this.y);\r\n let rpoint = point.rotate(angle);\r\n return new Flatten.Vector(rpoint.x, rpoint.y);\r\n }\r\n\r\n /**\r\n * Returns vector rotated 90 degrees counter clockwise\r\n * @returns {Vector}\r\n */\r\n rotate90CCW() {\r\n return new Flatten.Vector(-this.y, this.x);\r\n };\r\n\r\n /**\r\n * Returns vector rotated 90 degrees clockwise\r\n * @returns {Vector}\r\n */\r\n rotate90CW() {\r\n return new Flatten.Vector(this.y, -this.x);\r\n };\r\n\r\n /**\r\n * Return inverted vector\r\n * @returns {Vector}\r\n */\r\n invert() {\r\n return new Flatten.Vector(-this.x, -this.y);\r\n }\r\n\r\n /**\r\n * Return result of addition of other vector to this vector as a new vector\r\n * @param {Vector} v Other vector\r\n * @returns {Vector}\r\n */\r\n add(v) {\r\n return new Flatten.Vector(this.x + v.x, this.y + v.y);\r\n }\r\n\r\n /**\r\n * Return result of subtraction of other vector from current vector as a new vector\r\n * @param {Vector} v Another vector\r\n * @returns {Vector}\r\n */\r\n subtract(v) {\r\n return new Flatten.Vector(this.x - v.x, this.y - v.y);\r\n }\r\n\r\n /**\r\n * Return angle between this vector and other vector.
\r\n * Angle is measured from 0 to 2*PI in the counter clockwise direction\r\n * from current vector to other.\r\n * @param {Vector} v Another vector\r\n * @returns {number}\r\n */\r\n angleTo(v) {\r\n let norm1 = this.normalize();\r\n let norm2 = v.normalize();\r\n let angle = Math.atan2(norm1.cross(norm2), norm1.dot(norm2));\r\n if (angle < 0) angle += 2 * Math.PI;\r\n return angle;\r\n }\r\n\r\n /**\r\n * Return vector projection of the current vector on another vector\r\n * @param {Vector} v Another vector\r\n * @returns {Vector}\r\n */\r\n projectionOn(v) {\r\n let n = v.normalize();\r\n let d = this.dot(n);\r\n return n.multiply(d);\r\n }\r\n\r\n /**\r\n * This method returns an object that defines how data will be\r\n * serialized when called JSON.stringify() method\r\n * @returns {Object}\r\n */\r\n toJSON() {\r\n return Object.assign({}, this, {name: \"vector\"});\r\n }\r\n}\r\nFlatten.Vector = Vector;\r\n\r\n/**\r\n * Function to create vector equivalent to \"new\" constructor\r\n * @param args\r\n */\r\nconst vector = (...args) => new Flatten.Vector(...args);\r\nFlatten.vector = vector;\r\n\r\n/**\r\n * Created by Alex Bol on 3/10/2017.\r\n */\r\n\r\n/**\r\n * Class representing a segment\r\n * @type {Segment}\r\n */\r\nclass Segment {\r\n /**\r\n *\r\n * @param {Point} ps - start point\r\n * @param {Point} pe - end point\r\n */\r\n constructor(...args) {\r\n /**\r\n * Start point\r\n * @type {Point}\r\n */\r\n this.ps = new Flatten.Point();\r\n /**\r\n * End Point\r\n * @type {Point}\r\n */\r\n this.pe = new Flatten.Point();\r\n\r\n if (args.length === 0) {\r\n return;\r\n }\r\n\r\n if (args.length === 1 && args[0] instanceof Array && args[0].length === 4) {\r\n let coords = args[0];\r\n this.ps = new Flatten.Point(coords[0], coords[1]);\r\n this.pe = new Flatten.Point(coords[2], coords[3]);\r\n return;\r\n }\r\n\r\n if (args.length === 1 && args[0] instanceof Object && args[0].name === \"segment\") {\r\n let {ps, pe} = args[0];\r\n this.ps = new Flatten.Point(ps.x, ps.y);\r\n this.pe = new Flatten.Point(pe.x, pe.y);\r\n return;\r\n }\r\n\r\n // second point omitted issue #84\r\n if (args.length === 1 && args[0] instanceof Flatten.Point) {\r\n this.ps = args[0].clone();\r\n return;\r\n }\r\n\r\n if (args.length === 2 && args[0] instanceof Flatten.Point && args[1] instanceof Flatten.Point) {\r\n this.ps = args[0].clone();\r\n this.pe = args[1].clone();\r\n return;\r\n }\r\n\r\n if (args.length === 4) {\r\n this.ps = new Flatten.Point(args[0], args[1]);\r\n this.pe = new Flatten.Point(args[2], args[3]);\r\n return;\r\n }\r\n\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n\r\n /**\r\n * Return new cloned instance of segment\r\n * @returns {Segment}\r\n */\r\n clone() {\r\n return new Flatten.Segment(this.start, this.end);\r\n }\r\n\r\n /**\r\n * Start point\r\n * @returns {Point}\r\n */\r\n get start() {\r\n return this.ps;\r\n }\r\n\r\n /**\r\n * End point\r\n * @returns {Point}\r\n */\r\n get end() {\r\n return this.pe;\r\n }\r\n\r\n\r\n /**\r\n * Returns array of start and end point\r\n * @returns [Point,Point]\r\n */\r\n get vertices() {\r\n return [this.ps.clone(), this.pe.clone()];\r\n }\r\n\r\n /**\r\n * Length of a segment\r\n * @returns {number}\r\n */\r\n get length() {\r\n return this.start.distanceTo(this.end)[0];\r\n }\r\n\r\n /**\r\n * Slope of the line - angle to axe x in radians from 0 to 2PI\r\n * @returns {number}\r\n */\r\n get slope() {\r\n let vec = new Flatten.Vector(this.start, this.end);\r\n return vec.slope;\r\n }\r\n\r\n /**\r\n * Bounding box\r\n * @returns {Box}\r\n */\r\n get box() {\r\n return new Flatten.Box(\r\n Math.min(this.start.x, this.end.x),\r\n Math.min(this.start.y, this.end.y),\r\n Math.max(this.start.x, this.end.x),\r\n Math.max(this.start.y, this.end.y)\r\n )\r\n }\r\n\r\n /**\r\n * Returns true if equals to query segment, false otherwise\r\n * @param {Seg} seg - query segment\r\n * @returns {boolean}\r\n */\r\n equalTo(seg) {\r\n return this.ps.equalTo(seg.ps) && this.pe.equalTo(seg.pe);\r\n }\r\n\r\n /**\r\n * Returns true if segment contains point\r\n * @param {Point} pt Query point\r\n * @returns {boolean}\r\n */\r\n contains(pt) {\r\n return Flatten.Utils.EQ_0(this.distanceToPoint(pt));\r\n }\r\n\r\n /**\r\n * Returns array of intersection points between segment and other shape\r\n * @param {Shape} shape - Shape of the one of supported types
\r\n * @returns {Point[]}\r\n */\r\n intersect(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n return this.contains(shape) ? [shape] : [];\r\n }\r\n\r\n if (shape instanceof Flatten.Line) {\r\n return intersectSegment2Line(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n return intersectSegment2Segment(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n return intersectSegment2Circle(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Box) {\r\n return intersectSegment2Box(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n return intersectSegment2Arc(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Polygon) {\r\n return intersectSegment2Polygon(this, shape);\r\n }\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment from segment to shape and return as array [distance, shortest segment]\r\n * @param {Shape} shape Shape of the one of supported types Point, Line, Circle, Segment, Arc, Polygon or Planar Set\r\n * @returns {number} distance from segment to shape\r\n * @returns {Segment} shortest segment between segment and shape (started at segment, ended at shape)\r\n */\r\n distanceTo(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n let [dist, shortest_segment] = Flatten.Distance.point2segment(shape, this);\r\n shortest_segment = shortest_segment.reverse();\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n let [dist, shortest_segment] = Flatten.Distance.segment2circle(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Line) {\r\n let [dist, shortest_segment] = Flatten.Distance.segment2line(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n let [dist, shortest_segment] = Flatten.Distance.segment2segment(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n let [dist, shortest_segment] = Flatten.Distance.segment2arc(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Polygon) {\r\n let [dist, shortest_segment] = Flatten.Distance.shape2polygon(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.PlanarSet) {\r\n let [dist, shortest_segment] = Flatten.Distance.shape2planarSet(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n }\r\n\r\n /**\r\n * Returns unit vector in the direction from start to end\r\n * @returns {Vector}\r\n */\r\n tangentInStart() {\r\n let vec = new Flatten.Vector(this.start, this.end);\r\n return vec.normalize();\r\n }\r\n\r\n /**\r\n * Return unit vector in the direction from end to start\r\n * @returns {Vector}\r\n */\r\n tangentInEnd() {\r\n let vec = new Flatten.Vector(this.end, this.start);\r\n return vec.normalize();\r\n }\r\n\r\n /**\r\n * Returns new segment with swapped start and end points\r\n * @returns {Segment}\r\n */\r\n reverse() {\r\n return new Segment(this.end, this.start);\r\n }\r\n\r\n /**\r\n * When point belongs to segment, return array of two segments split by given point,\r\n * if point is inside segment. Returns clone of this segment if query point is incident\r\n * to start or end point of the segment. Returns empty array if point does not belong to segment\r\n * @param {Point} pt Query point\r\n * @returns {Segment[]}\r\n */\r\n split(pt) {\r\n if (this.start.equalTo(pt))\r\n return [null, this.clone()];\r\n\r\n if (this.end.equalTo(pt))\r\n return [this.clone(), null];\r\n\r\n return [\r\n new Flatten.Segment(this.start, pt),\r\n new Flatten.Segment(pt, this.end)\r\n ]\r\n }\r\n\r\n /**\r\n * Return middle point of the segment\r\n * @returns {Point}\r\n */\r\n middle() {\r\n return new Flatten.Point((this.start.x + this.end.x) / 2, (this.start.y + this.end.y) / 2);\r\n }\r\n\r\n /**\r\n * Get point at given length\r\n * @param {number} length - The length along the segment\r\n * @returns {Point}\r\n */\r\n pointAtLength(length) {\r\n if (length > this.length || length < 0) return null;\r\n if (length == 0) return this.start;\r\n if (length == this.length) return this.end;\r\n let factor = length / this.length;\r\n return new Flatten.Point(\r\n (this.end.x - this.start.x) * factor + this.start.x,\r\n (this.end.y - this.start.y) * factor + this.start.y\r\n );\r\n }\r\n\r\n distanceToPoint(pt) {\r\n let [dist, ...rest] = Flatten.Distance.point2segment(pt, this);\r\n return dist;\r\n };\r\n\r\n definiteIntegral(ymin = 0.0) {\r\n let dx = this.end.x - this.start.x;\r\n let dy1 = this.start.y - ymin;\r\n let dy2 = this.end.y - ymin;\r\n return (dx * (dy1 + dy2) / 2);\r\n }\r\n\r\n /**\r\n * Returns new segment translated by vector vec\r\n * @param {Vector} vec\r\n * @returns {Segment}\r\n */\r\n translate(...args) {\r\n return new Segment(this.ps.translate(...args), this.pe.translate(...args));\r\n }\r\n\r\n /**\r\n * Return new segment rotated by given angle around given point\r\n * If point omitted, rotate around origin (0,0)\r\n * Positive value of angle defines rotation counter clockwise, negative - clockwise\r\n * @param {number} angle - rotation angle in radians\r\n * @param {Point} center - center point, default is (0,0)\r\n * @returns {Segment}\r\n */\r\n rotate(angle = 0, center = new Flatten.Point()) {\r\n let m = new Flatten.Matrix();\r\n m = m.translate(center.x, center.y).rotate(angle).translate(-center.x, -center.y);\r\n return this.transform(m);\r\n }\r\n\r\n /**\r\n * Return new segment transformed using affine transformation matrix\r\n * @param {Matrix} matrix - affine transformation matrix\r\n * @returns {Segment} - transformed segment\r\n */\r\n transform(matrix = new Flatten.Matrix()) {\r\n return new Segment(this.ps.transform(matrix), this.pe.transform(matrix))\r\n }\r\n\r\n /**\r\n * Returns true if segment start is equal to segment end up to DP_TOL\r\n * @returns {boolean}\r\n */\r\n isZeroLength() {\r\n return this.ps.equalTo(this.pe)\r\n }\r\n\r\n /**\r\n * Sort given array of points from segment start to end, assuming all points lay on the segment\r\n * @param {Point[]} - array of points\r\n * @returns {Point[]} new array sorted\r\n */\r\n sortPoints(pts) {\r\n let line = new Flatten.Line(this.start, this.end);\r\n return line.sortPoints(pts);\r\n }\r\n\r\n /**\r\n * This method returns an object that defines how data will be\r\n * serialized when called JSON.stringify() method\r\n * @returns {Object}\r\n */\r\n toJSON() {\r\n return Object.assign({}, this, {name: \"segment\"});\r\n }\r\n\r\n /**\r\n * Return string to draw segment in svg\r\n * @param {Object} attrs - an object with attributes for svg path element,\r\n * like \"stroke\", \"strokeWidth\"
\r\n * Defaults are stroke:\"black\", strokeWidth:\"1\"\r\n * @returns {string}\r\n */\r\n svg(attrs = {}) {\r\n let {stroke, strokeWidth, id, className} = attrs;\r\n // let rest_str = Object.keys(rest).reduce( (acc, key) => acc += ` ${key}=\"${rest[key]}\"`, \"\");\r\n let id_str = (id && id.length > 0) ? `id=\"${id}\"` : \"\";\r\n let class_str = (className && className.length > 0) ? `class=\"${className}\"` : \"\";\r\n\r\n return `\\n`;\r\n\r\n }\r\n\r\n}\r\nFlatten.Segment = Segment;\r\n/**\r\n * Shortcut method to create new segment\r\n */\r\nconst segment = (...args) => new Flatten.Segment(...args);\r\nFlatten.segment = segment;\r\n\r\n/**\r\n * Created by Alex Bol on 2/20/2017.\r\n */\r\n\r\nlet {vector: vector$1} = Flatten;\r\n\r\n/**\r\n * Class representing a line\r\n * @type {Line}\r\n */\r\nclass Line {\r\n /**\r\n * Line may be constructed by point and normal vector or by two points that a line passes through\r\n * @param {Point} pt - point that a line passes through\r\n * @param {Vector|Point} norm - normal vector to a line or second point a line passes through\r\n */\r\n constructor(...args) {\r\n /**\r\n * Point a line passes through\r\n * @type {Point}\r\n */\r\n this.pt = new Flatten.Point();\r\n /**\r\n * Normal vector to a line
\r\n * Vector is normalized (length == 1)
\r\n * Direction of the vector is chosen to satisfy inequality norm * p >= 0\r\n * @type {Vector}\r\n */\r\n this.norm = new Flatten.Vector(0, 1);\r\n\r\n if (args.length == 0) {\r\n return;\r\n }\r\n\r\n if (args.length == 1 && args[0] instanceof Object && args[0].name === \"line\") {\r\n let {pt, norm} = args[0];\r\n this.pt = new Flatten.Point(pt);\r\n this.norm = new Flatten.Vector(norm);\r\n return;\r\n }\r\n\r\n if (args.length == 2) {\r\n let a1 = args[0];\r\n let a2 = args[1];\r\n\r\n if (a1 instanceof Flatten.Point && a2 instanceof Flatten.Point) {\r\n this.pt = a1;\r\n this.norm = Line.points2norm(a1, a2);\r\n if (this.norm.dot(vector$1(this.pt.x,this.pt.y)) >= 0) {\r\n this.norm.invert();\r\n }\r\n return;\r\n }\r\n\r\n if (a1 instanceof Flatten.Point && a2 instanceof Flatten.Vector) {\r\n if (Flatten.Utils.EQ_0(a2.x) && Flatten.Utils.EQ_0(a2.y)) {\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n this.pt = a1.clone();\r\n this.norm = a2.clone();\r\n this.norm = this.norm.normalize();\r\n if (this.norm.dot(vector$1(this.pt.x,this.pt.y)) >= 0) {\r\n this.norm.invert();\r\n }\r\n return;\r\n }\r\n\r\n if (a1 instanceof Flatten.Vector && a2 instanceof Flatten.Point) {\r\n if (Flatten.Utils.EQ_0(a1.x) && Flatten.Utils.EQ_0(a1.y)) {\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n this.pt = a2.clone();\r\n this.norm = a1.clone();\r\n this.norm = this.norm.normalize();\r\n if (this.norm.dot(vector$1(this.pt.x,this.pt.y)) >= 0) {\r\n this.norm.invert();\r\n }\r\n return;\r\n }\r\n }\r\n\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n\r\n /**\r\n * Return new cloned instance of line\r\n * @returns {Line}\r\n */\r\n clone() {\r\n return new Flatten.Line(this.pt, this.norm);\r\n }\r\n\r\n /* The following methods need for implementation of Edge interface\r\n /**\r\n * Line has no start point\r\n * @returns {undefined}\r\n */\r\n get start() {return undefined;}\r\n\r\n /**\r\n * Line has no end point\r\n */\r\n get end() {return undefined;}\r\n\r\n /**\r\n * Return positive infinity number as length\r\n * @returns {number}\r\n */\r\n get length() {return Number.POSITIVE_INFINITY;}\r\n\r\n /**\r\n * Returns infinite box\r\n * @returns {Box}\r\n */\r\n get box() {\r\n return new Flatten.Box(\r\n Number.NEGATIVE_INFINITY,\r\n Number.NEGATIVE_INFINITY,\r\n Number.POSITIVE_INFINITY,\r\n Number.POSITIVE_INFINITY\r\n )\r\n }\r\n\r\n /**\r\n * Middle point is undefined\r\n * @returns {undefined}\r\n */\r\n get middle() {return undefined}\r\n\r\n /**\r\n * Slope of the line - angle in radians between line and axe x from 0 to 2PI\r\n * @returns {number} - slope of the line\r\n */\r\n get slope() {\r\n let vec = new Flatten.Vector(this.norm.y, -this.norm.x);\r\n return vec.slope;\r\n }\r\n\r\n /**\r\n * Get coefficients [A,B,C] of a standard line equation in the form Ax + By = C\r\n * @code [A, B, C] = line.standard\r\n * @returns {number[]} - array of coefficients\r\n */\r\n get standard() {\r\n let A = this.norm.x;\r\n let B = this.norm.y;\r\n let C = this.norm.dot(this.pt);\r\n\r\n return [A, B, C];\r\n }\r\n\r\n /**\r\n * Return true if parallel or incident to other line\r\n * @param {Line} other_line - line to check\r\n * @returns {boolean}\r\n */\r\n parallelTo(other_line) {\r\n return Flatten.Utils.EQ_0(this.norm.cross(other_line.norm));\r\n }\r\n\r\n /**\r\n * Returns true if incident to other line\r\n * @param {Line} other_line - line to check\r\n * @returns {boolean}\r\n */\r\n incidentTo(other_line) {\r\n return this.parallelTo(other_line) && this.pt.on(other_line);\r\n }\r\n\r\n /**\r\n * Returns true if point belongs to line\r\n * @param {Point} pt Query point\r\n * @returns {boolean}\r\n */\r\n contains(pt) {\r\n if (this.pt.equalTo(pt)) {\r\n return true;\r\n }\r\n /* Line contains point if vector to point is orthogonal to the line normal vector */\r\n let vec = new Flatten.Vector(this.pt, pt);\r\n return Flatten.Utils.EQ_0(this.norm.dot(vec));\r\n }\r\n\r\n /**\r\n * Return coordinate of the point that lays on the line in the transformed\r\n * coordinate system where center is the projection of the point(0,0) to\r\n * the line and axe y is collinear to the normal vector.
\r\n * This method assumes that point lays on the line and does not check it\r\n * @param {Point} pt - point on line\r\n * @returns {number}\r\n */\r\n coord(pt) {\r\n return vector$1(pt.x, pt.y).cross(this.norm);\r\n }\r\n\r\n /**\r\n * Returns array of intersection points\r\n * @param {Shape} shape - shape to intersect with\r\n * @returns {Point[]}\r\n */\r\n intersect(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n return this.contains(shape) ? [shape] : [];\r\n }\r\n\r\n if (shape instanceof Flatten.Line) {\r\n return intersectLine2Line(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n return intersectLine2Circle(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Box) {\r\n return intersectLine2Box(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n return intersectSegment2Line(shape, this);\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n return intersectLine2Arc(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Polygon) {\r\n return intersectLine2Polygon(this, shape);\r\n }\r\n\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment from line to shape and returns array [distance, shortest_segment]\r\n * @param {Shape} shape Shape of the one of the types Point, Circle, Segment, Arc, Polygon\r\n * @returns {Number}\r\n * @returns {Segment}\r\n */\r\n distanceTo(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n let [distance, shortest_segment] = Flatten.Distance.point2line(shape, this);\r\n shortest_segment = shortest_segment.reverse();\r\n return [distance, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n let [distance, shortest_segment] = Flatten.Distance.circle2line(shape, this);\r\n shortest_segment = shortest_segment.reverse();\r\n return [distance, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n let [distance, shortest_segment] = Flatten.Distance.segment2line(shape, this);\r\n return [distance, shortest_segment.reverse()];\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n let [distance, shortest_segment] = Flatten.Distance.arc2line(shape, this);\r\n return [distance, shortest_segment.reverse()];\r\n }\r\n\r\n if (shape instanceof Flatten.Polygon) {\r\n let [distance, shortest_segment] = Flatten.Distance.shape2polygon(this, shape);\r\n return [distance, shortest_segment];\r\n }\r\n }\r\n\r\n /**\r\n * Split line with array of points and return array of shapes\r\n * Assumed that all points lay on the line\r\n * @param {Point[]}\r\n * @returns {Shape[]}\r\n */\r\n split(pt) {\r\n if (pt instanceof Flatten.Point) {\r\n return [new Flatten.Ray(pt, this.norm.invert()), new Flatten.Ray(pt, this.norm)]\r\n }\r\n else {\r\n let multiline = new Flatten.Multiline([this]);\r\n let sorted_points = this.sortPoints(pt);\r\n multiline.split(sorted_points);\r\n return multiline.toShapes();\r\n }\r\n }\r\n\r\n /**\r\n * Sort given array of points that lay on line with respect to coordinate on a line\r\n * The method assumes that points lay on the line and does not check this\r\n * @param {Point[]} pts - array of points\r\n * @returns {Point[]} new array sorted\r\n */\r\n sortPoints(pts) {\r\n return pts.slice().sort( (pt1, pt2) => {\r\n if (this.coord(pt1) < this.coord(pt2)) {\r\n return -1;\r\n }\r\n if (this.coord(pt1) > this.coord(pt2)) {\r\n return 1;\r\n }\r\n return 0;\r\n })\r\n }\r\n\r\n /**\r\n * This method returns an object that defines how data will be\r\n * serialized when called JSON.stringify() method\r\n * @returns {Object}\r\n */\r\n toJSON() {\r\n return Object.assign({}, this, {name: \"line\"});\r\n }\r\n\r\n /**\r\n * Return string to draw svg segment representing line inside given box\r\n * @param {Box} box Box representing drawing area\r\n * @param {Object} attrs - an object with attributes of svg circle element\r\n */\r\n svg(box, attrs = {}) {\r\n let ip = intersectLine2Box(this, box);\r\n if (ip.length === 0)\r\n return \"\";\r\n let ps = ip[0];\r\n let pe = ip.length == 2 ? ip[1] : ip.find(pt => !pt.equalTo(ps));\r\n if (pe === undefined) pe = ps;\r\n let segment = new Flatten.Segment(ps, pe);\r\n return segment.svg(attrs);\r\n }\r\n\r\n static points2norm(pt1, pt2) {\r\n if (pt1.equalTo(pt2)) {\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n let vec = new Flatten.Vector(pt1, pt2);\r\n let unit = vec.normalize();\r\n return unit.rotate90CCW();\r\n }\r\n}\r\nFlatten.Line = Line;\r\n/**\r\n * Function to create line equivalent to \"new\" constructor\r\n * @param args\r\n */\r\nconst line = (...args) => new Flatten.Line(...args);\r\nFlatten.line = line;\r\n\r\n/**\r\n * Created by Alex Bol on 3/6/2017.\r\n */\r\n\r\n/**\r\n * Class representing a circle\r\n * @type {Circle}\r\n */\r\nclass Circle {\r\n /**\r\n *\r\n * @param {Point} pc - circle center point\r\n * @param {number} r - circle radius\r\n */\r\n constructor(...args) {\r\n /**\r\n * Circle center\r\n * @type {Point}\r\n */\r\n this.pc = new Flatten.Point();\r\n /**\r\n * Circle radius\r\n * @type {number}\r\n */\r\n this.r = 1;\r\n\r\n if (args.length == 1 && args[0] instanceof Object && args[0].name === \"circle\") {\r\n let {pc, r} = args[0];\r\n this.pc = new Flatten.Point(pc);\r\n this.r = r;\r\n return;\r\n } else {\r\n let [pc, r] = [...args];\r\n if (pc && pc instanceof Flatten.Point) this.pc = pc.clone();\r\n if (r !== undefined) this.r = r;\r\n return;\r\n }\r\n\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n\r\n /**\r\n * Return new cloned instance of circle\r\n * @returns {Circle}\r\n */\r\n clone() {\r\n return new Flatten.Circle(this.pc.clone(), this.r);\r\n }\r\n\r\n /**\r\n * Circle center\r\n * @returns {Point}\r\n */\r\n get center() {\r\n return this.pc;\r\n }\r\n\r\n /**\r\n * Circle bounding box\r\n * @returns {Box}\r\n */\r\n get box() {\r\n return new Flatten.Box(\r\n this.pc.x - this.r,\r\n this.pc.y - this.r,\r\n this.pc.x + this.r,\r\n this.pc.y + this.r\r\n );\r\n }\r\n\r\n /**\r\n * Return true if circle contains shape: no point of shape lies outside of the circle\r\n * @param {Shape} shape - test shape\r\n * @returns {boolean}\r\n */\r\n contains(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n return Flatten.Utils.LE(shape.distanceTo(this.center)[0], this.r);\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n return Flatten.Utils.LE(shape.start.distanceTo(this.center)[0], this.r) &&\r\n Flatten.Utils.LE(shape.end.distanceTo(this.center)[0], this.r);\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n return this.intersect(shape).length === 0 &&\r\n Flatten.Utils.LE(shape.start.distanceTo(this.center)[0], this.r) &&\r\n Flatten.Utils.LE(shape.end.distanceTo(this.center)[0], this.r);\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n return this.intersect(shape).length === 0 &&\r\n Flatten.Utils.LE(shape.r, this.r) &&\r\n Flatten.Utils.LE(shape.center.distanceTo(this.center)[0], this.r);\r\n }\r\n\r\n /* TODO: box, polygon */\r\n }\r\n\r\n /**\r\n * Transform circle to closed arc\r\n * @param {boolean} counterclockwise\r\n * @returns {Arc}\r\n */\r\n toArc(counterclockwise = true) {\r\n return new Flatten.Arc(this.center, this.r, Math.PI, -Math.PI, counterclockwise);\r\n }\r\n\r\n /**\r\n * Returns array of intersection points between circle and other shape\r\n * @param {Shape} shape Shape of the one of supported types\r\n * @returns {Point[]}\r\n */\r\n intersect(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n return this.contains(shape) ? [shape] : [];\r\n }\r\n if (shape instanceof Flatten.Line) {\r\n return intersectLine2Circle(shape, this);\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n return intersectSegment2Circle(shape, this);\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n return intersectCircle2Circle(shape, this);\r\n }\r\n\r\n if (shape instanceof Flatten.Box) {\r\n return intersectCircle2Box(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n return intersectArc2Circle(shape, this);\r\n }\r\n if (shape instanceof Flatten.Polygon) {\r\n return intersectCircle2Polygon(this, shape);\r\n }\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment from circle to shape and return array [distance, shortest segment]\r\n * @param {Shape} shape Shape of the one of supported types Point, Line, Circle, Segment, Arc, Polygon or Planar Set\r\n * @returns {number} distance from circle to shape\r\n * @returns {Segment} shortest segment between circle and shape (started at circle, ended at shape)\r\n\r\n */\r\n distanceTo(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n let [distance, shortest_segment] = Flatten.Distance.point2circle(shape, this);\r\n shortest_segment = shortest_segment.reverse();\r\n return [distance, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n let [distance, shortest_segment] = Flatten.Distance.circle2circle(this, shape);\r\n return [distance, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Line) {\r\n let [distance, shortest_segment] = Flatten.Distance.circle2line(this, shape);\r\n return [distance, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n let [distance, shortest_segment] = Flatten.Distance.segment2circle(shape, this);\r\n shortest_segment = shortest_segment.reverse();\r\n return [distance, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n let [distance, shortest_segment] = Flatten.Distance.arc2circle(shape, this);\r\n shortest_segment = shortest_segment.reverse();\r\n return [distance, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Polygon) {\r\n let [distance, shortest_segment] = Flatten.Distance.shape2polygon(this, shape);\r\n return [distance, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.PlanarSet) {\r\n let [dist, shortest_segment] = Flatten.Distance.shape2planarSet(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n }\r\n\r\n /**\r\n * This method returns an object that defines how data will be\r\n * serialized when called JSON.stringify() method\r\n * @returns {Object}\r\n */\r\n toJSON() {\r\n return Object.assign({}, this, {name: \"circle\"});\r\n }\r\n\r\n /**\r\n * Return string to draw circle in svg\r\n * @param {Object} attrs - an object with attributes of svg circle element,\r\n * like \"stroke\", \"strokeWidth\", \"fill\"
\r\n * Defaults are stroke:\"black\", strokeWidth:\"1\", fill:\"none\"\r\n * @returns {string}\r\n */\r\n svg(attrs = {}) {\r\n let {stroke, strokeWidth, fill, fillOpacity, id, className} = attrs;\r\n // let rest_str = Object.keys(rest).reduce( (acc, key) => acc += ` ${key}=\"${rest[key]}\"`, \"\");\r\n let id_str = (id && id.length > 0) ? `id=\"${id}\"` : \"\";\r\n let class_str = (className && className.length > 0) ? `class=\"${className}\"` : \"\";\r\n\r\n return `\\n`;\r\n }\r\n\r\n}\r\nFlatten.Circle = Circle;\r\n/**\r\n * Shortcut to create new circle\r\n * @param args\r\n */\r\nconst circle = (...args) => new Flatten.Circle(...args);\r\nFlatten.circle = circle;\r\n\r\n/**\r\n * Created by Alex Bol on 3/10/2017.\r\n */\r\n\r\n/**\r\n * Class representing a circular arc\r\n * @type {Arc}\r\n */\r\nclass Arc {\r\n /**\r\n *\r\n * @param {Point} pc - arc center\r\n * @param {number} r - arc radius\r\n * @param {number} startAngle - start angle in radians from 0 to 2*PI\r\n * @param {number} endAngle - end angle in radians from 0 to 2*PI\r\n * @param {boolean} counterClockwise - arc direction, true - clockwise, false - counter clockwise\r\n */\r\n constructor(...args) {\r\n /**\r\n * Arc center\r\n * @type {Point}\r\n */\r\n this.pc = new Flatten.Point();\r\n /**\r\n * Arc radius\r\n * @type {number}\r\n */\r\n this.r = 1;\r\n /**\r\n * Arc start angle in radians\r\n * @type {number}\r\n */\r\n this.startAngle = 0;\r\n /**\r\n * Arc end angle in radians\r\n * @type {number}\r\n */\r\n this.endAngle = 2 * Math.PI;\r\n /**\r\n * Arc orientation\r\n * @type {boolean}\r\n */\r\n this.counterClockwise = Flatten.CCW;\r\n\r\n if (args.length == 0)\r\n return;\r\n\r\n if (args.length == 1 && args[0] instanceof Object && args[0].name === \"arc\") {\r\n let {pc, r, startAngle, endAngle, counterClockwise} = args[0];\r\n this.pc = new Flatten.Point(pc.x, pc.y);\r\n this.r = r;\r\n this.startAngle = startAngle;\r\n this.endAngle = endAngle;\r\n this.counterClockwise = counterClockwise;\r\n return;\r\n } else {\r\n let [pc, r, startAngle, endAngle, counterClockwise] = [...args];\r\n if (pc && pc instanceof Flatten.Point) this.pc = pc.clone();\r\n if (r !== undefined) this.r = r;\r\n if (startAngle !== undefined) this.startAngle = startAngle;\r\n if (endAngle !== undefined) this.endAngle = endAngle;\r\n if (counterClockwise !== undefined) this.counterClockwise = counterClockwise;\r\n return;\r\n }\r\n\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n\r\n /**\r\n * Return new cloned instance of arc\r\n * @returns {Arc}\r\n */\r\n clone() {\r\n return new Flatten.Arc(this.pc.clone(), this.r, this.startAngle, this.endAngle, this.counterClockwise);\r\n }\r\n\r\n /**\r\n * Get sweep angle in radians. Sweep angle is non-negative number from 0 to 2*PI\r\n * @returns {number}\r\n */\r\n get sweep() {\r\n if (Flatten.Utils.EQ(this.startAngle, this.endAngle))\r\n return 0.0;\r\n if (Flatten.Utils.EQ(Math.abs(this.startAngle - this.endAngle), Flatten.PIx2)) {\r\n return Flatten.PIx2;\r\n }\r\n let sweep;\r\n if (this.counterClockwise) {\r\n sweep = Flatten.Utils.GT(this.endAngle, this.startAngle) ?\r\n this.endAngle - this.startAngle : this.endAngle - this.startAngle + Flatten.PIx2;\r\n } else {\r\n sweep = Flatten.Utils.GT(this.startAngle, this.endAngle) ?\r\n this.startAngle - this.endAngle : this.startAngle - this.endAngle + Flatten.PIx2;\r\n }\r\n\r\n if (Flatten.Utils.GT(sweep, Flatten.PIx2)) {\r\n sweep -= Flatten.PIx2;\r\n }\r\n if (Flatten.Utils.LT(sweep, 0)) {\r\n sweep += Flatten.PIx2;\r\n }\r\n return sweep;\r\n }\r\n\r\n /**\r\n * Get start point of arc\r\n * @returns {Point}\r\n */\r\n get start() {\r\n let p0 = new Flatten.Point(this.pc.x + this.r, this.pc.y);\r\n return p0.rotate(this.startAngle, this.pc);\r\n }\r\n\r\n /**\r\n * Get end point of arc\r\n * @returns {Point}\r\n */\r\n get end() {\r\n let p0 = new Flatten.Point(this.pc.x + this.r, this.pc.y);\r\n return p0.rotate(this.endAngle, this.pc);\r\n }\r\n\r\n /**\r\n * Get center of arc\r\n * @returns {Point}\r\n */\r\n get center() {\r\n return this.pc.clone();\r\n }\r\n\r\n get vertices() {\r\n return [this.start.clone(), this.end.clone()];\r\n }\r\n\r\n /**\r\n * Get arc length\r\n * @returns {number}\r\n */\r\n get length() {\r\n return Math.abs(this.sweep * this.r);\r\n }\r\n\r\n /**\r\n * Get bounding box of the arc\r\n * @returns {Box}\r\n */\r\n get box() {\r\n let func_arcs = this.breakToFunctional();\r\n let box = func_arcs.reduce((acc, arc) => acc.merge(arc.start.box), new Flatten.Box());\r\n box = box.merge(this.end.box);\r\n return box;\r\n }\r\n\r\n /**\r\n * Returns true if arc contains point, false otherwise\r\n * @param {Point} pt - point to test\r\n * @returns {boolean}\r\n */\r\n contains(pt) {\r\n // first check if point on circle (pc,r)\r\n if (!Flatten.Utils.EQ(this.pc.distanceTo(pt)[0], this.r))\r\n return false;\r\n\r\n // point on circle\r\n\r\n if (pt.equalTo(this.start))\r\n return true;\r\n\r\n let angle = new Flatten.Vector(this.pc, pt).slope;\r\n let test_arc = new Flatten.Arc(this.pc, this.r, this.startAngle, angle, this.counterClockwise);\r\n return Flatten.Utils.LE(test_arc.length, this.length);\r\n }\r\n\r\n /**\r\n * When given point belongs to arc, return array of two arcs split by this point. If points is incident\r\n * to start or end point of the arc, return clone of the arc. If point does not belong to the arcs, return\r\n * empty array.\r\n * @param {Point} pt Query point\r\n * @returns {Arc[]}\r\n */\r\n split(pt) {\r\n if (this.start.equalTo(pt))\r\n return [null, this.clone()];\r\n\r\n if (this.end.equalTo(pt))\r\n return [this.clone(), null];\r\n\r\n let angle = new Flatten.Vector(this.pc, pt).slope;\r\n\r\n return [\r\n new Flatten.Arc(this.pc, this.r, this.startAngle, angle, this.counterClockwise),\r\n new Flatten.Arc(this.pc, this.r, angle, this.endAngle, this.counterClockwise)\r\n ]\r\n }\r\n\r\n /**\r\n * Return middle point of the arc\r\n * @returns {Point}\r\n */\r\n middle() {\r\n let endAngle = this.counterClockwise ? this.startAngle + this.sweep / 2 : this.startAngle - this.sweep / 2;\r\n let arc = new Flatten.Arc(this.pc, this.r, this.startAngle, endAngle, this.counterClockwise);\r\n return arc.end;\r\n }\r\n\r\n /**\r\n * Get point at given length\r\n * @param {number} length - The length along the arc\r\n * @returns {Point}\r\n */\r\n pointAtLength(length) {\r\n if (length > this.length || length < 0) return null;\r\n if (length == 0) return this.start;\r\n if (length == this.length) return this.end;\r\n let factor = length / this.length;\r\n let endAngle = this.counterClockwise ? this.startAngle + this.sweep * factor : this.startAngle - this.sweep * factor;\r\n let arc = new Flatten.Arc(this.pc, this.r, this.startAngle, endAngle, this.counterClockwise);\r\n return arc.end;\r\n }\r\n\r\n /**\r\n * Returns chord height (\"sagitta\") of the arc\r\n * @returns {number}\r\n */\r\n chordHeight() {\r\n return (1.0 - Math.cos(Math.abs(this.sweep / 2.0))) * this.r;\r\n }\r\n\r\n /**\r\n * Returns array of intersection points between arc and other shape\r\n * @param {Shape} shape Shape of the one of supported types
\r\n * @returns {Points[]}\r\n */\r\n intersect(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n return this.contains(shape) ? [shape] : [];\r\n }\r\n if (shape instanceof Flatten.Line) {\r\n return intersectLine2Arc(shape, this);\r\n }\r\n if (shape instanceof Flatten.Circle) {\r\n return intersectArc2Circle(this, shape);\r\n }\r\n if (shape instanceof Flatten.Segment) {\r\n return intersectSegment2Arc(shape, this);\r\n }\r\n if (shape instanceof Flatten.Box) {\r\n return intersectArc2Box(this, shape);\r\n }\r\n if (shape instanceof Flatten.Arc) {\r\n return intersectArc2Arc(this, shape);\r\n }\r\n if (shape instanceof Flatten.Polygon) {\r\n return intersectArc2Polygon(this, shape);\r\n }\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment from arc to shape and return array [distance, shortest segment]\r\n * @param {Shape} shape Shape of the one of supported types Point, Line, Circle, Segment, Arc, Polygon or Planar Set\r\n * @returns {number} distance from arc to shape\r\n * @returns {Segment} shortest segment between arc and shape (started at arc, ended at shape)\r\n\r\n */\r\n distanceTo(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n let [dist, shortest_segment] = Flatten.Distance.point2arc(shape, this);\r\n shortest_segment = shortest_segment.reverse();\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n let [dist, shortest_segment] = Flatten.Distance.arc2circle(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Line) {\r\n let [dist, shortest_segment] = Flatten.Distance.arc2line(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n let [dist, shortest_segment] = Flatten.Distance.segment2arc(shape, this);\r\n shortest_segment = shortest_segment.reverse();\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n let [dist, shortest_segment] = Flatten.Distance.arc2arc(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Polygon) {\r\n let [dist, shortest_segment] = Flatten.Distance.shape2polygon(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.PlanarSet) {\r\n let [dist, shortest_segment] = Flatten.Distance.shape2planarSet(this, shape);\r\n return [dist, shortest_segment];\r\n }\r\n }\r\n\r\n /**\r\n * Breaks arc in extreme point 0, pi/2, pi, 3*pi/2 and returns array of sub-arcs\r\n * @returns {Arcs[]}\r\n */\r\n breakToFunctional() {\r\n let func_arcs_array = [];\r\n let angles = [0, Math.PI / 2, 2 * Math.PI / 2, 3 * Math.PI / 2];\r\n let pts = [\r\n this.pc.translate(this.r, 0),\r\n this.pc.translate(0, this.r),\r\n this.pc.translate(-this.r, 0),\r\n this.pc.translate(0, -this.r)\r\n ];\r\n\r\n // If arc contains extreme point,\r\n // create test arc started at start point and ended at this extreme point\r\n let test_arcs = [];\r\n for (let i = 0; i < 4; i++) {\r\n if (pts[i].on(this)) {\r\n test_arcs.push(new Flatten.Arc(this.pc, this.r, this.startAngle, angles[i], this.counterClockwise));\r\n }\r\n }\r\n\r\n if (test_arcs.length == 0) { // arc does contain any extreme point\r\n func_arcs_array.push(this.clone());\r\n } else { // arc passes extreme point\r\n // sort these arcs by length\r\n test_arcs.sort((arc1, arc2) => arc1.length - arc2.length);\r\n\r\n for (let i = 0; i < test_arcs.length; i++) {\r\n let prev_arc = func_arcs_array.length > 0 ? func_arcs_array[func_arcs_array.length - 1] : undefined;\r\n let new_arc;\r\n if (prev_arc) {\r\n new_arc = new Flatten.Arc(this.pc, this.r, prev_arc.endAngle, test_arcs[i].endAngle, this.counterClockwise);\r\n } else {\r\n new_arc = new Flatten.Arc(this.pc, this.r, this.startAngle, test_arcs[i].endAngle, this.counterClockwise);\r\n }\r\n if (!Flatten.Utils.EQ_0(new_arc.length)) {\r\n func_arcs_array.push(new_arc.clone());\r\n }\r\n }\r\n\r\n // add last sub arc\r\n let prev_arc = func_arcs_array.length > 0 ? func_arcs_array[func_arcs_array.length - 1] : undefined;\r\n let new_arc;\r\n if (prev_arc) {\r\n new_arc = new Flatten.Arc(this.pc, this.r, prev_arc.endAngle, this.endAngle, this.counterClockwise);\r\n } else {\r\n new_arc = new Flatten.Arc(this.pc, this.r, this.startAngle, this.endAngle, this.counterClockwise);\r\n }\r\n // It could be 2*PI when occasionally start = 0 and end = 2*PI but this is not valid for breakToFunctional\r\n if (!Flatten.Utils.EQ_0(new_arc.length) && !Flatten.Utils.EQ(new_arc.sweep, 2*Math.PI)) {\r\n func_arcs_array.push(new_arc.clone());\r\n }\r\n }\r\n return func_arcs_array;\r\n }\r\n\r\n /**\r\n * Return tangent unit vector in the start point in the direction from start to end\r\n * @returns {Vector}\r\n */\r\n tangentInStart() {\r\n let vec = new Flatten.Vector(this.pc, this.start);\r\n let angle = this.counterClockwise ? Math.PI / 2. : -Math.PI / 2.;\r\n let tangent = vec.rotate(angle).normalize();\r\n return tangent;\r\n }\r\n\r\n /**\r\n * Return tangent unit vector in the end point in the direction from end to start\r\n * @returns {Vector}\r\n */\r\n tangentInEnd() {\r\n let vec = new Flatten.Vector(this.pc, this.end);\r\n let angle = this.counterClockwise ? -Math.PI / 2. : Math.PI / 2.;\r\n let tangent = vec.rotate(angle).normalize();\r\n return tangent;\r\n }\r\n\r\n /**\r\n * Returns new arc with swapped start and end angles and reversed direction\r\n * @returns {Arc}\r\n */\r\n reverse() {\r\n return new Flatten.Arc(this.pc, this.r, this.endAngle, this.startAngle, !this.counterClockwise);\r\n }\r\n\r\n /**\r\n * Returns new arc translated by vector vec\r\n * @param {Vector} vec\r\n * @returns {Segment}\r\n */\r\n translate(...args) {\r\n let arc = this.clone();\r\n arc.pc = this.pc.translate(...args);\r\n return arc;\r\n }\r\n\r\n /**\r\n * Return new segment rotated by given angle around given point\r\n * If point omitted, rotate around origin (0,0)\r\n * Positive value of angle defines rotation counter clockwise, negative - clockwise\r\n * @param {number} angle - rotation angle in radians\r\n * @param {Point} center - center point, default is (0,0)\r\n * @returns {Arc}\r\n */\r\n rotate(angle = 0, center = new Flatten.Point()) {\r\n let m = new Flatten.Matrix();\r\n m = m.translate(center.x, center.y).rotate(angle).translate(-center.x, -center.y);\r\n return this.transform(m);\r\n }\r\n\r\n /**\r\n * Return new arc scaled by scaleX, scaleY.\r\n * @param {number} scaleX - scale value by X\r\n * @param {number} scaleY - scale value by Y\r\n * @returns {Arc}\r\n */\r\n scale(scaleX = 1, scaleY = 1) {\r\n let m = new Flatten.Matrix();\r\n m = m.scale(scaleX, scaleY);\r\n return this.transform(m);\r\n }\r\n\r\n /**\r\n * Return new arc transformed using affine transformation matrix
\r\n * Note 1. Non-equal scaling by x and y (abs(matrix[0]) != abs(matrix[3])) produce illegal result because\r\n * it should create elliptic arc but this package does not support ellipses\r\n * Note 2. Mirror transformation (matrix[0] * matrix[3] < 0) change direction of the arc to the opposite\r\n * TODO: support non-equal scaling arc to ellipse or throw exception ?\r\n * @param {Matrix} matrix - affine transformation matrix\r\n * @returns {Arc}\r\n */\r\n transform(matrix = new Flatten.Matrix()) {\r\n let newStart = this.start.transform(matrix);\r\n let newEnd = this.end.transform(matrix);\r\n let newCenter = this.pc.transform(matrix);\r\n let newDirection = this.counterClockwise;\r\n if (matrix.a * matrix.d < 0) {\r\n newDirection = !newDirection;\r\n }\r\n let arc = Flatten.Arc.arcSE(newCenter, newStart, newEnd, newDirection);\r\n return arc;\r\n }\r\n\r\n static arcSE(center, start, end, counterClockwise) {\r\n let {vector} = Flatten;\r\n let startAngle = vector(center, start).slope;\r\n let endAngle = vector(center, end).slope;\r\n if (Flatten.Utils.EQ(startAngle, endAngle)) {\r\n endAngle += 2 * Math.PI;\r\n counterClockwise = true;\r\n }\r\n let r = vector(center, start).length;\r\n\r\n return new Flatten.Arc(center, r, startAngle, endAngle, counterClockwise);\r\n }\r\n\r\n definiteIntegral(ymin = 0) {\r\n let f_arcs = this.breakToFunctional();\r\n let area = f_arcs.reduce((acc, arc) => acc + arc.circularSegmentDefiniteIntegral(ymin), 0.0);\r\n return area;\r\n }\r\n\r\n circularSegmentDefiniteIntegral(ymin) {\r\n let line = new Flatten.Line(this.start, this.end);\r\n let onLeftSide = this.pc.leftTo(line);\r\n let segment = new Flatten.Segment(this.start, this.end);\r\n let areaTrapez = segment.definiteIntegral(ymin);\r\n let areaCircularSegment = this.circularSegmentArea();\r\n let area = onLeftSide ? areaTrapez - areaCircularSegment : areaTrapez + areaCircularSegment;\r\n return area;\r\n }\r\n\r\n circularSegmentArea() {\r\n return (0.5 * this.r * this.r * (this.sweep - Math.sin(this.sweep)))\r\n }\r\n\r\n /**\r\n * Sort given array of points from arc start to end, assuming all points lay on the arc\r\n * @param {Point[]} array of points\r\n * @returns {Point[]} new array sorted\r\n */\r\n sortPoints(pts) {\r\n let {vector} = Flatten;\r\n return pts.slice().sort( (pt1, pt2) => {\r\n let slope1 = vector(this.pc, pt1).slope;\r\n let slope2 = vector(this.pc, pt2).slope;\r\n if (slope1 < slope2) {\r\n return -1;\r\n }\r\n if (slope1 > slope2) {\r\n return 1;\r\n }\r\n return 0;\r\n })\r\n }\r\n\r\n /**\r\n * This method returns an object that defines how data will be\r\n * serialized when called JSON.stringify() method\r\n * @returns {Object}\r\n */\r\n toJSON() {\r\n return Object.assign({}, this, {name: \"arc\"});\r\n }\r\n\r\n /**\r\n * Return string to draw arc in svg\r\n * @param {Object} attrs - an object with attributes of svg path element,\r\n * like \"stroke\", \"strokeWidth\", \"fill\"
\r\n * Defaults are stroke:\"black\", strokeWidth:\"1\", fill:\"none\"\r\n * @returns {string}\r\n */\r\n svg(attrs = {}) {\r\n let largeArcFlag = this.sweep <= Math.PI ? \"0\" : \"1\";\r\n let sweepFlag = this.counterClockwise ? \"1\" : \"0\";\r\n let {stroke, strokeWidth, fill, id, className} = attrs;\r\n // let rest_str = Object.keys(rest).reduce( (acc, key) => acc += ` ${key}=\"${rest[key]}\"`, \"\");\r\n let id_str = (id && id.length > 0) ? `id=\"${id}\"` : \"\";\r\n let class_str = (className && className.length > 0) ? `class=\"${className}\"` : \"\";\r\n\r\n if (Flatten.Utils.EQ(this.sweep, 2 * Math.PI)) {\r\n let circle = new Flatten.Circle(this.pc, this.r);\r\n return circle.svg(attrs);\r\n } else {\r\n return `\\n`\r\n }\r\n }\r\n\r\n}\r\nFlatten.Arc = Arc;\r\n/**\r\n * Function to create arc equivalent to \"new\" constructor\r\n * @param args\r\n */\r\nconst arc = (...args) => new Flatten.Arc(...args);\r\nFlatten.arc = arc;\r\n\r\n/**\r\n * Created by Alex Bol on 3/7/2017.\r\n */\r\n\r\n/**\r\n * Class Box represent bounding box of the shape\r\n * @type {Box}\r\n */\r\nclass Box {\r\n /**\r\n *\r\n * @param {number} xmin - minimal x coordinate\r\n * @param {number} ymin - minimal y coordinate\r\n * @param {number} xmax - maximal x coordinate\r\n * @param {number} ymax - maximal y coordinate\r\n */\r\n constructor(xmin = undefined, ymin = undefined, xmax = undefined, ymax = undefined) {\r\n /**\r\n * Minimal x coordinate\r\n * @type {number}\r\n */\r\n this.xmin = xmin;\r\n /**\r\n * Minimal y coordinate\r\n * @type {number}\r\n */\r\n this.ymin = ymin;\r\n /**\r\n * Maximal x coordinate\r\n * @type {number}\r\n */\r\n this.xmax = xmax;\r\n /**\r\n * Maximal y coordinate\r\n * @type {number}\r\n */\r\n this.ymax = ymax;\r\n }\r\n\r\n /**\r\n * Return new cloned instance of box\r\n * @returns {Box}\r\n */\r\n clone() {\r\n return new Box(this.xmin, this.ymin, this.xmax, this.ymax);\r\n }\r\n\r\n /**\r\n * Property low need for interval tree interface\r\n * @returns {Point}\r\n */\r\n get low() {\r\n return new Flatten.Point(this.xmin, this.ymin);\r\n }\r\n\r\n /**\r\n * Property high need for interval tree interface\r\n * @returns {Point}\r\n */\r\n get high() {\r\n return new Flatten.Point(this.xmax, this.ymax);\r\n }\r\n\r\n /**\r\n * Property max returns the box itself !\r\n * @returns {Box}\r\n */\r\n get max() {\r\n return this.clone();\r\n }\r\n \r\n /**\r\n * Return center of the box\r\n * @returns {Point}\r\n */\r\n get center() {\r\n return new Flatten.Point((this.xmin + this.xmax) / 2, (this.ymin + this.ymax) / 2);\r\n }\r\n\r\n /**\r\n * Return the width of the box\r\n * @returns {number}\r\n */\r\n get width() {\r\n return Math.abs(this.xmax - this.xmin);\r\n }\r\n\r\n /**\r\n * Return the height of the box\r\n * @returns {number}\r\n */\r\n get height() {\r\n return Math.abs(this.ymax - this.ymin);\r\n }\r\n \r\n /**\r\n * Return property box like all other shapes\r\n * @returns {Box}\r\n */\r\n get box() {\r\n return this.clone();\r\n }\r\n\r\n /**\r\n * Returns true if not intersected with other box\r\n * @param {Box} other_box - other box to test\r\n * @returns {boolean}\r\n */\r\n not_intersect(other_box) {\r\n return (\r\n this.xmax < other_box.xmin ||\r\n this.xmin > other_box.xmax ||\r\n this.ymax < other_box.ymin ||\r\n this.ymin > other_box.ymax\r\n );\r\n }\r\n\r\n /**\r\n * Returns true if intersected with other box\r\n * @param {Box} other_box - Query box\r\n * @returns {boolean}\r\n */\r\n intersect(other_box) {\r\n return !this.not_intersect(other_box);\r\n }\r\n\r\n /**\r\n * Returns new box merged with other box\r\n * @param {Box} other_box - Other box to merge with\r\n * @returns {Box}\r\n */\r\n merge(other_box) {\r\n return new Box(\r\n this.xmin === undefined ? other_box.xmin : Math.min(this.xmin, other_box.xmin),\r\n this.ymin === undefined ? other_box.ymin : Math.min(this.ymin, other_box.ymin),\r\n this.xmax === undefined ? other_box.xmax : Math.max(this.xmax, other_box.xmax),\r\n this.ymax === undefined ? other_box.ymax : Math.max(this.ymax, other_box.ymax)\r\n );\r\n }\r\n\r\n /**\r\n * Defines predicate \"less than\" between two boxes. Need for interval index\r\n * @param {Box} other_box - other box\r\n * @returns {boolean} - true if this box less than other box, false otherwise\r\n */\r\n less_than(other_box) {\r\n if (this.low.lessThan(other_box.low))\r\n return true;\r\n if (this.low.equalTo(other_box.low) && this.high.lessThan(other_box.high))\r\n return true;\r\n return false;\r\n }\r\n\r\n /**\r\n * Returns true if this box is equal to other box, false otherwise\r\n * @param {Box} other_box - query box\r\n * @returns {boolean}\r\n */\r\n equal_to(other_box) {\r\n return (this.low.equalTo(other_box.low) && this.high.equalTo(other_box.high));\r\n }\r\n\r\n output() {\r\n return this.clone();\r\n }\r\n\r\n static comparable_max(box1, box2) {\r\n // return pt1.lessThan(pt2) ? pt2.clone() : pt1.clone();\r\n return box1.merge(box2);\r\n }\r\n\r\n static comparable_less_than(pt1, pt2) {\r\n return pt1.lessThan(pt2);\r\n }\r\n\r\n /**\r\n * Set new values to the box object\r\n * @param {number} xmin - miminal x coordinate\r\n * @param {number} ymin - minimal y coordinate\r\n * @param {number} xmax - maximal x coordinate\r\n * @param {number} ymax - maximal y coordinate\r\n */\r\n set(xmin, ymin, xmax, ymax) {\r\n this.xmin = xmin;\r\n this.ymin = ymin;\r\n this.xmax = xmax;\r\n this.ymax = ymax;\r\n }\r\n\r\n /**\r\n * Transform box into array of points from low left corner in counter clockwise\r\n * @returns {Point[]}\r\n */\r\n toPoints() {\r\n return [\r\n new Flatten.Point(this.xmin, this.ymin),\r\n new Flatten.Point(this.xmax, this.ymin),\r\n new Flatten.Point(this.xmax, this.ymax),\r\n new Flatten.Point(this.xmin, this.ymax)\r\n ];\r\n }\r\n\r\n /**\r\n * Transform box into array of segments from low left corner in counter clockwise\r\n * @returns {Segment[]}\r\n */\r\n toSegments() {\r\n let pts = this.toPoints();\r\n return [\r\n new Flatten.Segment(pts[0], pts[1]),\r\n new Flatten.Segment(pts[1], pts[2]),\r\n new Flatten.Segment(pts[2], pts[3]),\r\n new Flatten.Segment(pts[3], pts[0])\r\n ];\r\n }\r\n\r\n /**\r\n * Return string to draw circle in svg\r\n * @param {Object} attrs - an object with attributes of svg rectangle element,\r\n * like \"stroke\", \"strokeWidth\", \"fill\"
\r\n * Defaults are stroke:\"black\", strokeWidth:\"1\", fill:\"none\"\r\n * @returns {string}\r\n */\r\n svg(attrs = {}) {\r\n let {stroke, strokeWidth, fill, id, className} = attrs;\r\n // let rest_str = Object.keys(rest).reduce( (acc, key) => acc += ` ${key}=\"${rest[key]}\"`, \"\");\r\n let id_str = (id && id.length > 0) ? `id=\"${id}\"` : \"\";\r\n let class_str = (className && className.length > 0) ? `class=\"${className}\"` : \"\";\r\n let width = this.xmax - this.xmin;\r\n let height = this.ymax - this.ymin;\r\n\r\n return `\\n`;\r\n };\r\n}\r\nFlatten.Box = Box;\r\n/**\r\n * Shortcut to create new box\r\n * @param args\r\n * @returns {Box}\r\n */\r\nconst box = (...args) => new Flatten.Box(...args);\r\nFlatten.box = box;\r\n\r\n/**\r\n * Created by Alex Bol on 3/17/2017.\r\n */\r\n\r\n/**\r\n * Class representing an edge of polygon. Edge shape may be Segment or Arc.\r\n * Each edge contains references to the next and previous edges in the face of the polygon.\r\n *\r\n * @type {Edge}\r\n */\r\nclass Edge {\r\n /**\r\n * Construct new instance of edge\r\n * @param {Shape} shape Shape of type Segment or Arc\r\n */\r\n constructor(shape) {\r\n /**\r\n * Shape of the edge: Segment or Arc\r\n * @type {Segment|Arc}\r\n */\r\n this.shape = shape;\r\n /**\r\n * Pointer to the next edge in the face\r\n * @type {Edge}\r\n */\r\n this.next = undefined;\r\n /**\r\n * Pointer to the previous edge in the face\r\n * @type {Edge}\r\n */\r\n this.prev = undefined;\r\n /**\r\n * Pointer to the face containing this edge\r\n * @type {Face}\r\n */\r\n this.face = undefined;\r\n /**\r\n * \"Arc distance\" from the face start\r\n * @type {number}\r\n */\r\n this.arc_length = 0;\r\n /**\r\n * Start inclusion flag (inside/outside/boundary)\r\n * @type {*}\r\n */\r\n this.bvStart = undefined;\r\n /**\r\n * End inclusion flag (inside/outside/boundary)\r\n * @type {*}\r\n */\r\n this.bvEnd = undefined;\r\n /**\r\n * Edge inclusion flag (Flatten.INSIDE, Flatten.OUTSIDE, Flatten.BOUNDARY)\r\n * @type {*}\r\n */\r\n this.bv = undefined;\r\n /**\r\n * Overlap flag for boundary edge (Flatten.OVERLAP_SAME/Flatten.OVERLAP_OPPOSITE)\r\n * @type {*}\r\n */\r\n this.overlap = undefined;\r\n }\r\n\r\n /**\r\n * Get edge start point\r\n */\r\n get start() {\r\n return this.shape.start;\r\n }\r\n\r\n /**\r\n * Get edge end point\r\n */\r\n get end() {\r\n return this.shape.end;\r\n }\r\n\r\n /**\r\n * Get edge length\r\n */\r\n get length() {\r\n return this.shape.length;\r\n }\r\n\r\n /**\r\n * Get bounding box of the edge\r\n * @returns {Box}\r\n */\r\n get box() {\r\n return this.shape.box;\r\n }\r\n\r\n isSegment() {\r\n return this.shape instanceof Flatten.Segment;\r\n }\r\n\r\n isArc() {\r\n return this.shape instanceof Flatten.Arc;\r\n }\r\n\r\n /**\r\n * Get middle point of the edge\r\n * @returns {Point}\r\n */\r\n middle() {\r\n return this.shape.middle();\r\n }\r\n\r\n /**\r\n * Get point at given length\r\n * @param {number} length - The length along the edge\r\n * @returns {Point}\r\n */\r\n pointAtLength(length) {\r\n return this.shape.pointAtLength(length);\r\n }\r\n\r\n /**\r\n * Returns true if point belongs to the edge, false otherwise\r\n * @param {Point} pt - test point\r\n */\r\n contains(pt) {\r\n return this.shape.contains(pt);\r\n }\r\n\r\n /**\r\n * Set inclusion flag of the edge with respect to another polygon\r\n * Inclusion flag is one of Flatten.INSIDE, Flatten.OUTSIDE, Flatten.BOUNDARY\r\n * @param polygon\r\n */\r\n setInclusion(polygon) {\r\n if (this.bv !== undefined) return this.bv;\r\n\r\n if (this.shape instanceof Flatten.Line || this.shape instanceof Flatten.Ray) {\r\n this.bv = Flatten.OUTSIDE;\r\n return this.bv;\r\n }\r\n\r\n if (this.bvStart === undefined) {\r\n this.bvStart = ray_shoot(polygon, this.start);\r\n }\r\n if (this.bvEnd === undefined) {\r\n this.bvEnd = ray_shoot(polygon, this.end);\r\n }\r\n /* At least one end outside - the whole edge outside */\r\n if (this.bvStart === Flatten.OUTSIDE || this.bvEnd == Flatten.OUTSIDE) {\r\n this.bv = Flatten.OUTSIDE;\r\n }\r\n /* At least one end inside - the whole edge inside */\r\n else if (this.bvStart === Flatten.INSIDE || this.bvEnd == Flatten.INSIDE) {\r\n this.bv = Flatten.INSIDE;\r\n }\r\n /* Both are boundary - check the middle point */\r\n else {\r\n let bvMiddle = ray_shoot(polygon, this.middle());\r\n // let boundary = this.middle().distanceTo(polygon)[0] < 10*Flatten.DP_TOL;\r\n // let bvMiddle = boundary ? Flatten.BOUNDARY : ray_shoot(polygon, this.middle());\r\n this.bv = bvMiddle;\r\n }\r\n return this.bv;\r\n }\r\n\r\n /**\r\n * Set overlapping between two coincident boundary edges\r\n * Overlapping flag is one of Flatten.OVERLAP_SAME or Flatten.OVERLAP_OPPOSITE\r\n * @param edge\r\n */\r\n setOverlap(edge) {\r\n let flag = undefined;\r\n let shape1 = this.shape;\r\n let shape2 = edge.shape;\r\n\r\n if (shape1 instanceof Flatten.Segment && shape2 instanceof Flatten.Segment) {\r\n if (shape1.start.equalTo(shape2.start) && shape1.end.equalTo(shape2.end)) {\r\n flag = Flatten.OVERLAP_SAME;\r\n } else if (shape1.start.equalTo(shape2.end) && shape1.end.equalTo(shape2.start)) {\r\n flag = Flatten.OVERLAP_OPPOSITE;\r\n }\r\n } else if (shape1 instanceof Flatten.Arc && shape2 instanceof Flatten.Arc) {\r\n if (shape1.start.equalTo(shape2.start) && shape1.end.equalTo(shape2.end) && /*shape1.counterClockwise === shape2.counterClockwise &&*/\r\n shape1.middle().equalTo(shape2.middle())) {\r\n flag = Flatten.OVERLAP_SAME;\r\n } else if (shape1.start.equalTo(shape2.end) && shape1.end.equalTo(shape2.start) && /*shape1.counterClockwise !== shape2.counterClockwise &&*/\r\n shape1.middle().equalTo(shape2.middle())) {\r\n flag = Flatten.OVERLAP_OPPOSITE;\r\n }\r\n } else if (shape1 instanceof Flatten.Segment && shape2 instanceof Flatten.Arc ||\r\n shape1 instanceof Flatten.Arc && shape2 instanceof Flatten.Segment) {\r\n if (shape1.start.equalTo(shape2.start) && shape1.end.equalTo(shape2.end) && shape1.middle().equalTo(shape2.middle())) {\r\n flag = Flatten.OVERLAP_SAME;\r\n } else if (shape1.start.equalTo(shape2.end) && shape1.end.equalTo(shape2.start) && shape1.middle().equalTo(shape2.middle())) {\r\n flag = Flatten.OVERLAP_OPPOSITE;\r\n }\r\n }\r\n\r\n /* Do not update overlap flag if already set on previous chain */\r\n if (this.overlap === undefined) this.overlap = flag;\r\n if (edge.overlap === undefined) edge.overlap = flag;\r\n }\r\n\r\n svg() {\r\n if (this.shape instanceof Flatten.Segment) {\r\n return ` L${this.shape.end.x},${this.shape.end.y}`;\r\n } else if (this.shape instanceof Flatten.Arc) {\r\n let arc = this.shape;\r\n let largeArcFlag;\r\n let sweepFlag = arc.counterClockwise ? \"1\" : \"0\";\r\n\r\n // Draw full circe arc as special case: split it into two half-circles\r\n if (Flatten.Utils.EQ(arc.sweep, 2 * Math.PI)) {\r\n let sign = arc.counterClockwise ? 1 : -1;\r\n let halfArc1 = new Flatten.Arc(arc.pc, arc.r, arc.startAngle, arc.startAngle + sign * Math.PI, arc.counterClockwise);\r\n let halfArc2 = new Flatten.Arc(arc.pc, arc.r, arc.startAngle + sign * Math.PI, arc.endAngle, arc.counterClockwise);\r\n\r\n largeArcFlag = \"0\";\r\n\r\n return ` A${halfArc1.r},${halfArc1.r} 0 ${largeArcFlag},${sweepFlag} ${halfArc1.end.x},${halfArc1.end.y}\r\n A${halfArc2.r},${halfArc2.r} 0 ${largeArcFlag},${sweepFlag} ${halfArc2.end.x},${halfArc2.end.y}`\r\n } else {\r\n largeArcFlag = arc.sweep <= Math.PI ? \"0\" : \"1\";\r\n\r\n return ` A${arc.r},${arc.r} 0 ${largeArcFlag},${sweepFlag} ${arc.end.x},${arc.end.y}`;\r\n }\r\n }\r\n }\r\n\r\n toJSON() {\r\n return this.shape.toJSON();\r\n }\r\n}\r\nFlatten.Edge = Edge;\r\n\r\n/**\r\n * Class implements circular bidirectional linked list
\r\n * LinkedListElement - object of any type that has properties next and prev.\r\n */\r\nclass CircularLinkedList extends LinkedList {\r\n constructor(first, last) {\r\n super(first, last);\r\n this.setCircularLinks();\r\n }\r\n\r\n setCircularLinks() {\r\n if (this.isEmpty()) return;\r\n this.last.next = this.first;\r\n this.first.prev = this.last;\r\n }\r\n\r\n [Symbol.iterator]() {\r\n let element = undefined;\r\n return {\r\n next: () => {\r\n let value = element ? element : this.first;\r\n let done = this.first ? (element ? element === this.first : false) : true;\r\n element = value ? value.next : undefined;\r\n return {value: value, done: done};\r\n }\r\n };\r\n };\r\n\r\n /**\r\n * Append new element to the end of the list\r\n * @param {LinkedListElement} element - new element to be appended\r\n * @returns {CircularLinkedList}\r\n */\r\n append(element) {\r\n super.append(element);\r\n this.setCircularLinks();\r\n return this;\r\n }\r\n\r\n /**\r\n * Insert new element to the list after elementBefore\r\n * @param {LinkedListElement} newElement - new element to be inserted\r\n * @param {LinkedListElement} elementBefore - element in the list to insert after it\r\n * @returns {CircularLinkedList}\r\n */\r\n insert(newElement, elementBefore) {\r\n super.insert(newElement, elementBefore);\r\n this.setCircularLinks();\r\n return this;\r\n }\r\n\r\n /**\r\n * Remove element from the list\r\n * @param {LinkedListElement} element - element to be removed from the list\r\n * @returns {CircularLinkedList}\r\n */\r\n remove(element) {\r\n super.remove(element);\r\n // this.setCircularLinks();\r\n return this;\r\n }\r\n}\r\n\r\n/**\r\n * Created by Alex Bol on 3/17/2017.\r\n */\r\n\r\n/**\r\n * Class representing a face (closed loop) in a [polygon]{@link Flatten.Polygon} object.\r\n * Face is a circular bidirectional linked list of [edges]{@link Flatten.Edge}.\r\n * Face object cannot be instantiated with a constructor.\r\n * Instead, use [polygon.addFace()]{@link Flatten.Polygon#addFace} method.\r\n *
\r\n * Note, that face only set entry point to the linked list of edges but does not contain edges by itself.\r\n * Container of edges is a property of the polygon object.
\r\n *\r\n * @example\r\n * // Face implements \"next\" iterator which enables to iterate edges in for loop:\r\n * for (let edge of face) {\r\n * console.log(edge.shape.length) // do something\r\n * }\r\n *\r\n * // Instead, it is possible to iterate edges as linked list, starting from face.first:\r\n * let edge = face.first;\r\n * do {\r\n * console.log(edge.shape.length); // do something\r\n * edge = edge.next;\r\n * } while (edge != face.first)\r\n */\r\nclass Face extends CircularLinkedList {\r\n constructor(polygon, ...args) {\r\n super(); // construct empty list of edges\r\n /**\r\n * Reference to the first edge in face\r\n */\r\n // this.first;\r\n /**\r\n * Reference to the last edge in face\r\n */\r\n // this.last;\r\n\r\n this._box = undefined; // new Box();\r\n this._orientation = undefined;\r\n\r\n if (args.length == 0) {\r\n return;\r\n }\r\n\r\n /* If passed an array it supposed to be:\r\n 1) array of shapes that performs close loop or\r\n 2) array of points that performs set of vertices\r\n */\r\n if (args.length == 1) {\r\n if (args[0] instanceof Array) {\r\n // let argsArray = args[0];\r\n let shapes = args[0]; // argsArray[0];\r\n if (shapes.length == 0)\r\n return;\r\n\r\n /* array of Flatten.Points */\r\n if (shapes.every((shape) => {return shape instanceof Flatten.Point})) {\r\n let segments = Face.points2segments(shapes);\r\n this.shapes2face(polygon.edges, segments);\r\n }\r\n /* array of points as pairs of numbers */\r\n else if (shapes.every((shape) => {return shape instanceof Array && shape.length === 2})) {\r\n let points = shapes.map((shape) => new Flatten.Point(shape[0],shape[1]));\r\n let segments = Face.points2segments(points);\r\n this.shapes2face(polygon.edges, segments);\r\n }\r\n /* array of segments ot arcs */\r\n else if (shapes.every((shape) => {\r\n return (shape instanceof Flatten.Segment || shape instanceof Flatten.Arc)\r\n })) {\r\n this.shapes2face(polygon.edges, shapes);\r\n }\r\n // this is from JSON.parse object\r\n else if (shapes.every((shape) => {\r\n return (shape.name === \"segment\" || shape.name === \"arc\")\r\n })) {\r\n let flattenShapes = [];\r\n for (let shape of shapes) {\r\n let flattenShape;\r\n if (shape.name === \"segment\") {\r\n flattenShape = new Flatten.Segment(shape);\r\n } else {\r\n flattenShape = new Flatten.Arc(shape);\r\n }\r\n flattenShapes.push(flattenShape);\r\n }\r\n this.shapes2face(polygon.edges, flattenShapes);\r\n }\r\n }\r\n /* Create new face and copy edges into polygon.edges set */\r\n else if (args[0] instanceof Face) {\r\n let face = args[0];\r\n this.first = face.first;\r\n this.last = face.last;\r\n for (let edge of face) {\r\n polygon.edges.add(edge);\r\n }\r\n }\r\n /* Instantiate face from a circle in CCW orientation */\r\n else if (args[0] instanceof Flatten.Circle) {\r\n this.shapes2face(polygon.edges, [args[0].toArc(Flatten.CCW)]);\r\n }\r\n /* Instantiate face from a box in CCW orientation */\r\n else if (args[0] instanceof Flatten.Box) {\r\n let box = args[0];\r\n this.shapes2face(polygon.edges, [\r\n new Flatten.Segment(new Flatten.Point(box.xmin, box.ymin), new Flatten.Point(box.xmax, box.ymin)),\r\n new Flatten.Segment(new Flatten.Point(box.xmax, box.ymin), new Flatten.Point(box.xmax, box.ymax)),\r\n new Flatten.Segment(new Flatten.Point(box.xmax, box.ymax), new Flatten.Point(box.xmin, box.ymax)),\r\n new Flatten.Segment(new Flatten.Point(box.xmin, box.ymax), new Flatten.Point(box.xmin, box.ymin))\r\n ]);\r\n }\r\n }\r\n /* If passed two edges, consider them as start and end of the face loop */\r\n /* THIS METHOD WILL BE USED BY BOOLEAN OPERATIONS */\r\n /* Assume that edges already copied to polygon.edges set in the clip algorithm !!! */\r\n if (args.length == 2 && args[0] instanceof Flatten.Edge && args[1] instanceof Flatten.Edge) {\r\n this.first = args[0]; // first edge in face or undefined\r\n this.last = args[1]; // last edge in face or undefined\r\n this.last.next = this.first;\r\n this.first.prev = this.last;\r\n\r\n // set arc length\r\n this.setArcLength();\r\n\r\n // this.box = this.getBox();\r\n // this.orientation = this.getOrientation(); // face direction cw or ccw\r\n }\r\n }\r\n\r\n /**\r\n * Return array of edges from first to last\r\n * @returns {Array}\r\n */\r\n get edges() {\r\n return this.toArray();\r\n }\r\n\r\n /**\r\n * Return array of shapes which comprise face\r\n * @returns {Array}\r\n */\r\n get shapes() {\r\n return this.edges.map(edge => edge.shape.clone());\r\n }\r\n\r\n /**\r\n * Return bounding box of the face\r\n * @returns {Box}\r\n */\r\n get box() {\r\n if (this._box === undefined) {\r\n let box = new Flatten.Box();\r\n for (let edge of this) {\r\n box = box.merge(edge.box);\r\n }\r\n this._box = box;\r\n }\r\n return this._box;\r\n }\r\n\r\n /**\r\n * Get all edges length\r\n * @returns {number}\r\n */\r\n get perimeter() {\r\n return this.last.arc_length + this.last.length\r\n }\r\n\r\n /**\r\n * Get point on face boundary at given length\r\n * @param {number} length - The length along the face boundary\r\n * @returns {Point}\r\n */\r\n pointAtLength(length) {\r\n if (length > this.perimeter || length < 0) return null;\r\n let point = null;\r\n for (let edge of this) {\r\n if (length >= edge.arc_length &&\r\n (edge === this.last || length < edge.next.arc_length)) {\r\n point = edge.pointAtLength(length - edge.arc_length);\r\n break;\r\n }\r\n }\r\n return point;\r\n }\r\n\r\n static points2segments(points) {\r\n let segments = [];\r\n for (let i = 0; i < points.length; i++) {\r\n // skip zero length segment\r\n if (points[i].equalTo(points[(i + 1) % points.length]))\r\n continue;\r\n segments.push(new Flatten.Segment(points[i], points[(i + 1) % points.length]));\r\n }\r\n return segments;\r\n }\r\n\r\n shapes2face(edges, shapes) {\r\n for (let shape of shapes) {\r\n let edge = new Flatten.Edge(shape);\r\n this.append(edge);\r\n // this.box = this.box.merge(shape.box);\r\n edges.add(edge);\r\n }\r\n // this.orientation = this.getOrientation(); // face direction cw or ccw\r\n }\r\n\r\n /**\r\n * Append edge after the last edge of the face (and before the first edge).
\r\n * @param {Edge} edge - Edge to be appended to the linked list\r\n * @returns {Face}\r\n */\r\n append(edge) {\r\n super.append(edge);\r\n // set arc length\r\n this.setOneEdgeArcLength(edge);\r\n edge.face = this;\r\n // edges.add(edge); // Add new edges into edges container\r\n return this;\r\n }\r\n\r\n /**\r\n * Insert edge newEdge into the linked list after the edge edgeBefore
\r\n * @param {Edge} newEdge - Edge to be inserted into linked list\r\n * @param {Edge} edgeBefore - Edge to insert newEdge after it\r\n * @returns {Face}\r\n */\r\n insert(newEdge, edgeBefore) {\r\n super.insert(newEdge, edgeBefore);\r\n // set arc length\r\n this.setOneEdgeArcLength(newEdge);\r\n newEdge.face = this;\r\n return this;\r\n }\r\n\r\n /**\r\n * Remove the given edge from the linked list of the face
\r\n * @param {Edge} edge - Edge to be removed\r\n * @returns {Face}\r\n */\r\n remove(edge) {\r\n super.remove(edge);\r\n // Recalculate arc length\r\n this.setArcLength();\r\n return this;\r\n }\r\n\r\n /**\r\n * Reverse orientation of the face: first edge become last and vice a verse,\r\n * all edges starts and ends swapped, direction of arcs inverted. If face was oriented\r\n * clockwise, it becomes counter clockwise and vice versa\r\n */\r\n reverse() {\r\n // collect edges in revert order with reverted shapes\r\n let edges = [];\r\n let edge_tmp = this.last;\r\n do {\r\n // reverse shape\r\n edge_tmp.shape = edge_tmp.shape.reverse();\r\n edges.push(edge_tmp);\r\n edge_tmp = edge_tmp.prev;\r\n } while (edge_tmp !== this.last);\r\n\r\n // restore linked list\r\n this.first = undefined;\r\n this.last = undefined;\r\n for (let edge of edges) {\r\n if (this.first === undefined) {\r\n edge.prev = edge;\r\n edge.next = edge;\r\n this.first = edge;\r\n this.last = edge;\r\n } else {\r\n // append to end\r\n edge.prev = this.last;\r\n this.last.next = edge;\r\n\r\n // update edge to be last\r\n this.last = edge;\r\n\r\n // restore circular links\r\n this.last.next = this.first;\r\n this.first.prev = this.last;\r\n\r\n }\r\n // set arc length\r\n this.setOneEdgeArcLength(edge);\r\n }\r\n\r\n // Recalculate orientation, if set\r\n if (this._orientation !== undefined) {\r\n this._orientation = undefined;\r\n this._orientation = this.orientation();\r\n }\r\n }\r\n\r\n\r\n /**\r\n * Set arc_length property for each of the edges in the face.\r\n * Arc_length of the edge it the arc length from the first edge of the face\r\n */\r\n setArcLength() {\r\n for (let edge of this) {\r\n this.setOneEdgeArcLength(edge);\r\n edge.face = this;\r\n }\r\n }\r\n\r\n setOneEdgeArcLength(edge) {\r\n if (edge === this.first) {\r\n edge.arc_length = 0.0;\r\n } else {\r\n edge.arc_length = edge.prev.arc_length + edge.prev.length;\r\n }\r\n }\r\n\r\n /**\r\n * Returns the absolute value of the area of the face\r\n * @returns {number}\r\n */\r\n area() {\r\n return Math.abs(this.signedArea());\r\n }\r\n\r\n /**\r\n * Returns signed area of the simple face.\r\n * Face is simple if it has no self intersections that change its orientation.\r\n * Then the area will be positive if the orientation of the face is clockwise,\r\n * and negative if orientation is counterclockwise.\r\n * It may be zero if polygon is degenerated.\r\n * @returns {number}\r\n */\r\n signedArea() {\r\n let sArea = 0;\r\n let ymin = this.box.ymin;\r\n for (let edge of this) {\r\n sArea += edge.shape.definiteIntegral(ymin);\r\n }\r\n return sArea;\r\n }\r\n\r\n /**\r\n * Return face orientation: one of Flatten.ORIENTATION.CCW, Flatten.ORIENTATION.CW, Flatten.ORIENTATION.NOT_ORIENTABLE
\r\n * According to Green theorem the area of a closed curve may be calculated as double integral,\r\n * and the sign of the integral will be defined by the direction of the curve.\r\n * When the integral (\"signed area\") will be negative, direction is counter clockwise,\r\n * when positive - clockwise and when it is zero, polygon is not orientable.\r\n * See {@link https://mathinsight.org/greens_theorem_find_area}\r\n * @returns {number}\r\n */\r\n orientation() {\r\n if (this._orientation === undefined) {\r\n let area = this.signedArea();\r\n if (Flatten.Utils.EQ_0(area)) {\r\n this._orientation = Flatten.ORIENTATION.NOT_ORIENTABLE;\r\n } else if (Flatten.Utils.LT(area, 0)) {\r\n this._orientation = Flatten.ORIENTATION.CCW;\r\n } else {\r\n this._orientation = Flatten.ORIENTATION.CW;\r\n }\r\n }\r\n return this._orientation;\r\n }\r\n\r\n /**\r\n * Returns true if face of the polygon is simple (no self-intersection points found)\r\n * NOTE: this method is incomplete because it does not exclude touching points.\r\n * Self intersection test should check if polygon change orientation in the test point.\r\n * @param {Edges} edges - reference to polygon.edges to provide search index\r\n * @returns {boolean}\r\n */\r\n isSimple(edges) {\r\n let ip = Face.getSelfIntersections(this, edges, true);\r\n return ip.length == 0;\r\n }\r\n\r\n static getSelfIntersections(face, edges, exitOnFirst = false) {\r\n let int_points = [];\r\n\r\n // calculate intersections\r\n for (let edge1 of face) {\r\n\r\n // request edges of polygon in the box of edge1\r\n let resp = edges.search(edge1.box);\r\n\r\n // for each edge2 in response\r\n for (let edge2 of resp) {\r\n\r\n // Skip itself\r\n if (edge1 === edge2)\r\n continue;\r\n\r\n // Skip is edge2 belongs to another face\r\n if (edge2.face !== face)\r\n continue;\r\n\r\n // Skip next and previous edge if both are segment (if one of them arc - calc intersection)\r\n if (edge1.shape instanceof Flatten.Segment && edge2.shape instanceof Flatten.Segment &&\r\n (edge1.next === edge2 || edge1.prev === edge2))\r\n continue;\r\n\r\n // calculate intersections between edge1 and edge2\r\n let ip = edge1.shape.intersect(edge2.shape);\r\n\r\n // for each intersection point\r\n for (let pt of ip) {\r\n\r\n // skip start-end connections\r\n if (pt.equalTo(edge1.start) && pt.equalTo(edge2.end) && edge2 === edge1.prev)\r\n continue;\r\n if (pt.equalTo(edge1.end) && pt.equalTo(edge2.start) && edge2 === edge1.next)\r\n continue;\r\n\r\n int_points.push(pt);\r\n\r\n if (exitOnFirst)\r\n break;\r\n }\r\n\r\n if (int_points.length > 0 && exitOnFirst)\r\n break;\r\n }\r\n\r\n if (int_points.length > 0 && exitOnFirst)\r\n break;\r\n\r\n }\r\n return int_points;\r\n }\r\n\r\n /**\r\n * Returns edge which contains given point\r\n * @param {Point} pt - test point\r\n * @returns {Edge}\r\n */\r\n findEdgeByPoint(pt) {\r\n let edgeFound;\r\n for (let edge of this) {\r\n if (edge.shape.contains(pt)) {\r\n edgeFound = edge;\r\n break;\r\n }\r\n }\r\n return edgeFound;\r\n }\r\n\r\n /**\r\n * Returns new polygon created from one face\r\n * @returns {Polygon}\r\n */\r\n toPolygon() {\r\n return new Flatten.Polygon(this.shapes);\r\n }\r\n\r\n toJSON() {\r\n return this.edges.map(edge => edge.toJSON());\r\n }\r\n\r\n /**\r\n * Returns string to be assigned to \"d\" attribute inside defined \"path\"\r\n * @returns {string}\r\n */\r\n svg() {\r\n let svgStr = `\\nM${this.first.start.x},${this.first.start.y}`;\r\n for (let edge of this) {\r\n svgStr += edge.svg();\r\n }\r\n svgStr += ` z`;\r\n return svgStr;\r\n }\r\n\r\n}\r\nFlatten.Face = Face;\r\n\r\n/**\r\n * Class representing a ray (a half-infinite line).\r\n * @type {Ray}\r\n */\r\nclass Ray {\r\n /**\r\n * Ray may be constructed by setting an origin point and a normal vector, so that any point x\r\n * on a ray fit an equation:
\r\n * (x - origin) * vector = 0
\r\n * Ray defined by constructor is a right semi-infinite line with respect to the normal vector
\r\n * If normal vector is omitted ray is considered horizontal (normal vector is (0,1)).
\r\n * Don't be confused: direction of the normal vector is orthogonal to the ray
\r\n * @param {Point} pt - start point\r\n * @param {Vector} norm - normal vector\r\n */\r\n constructor(...args) {\r\n this.pt = new Flatten.Point();\r\n this.norm = new Flatten.Vector(0,1);\r\n\r\n if (args.length == 0) {\r\n return;\r\n }\r\n\r\n if (args.length >= 1 && args[0] instanceof Flatten.Point) {\r\n this.pt = args[0].clone();\r\n }\r\n\r\n if (args.length === 1) {\r\n return;\r\n }\r\n\r\n if (args.length === 2 && args[1] instanceof Flatten.Vector) {\r\n this.norm = args[1].clone();\r\n return;\r\n }\r\n\r\n // if (args.length == 2 && typeof (args[0]) == \"number\" && typeof (args[1]) == \"number\") {\r\n // this.pt = new Flatten.Point(args[0], args[1]);\r\n // return;\r\n // }\r\n\r\n throw Flatten.Errors.ILLEGAL_PARAMETERS;\r\n }\r\n\r\n /**\r\n * Return new cloned instance of ray\r\n * @returns {Ray}\r\n */\r\n clone() {\r\n return new Ray(this.pt, this.norm);\r\n }\r\n\r\n /**\r\n * Slope of the ray - angle in radians between ray and axe x from 0 to 2PI\r\n * @returns {number} - slope of the line\r\n */\r\n get slope() {\r\n let vec = new Flatten.Vector(this.norm.y, -this.norm.x);\r\n return vec.slope;\r\n }\r\n\r\n /**\r\n * Returns half-infinite bounding box of the ray\r\n * @returns {Box} - bounding box\r\n */\r\n get box() {\r\n let slope = this.slope;\r\n return new Flatten.Box(\r\n slope > Math.PI/2 && slope < 3*Math.PI/2 ? Number.NEGATIVE_INFINITY : this.pt.x,\r\n slope >= 0 && slope <= Math.PI ? this.pt.y : Number.NEGATIVE_INFINITY,\r\n slope >= Math.PI/2 && slope <= 3*Math.PI/2 ? this.pt.x : Number.POSITIVE_INFINITY,\r\n slope >= Math.PI && slope <= 2*Math.PI || slope == 0 ? this.pt.y : Number.POSITIVE_INFINITY\r\n )\r\n }\r\n\r\n /**\r\n * Return ray start point\r\n * @returns {Point} - ray start point\r\n */\r\n get start() {\r\n return this.pt;\r\n }\r\n\r\n /**\r\n * Ray has no end point?\r\n * @returns {undefined}\r\n */\r\n get end() {return undefined;}\r\n\r\n /**\r\n * Return positive infinity number as length\r\n * @returns {number}\r\n */\r\n get length() {return Number.POSITIVE_INFINITY;}\r\n\r\n /**\r\n * Returns true if point belongs to ray\r\n * @param {Point} pt Query point\r\n * @returns {boolean}\r\n */\r\n contains(pt) {\r\n if (this.pt.equalTo(pt)) {\r\n return true;\r\n }\r\n /* Ray contains point if vector to point is orthogonal to the ray normal vector\r\n and cross product from vector to point is positive */\r\n let vec = new Flatten.Vector(this.pt, pt);\r\n return Flatten.Utils.EQ_0(this.norm.dot(vec)) && Flatten.Utils.GE(vec.cross(this.norm),0);\r\n }\r\n\r\n /**\r\n * Split ray with point and return array of segment and new ray\r\n * @param {Point} pt\r\n * @returns [Segment,Ray]\r\n */\r\n split(pt) {\r\n if (!this.contains(pt))\r\n return [];\r\n\r\n if (this.pt.equalTo(pt)) {\r\n return [this]\r\n }\r\n\r\n return [\r\n new Flatten.Segment(this.pt, pt),\r\n new Flatten.Ray(pt, this.norm)\r\n ]\r\n }\r\n\r\n /**\r\n * Returns array of intersection points between ray and segment or arc\r\n * @param {Segment|Arc} - Shape to intersect with ray\r\n * @returns {Array} array of intersection points\r\n */\r\n intersect(shape) {\r\n if (shape instanceof Flatten.Segment) {\r\n return this.intersectRay2Segment(this, shape);\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n return this.intersectRay2Arc(this, shape);\r\n }\r\n }\r\n\r\n intersectRay2Segment(ray, segment) {\r\n let ip = [];\r\n\r\n // if (ray.box.not_intersect(segment.box)) {\r\n // return ip;\r\n // }\r\n\r\n let line = new Flatten.Line(ray.start, ray.norm);\r\n let ip_tmp = line.intersect(segment);\r\n\r\n for (let pt of ip_tmp) {\r\n // if (Flatten.Utils.GE(pt.x, ray.start.x)) {\r\n if (ray.contains(pt)) {\r\n ip.push(pt);\r\n }\r\n }\r\n\r\n /* If there were two intersection points between line and ray,\r\n and now there is exactly one left, it means ray starts between these points\r\n and there is another intersection point - start of the ray */\r\n if (ip_tmp.length == 2 && ip.length == 1 && ray.start.on(line)) {\r\n ip.push(ray.start);\r\n }\r\n\r\n return ip;\r\n }\r\n\r\n intersectRay2Arc(ray, arc) {\r\n let ip = [];\r\n\r\n // if (ray.box.not_intersect(arc.box)) {\r\n // return ip;\r\n // }\r\n\r\n let line = new Flatten.Line(ray.start, ray.norm);\r\n let ip_tmp = line.intersect(arc);\r\n\r\n for (let pt of ip_tmp) {\r\n // if (Flatten.Utils.GE(pt.x, ray.start.x)) {\r\n if (ray.contains(pt)) {\r\n ip.push(pt);\r\n }\r\n }\r\n return ip;\r\n }\r\n\r\n /**\r\n * Return string to draw svg segment representing ray inside given box\r\n * @param {Box} box Box representing drawing area\r\n * @param {Object} attrs - an object with attributes of svg segment element\r\n */\r\n svg(box, attrs = {}) {\r\n let line = new Flatten.Line(this.pt, this.norm);\r\n let ip = intersectLine2Box(line, box);\r\n ip = ip.filter( pt => this.contains(pt) );\r\n if (ip.length === 0 || ip.length === 2)\r\n return \"\";\r\n let segment = new Flatten.Segment(this.pt, ip[0]);\r\n return segment.svg(attrs);\r\n }\r\n\r\n}\r\nFlatten.Ray = Ray;\r\n\r\nconst ray = (...args) => new Flatten.Ray(...args);\r\nFlatten.ray = ray;\r\n\r\n/**\r\n * Created by Alex Bol on 3/15/2017.\r\n */\r\n\r\n/**\r\n * Class representing a polygon.
\r\n * Polygon in FlattenJS is a multipolygon comprised from a set of [faces]{@link Flatten.Face}.
\r\n * Face, in turn, is a closed loop of [edges]{@link Flatten.Edge}, where edge may be segment or circular arc
\r\n * @type {Polygon}\r\n */\r\nclass Polygon {\r\n /**\r\n * Constructor creates new instance of polygon. With no arguments new polygon is empty.
\r\n * Constructor accepts as argument array that define loop of shapes\r\n * or array of arrays in case of multi polygon
\r\n * Loop may be defined in different ways:
\r\n * - array of shapes of type Segment or Arc
\r\n * - array of points (Flatten.Point)
\r\n * - array of numeric pairs which represent points
\r\n * - box or circle object
\r\n * Alternatively, it is possible to use polygon.addFace method\r\n * @param {args} - array of shapes or array of arrays\r\n */\r\n constructor() {\r\n /**\r\n * Container of faces (closed loops), may be empty\r\n * @type {PlanarSet}\r\n */\r\n this.faces = new Flatten.PlanarSet();\r\n /**\r\n * Container of edges\r\n * @type {PlanarSet}\r\n */\r\n this.edges = new Flatten.PlanarSet();\r\n\r\n /* It may be array of something that may represent one loop (face) or\r\n array of arrays that represent multiple loops\r\n */\r\n let args = [...arguments];\r\n if (args.length === 1 &&\r\n ((args[0] instanceof Array && args[0].length > 0) ||\r\n args[0] instanceof Flatten.Circle || args[0] instanceof Flatten.Box)) {\r\n let argsArray = args[0];\r\n if (args[0] instanceof Array && args[0].every((loop) => {\r\n return loop instanceof Array\r\n })) {\r\n if (argsArray.every(el => {\r\n return el instanceof Array && el.length === 2 && typeof (el[0]) === \"number\" && typeof (el[1]) === \"number\"\r\n })) {\r\n this.faces.add(new Flatten.Face(this, argsArray)); // one-loop polygon as array of pairs of numbers\r\n } else {\r\n for (let loop of argsArray) { // multi-loop polygon\r\n /* Check extra level of nesting for GeoJSON-style multi polygons */\r\n if (loop instanceof Array && loop[0] instanceof Array &&\r\n loop[0].every(el => {\r\n return el instanceof Array && el.length === 2 && typeof (el[0]) === \"number\" && typeof (el[1]) === \"number\"\r\n })) {\r\n for (let loop1 of loop) {\r\n this.faces.add(new Flatten.Face(this, loop1));\r\n }\r\n } else {\r\n this.faces.add(new Flatten.Face(this, loop));\r\n }\r\n }\r\n }\r\n } else {\r\n this.faces.add(new Flatten.Face(this, argsArray)); // one-loop polygon\r\n }\r\n }\r\n }\r\n\r\n /**\r\n * (Getter) Returns bounding box of the polygon\r\n * @returns {Box}\r\n */\r\n get box() {\r\n return [...this.faces].reduce((acc, face) => acc.merge(face.box), new Flatten.Box());\r\n }\r\n\r\n /**\r\n * (Getter) Returns array of vertices\r\n * @returns {Array}\r\n */\r\n get vertices() {\r\n return [...this.edges].map(edge => edge.start);\r\n }\r\n\r\n /**\r\n * Create new cloned instance of the polygon\r\n * @returns {Polygon}\r\n */\r\n clone() {\r\n let polygon = new Polygon();\r\n for (let face of this.faces) {\r\n polygon.addFace(face.shapes);\r\n }\r\n return polygon;\r\n }\r\n\r\n /**\r\n * Return true is polygon has no edges\r\n * @returns {boolean}\r\n */\r\n isEmpty() {\r\n return this.edges.size === 0;\r\n }\r\n\r\n /**\r\n * Return true if polygon is valid for boolean operations\r\n * Polygon is valid if
\r\n * 1. All faces are simple polygons (there are no self-intersected polygons)
\r\n * 2. All faces are orientable and there is no island inside island or hole inside hole - TODO
\r\n * 3. There is no intersections between faces (excluding touching) - TODO
\r\n * @returns {boolean}\r\n */\r\n isValid() {\r\n let valid = true;\r\n // 1. Polygon is invalid if at least one face is not simple\r\n for (let face of this.faces) {\r\n if (!face.isSimple(this.edges)) {\r\n valid = false;\r\n break;\r\n }\r\n }\r\n // 2. TODO: check if no island inside island and no hole inside hole\r\n // 3. TODO: check the there is no intersection between faces\r\n return valid;\r\n }\r\n\r\n /**\r\n * Returns area of the polygon. Area of an island will be added, area of a hole will be subtracted\r\n * @returns {number}\r\n */\r\n area() {\r\n let signedArea = [...this.faces].reduce((acc, face) => acc + face.signedArea(), 0);\r\n return Math.abs(signedArea);\r\n }\r\n\r\n /**\r\n * Add new face to polygon. Returns added face\r\n * @param {Points[]|Segments[]|Arcs[]|Circle|Box} args - new face may be create with one of the following ways:
\r\n * 1) array of points that describe closed path (edges are segments)
\r\n * 2) array of shapes (segments and arcs) which describe closed path
\r\n * 3) circle - will be added as counterclockwise arc
\r\n * 4) box - will be added as counterclockwise rectangle
\r\n * You can chain method face.reverse() is you need to change direction of the creates face\r\n * @returns {Face}\r\n */\r\n addFace(...args) {\r\n let face = new Flatten.Face(this, ...args);\r\n this.faces.add(face);\r\n return face;\r\n }\r\n\r\n /**\r\n * Delete existing face from polygon\r\n * @param {Face} face Face to be deleted\r\n * @returns {boolean}\r\n */\r\n deleteFace(face) {\r\n for (let edge of face) {\r\n this.edges.delete(edge);\r\n }\r\n return this.faces.delete(face);\r\n }\r\n\r\n /**\r\n * Clear all faces and create new faces from edges\r\n */\r\n recreateFaces() {\r\n // Remove all faces\r\n this.faces.clear();\r\n for (let edge of this.edges) {\r\n edge.face = null;\r\n }\r\n\r\n // Restore faces\r\n let first;\r\n let unassignedEdgeFound = true;\r\n while (unassignedEdgeFound) {\r\n unassignedEdgeFound = false;\r\n for (let edge of this.edges) {\r\n if (edge.face === null) {\r\n first = edge;\r\n unassignedEdgeFound = true;\r\n break;\r\n }\r\n }\r\n\r\n if (unassignedEdgeFound) {\r\n let last = first;\r\n do {\r\n last = last.next;\r\n } while (last.next !== first)\r\n\r\n this.addFace(first, last);\r\n }\r\n }\r\n }\r\n\r\n /**\r\n * Delete chain of edges from the face.\r\n * @param {Face} face Face to remove chain\r\n * @param {Edge} edgeFrom Start of the chain of edges to be removed\r\n * @param {Edge} edgeTo End of the chain of edges to be removed\r\n */\r\n removeChain(face, edgeFrom, edgeTo) {\r\n // Special case: all edges removed\r\n if (edgeTo.next === edgeFrom) {\r\n this.deleteFace(face);\r\n return;\r\n }\r\n for (let edge = edgeFrom; edge !== edgeTo.next; edge = edge.next) {\r\n face.remove(edge);\r\n this.edges.delete(edge); // delete from PlanarSet of edges and update index\r\n if (face.isEmpty()) {\r\n this.deleteFace(face); // delete from PlanarSet of faces and update index\r\n break;\r\n }\r\n }\r\n }\r\n\r\n /**\r\n * Add point as a new vertex and split edge. Point supposed to belong to an edge.\r\n * When edge is split, new edge created from the start of the edge to the new vertex\r\n * and inserted before current edge.\r\n * Current edge is trimmed and updated.\r\n * Method returns new edge added. If no edge added, it returns edge before vertex\r\n * @param {Point} pt Point to be added as a new vertex\r\n * @param {Edge} edge Edge to be split with new vertex and then trimmed from start\r\n * @returns {Edge}\r\n */\r\n addVertex(pt, edge) {\r\n let shapes = edge.shape.split(pt);\r\n // if (shapes.length < 2) return;\r\n\r\n if (shapes[0] === null) // point incident to edge start vertex, return previous edge\r\n return edge.prev;\r\n\r\n if (shapes[1] === null) // point incident to edge end vertex, return edge itself\r\n return edge;\r\n\r\n let newEdge = new Flatten.Edge(shapes[0]);\r\n let edgeBefore = edge.prev;\r\n\r\n /* Insert first split edge into linked list after edgeBefore */\r\n edge.face.insert(newEdge, edgeBefore);\r\n\r\n // Remove old edge from edges container and 2d index\r\n this.edges.delete(edge);\r\n\r\n // Insert new edge to the edges container and 2d index\r\n this.edges.add(newEdge);\r\n\r\n // Update edge shape with second split edge keeping links\r\n edge.shape = shapes[1];\r\n\r\n // Add updated edge to the edges container and 2d index\r\n this.edges.add(edge);\r\n\r\n return newEdge;\r\n }\r\n\r\n /**\r\n * Cut polygon with multiline and return array of new polygons\r\n * Multiline should be constructed from a line with intersection point, see notebook:\r\n * https://next.observablehq.com/@alexbol99/cut-polygon-with-line\r\n * @param {Multiline} multiline\r\n * @returns {Polygon[]}\r\n */\r\n cut(multiline) {\r\n let cutPolygons = [this.clone()];\r\n for (let edge of multiline) {\r\n if (edge.setInclusion(this) !== INSIDE)\r\n continue;\r\n\r\n let cut_edge_start = edge.shape.start;\r\n let cut_edge_end = edge.shape.end;\r\n\r\n let newCutPolygons = [];\r\n for (let polygon of cutPolygons) {\r\n if (polygon.findEdgeByPoint(cut_edge_start) === undefined) {\r\n newCutPolygons.push(polygon);\r\n } else {\r\n let [cutPoly1, cutPoly2] = polygon.cutFace(cut_edge_start, cut_edge_end);\r\n newCutPolygons.push(cutPoly1, cutPoly2);\r\n }\r\n }\r\n cutPolygons = newCutPolygons;\r\n }\r\n return cutPolygons;\r\n }\r\n\r\n /**\r\n * Cut face of polygon with a segment between two points and create two new polygons\r\n * Supposed that a segments between points does not intersect any other edge\r\n * @param {Point} pt1\r\n * @param {Point} pt2\r\n * @returns {Polygon[]}\r\n */\r\n cutFace(pt1, pt2) {\r\n let edge1 = this.findEdgeByPoint(pt1);\r\n let edge2 = this.findEdgeByPoint(pt2);\r\n if (edge1.face !== edge2.face)\r\n return [];\r\n\r\n // Cut face into two and create new polygon with two faces\r\n let edgeBefore1 = this.addVertex(pt1, edge1);\r\n edge2 = this.findEdgeByPoint(pt2);\r\n let edgeBefore2 = this.addVertex(pt2, edge2);\r\n\r\n let face = edgeBefore1.face;\r\n let newEdge1 = new Flatten.Edge(\r\n new Flatten.Segment(edgeBefore1.end, edgeBefore2.end)\r\n );\r\n let newEdge2 = new Flatten.Edge(\r\n new Flatten.Segment(edgeBefore2.end, edgeBefore1.end)\r\n );\r\n\r\n // Swap links\r\n edgeBefore1.next.prev = newEdge2;\r\n newEdge2.next = edgeBefore1.next;\r\n\r\n edgeBefore1.next = newEdge1;\r\n newEdge1.prev = edgeBefore1;\r\n\r\n edgeBefore2.next.prev = newEdge1;\r\n newEdge1.next = edgeBefore2.next;\r\n\r\n edgeBefore2.next = newEdge2;\r\n newEdge2.prev = edgeBefore2;\r\n\r\n // Insert new edge to the edges container and 2d index\r\n this.edges.add(newEdge1);\r\n this.edges.add(newEdge2);\r\n\r\n // Add two new faces\r\n let face1 = this.addFace(newEdge1, edgeBefore1);\r\n let face2 = this.addFace(newEdge2, edgeBefore2);\r\n\r\n // Remove old face\r\n this.faces.delete(face);\r\n\r\n return [face1.toPolygon(), face2.toPolygon()];\r\n }\r\n\r\n /**\r\n * Return a result of cutting polygon with line\r\n * @param {Line} line - cutting line\r\n * @returns {Polygon} newPoly - resulted polygon\r\n */\r\n cutWithLine(line) {\r\n let newPoly = this.clone();\r\n\r\n let multiline = new Multiline([line]);\r\n\r\n // smart intersections\r\n let intersections = {\r\n int_points1: [],\r\n int_points2: [],\r\n int_points1_sorted: [],\r\n int_points2_sorted: []\r\n };\r\n\r\n // intersect line with each edge of the polygon\r\n // and create smart intersections\r\n for (let edge of newPoly.edges) {\r\n let ip = intersectEdge2Line(edge, line);\r\n // for each intersection point\r\n for (let pt of ip) {\r\n addToIntPoints(multiline.first, pt, intersections.int_points1);\r\n addToIntPoints(edge, pt, intersections.int_points2);\r\n }\r\n }\r\n\r\n // No intersections - return a copy of the original polygon\r\n if (intersections.int_points1.length === 0)\r\n return newPoly;\r\n\r\n // sort smart intersections\r\n intersections.int_points1_sorted = getSortedArrayOnLine(line, intersections.int_points1);\r\n intersections.int_points2_sorted = getSortedArray(intersections.int_points2);\r\n\r\n // split by intersection points\r\n splitByIntersections(multiline, intersections.int_points1_sorted);\r\n splitByIntersections(newPoly, intersections.int_points2_sorted);\r\n\r\n // filter duplicated intersection points\r\n filterDuplicatedIntersections(intersections);\r\n\r\n // sort intersection points again after filtering\r\n intersections.int_points1_sorted = getSortedArrayOnLine(line, intersections.int_points1);\r\n intersections.int_points2_sorted = getSortedArray(intersections.int_points2);\r\n\r\n // initialize inclusion flags for edges of multiline incident to intersections\r\n initializeInclusionFlags(intersections.int_points1);\r\n\r\n // calculate inclusion flag for edges of multiline incident to intersections\r\n calculateInclusionFlags(intersections.int_points1, newPoly);\r\n\r\n // filter intersections between two edges that got same inclusion flag\r\n for (let int_point1 of intersections.int_points1_sorted) {\r\n if (int_point1.edge_before.bv === int_point1.edge_after.bv) {\r\n intersections.int_points2[int_point1.id] = -1; // to be filtered out\r\n int_point1.id = -1; // to be filtered out\r\n }\r\n }\r\n intersections.int_points1 = intersections.int_points1.filter( int_point => int_point.id >= 0);\r\n intersections.int_points2 = intersections.int_points2.filter( int_point => int_point.id >= 0);\r\n\r\n // No intersections left after filtering - return a copy of the original polygon\r\n if (intersections.int_points1.length === 0)\r\n return newPoly;\r\n\r\n // sort intersection points 3d time after filtering\r\n intersections.int_points1_sorted = getSortedArrayOnLine(line, intersections.int_points1);\r\n intersections.int_points2_sorted = getSortedArray(intersections.int_points2);\r\n\r\n // Add 2 new inner edges between intersection points\r\n let int_point1_prev = intersections.int_points1[0];\r\n let new_edge;\r\n for (let int_point1_curr of intersections.int_points1_sorted) {\r\n if (int_point1_curr.edge_before.bv === INSIDE) {\r\n new_edge = new Flatten.Edge(new Flatten.Segment(int_point1_prev.pt, int_point1_curr.pt)); // (int_point1_curr.edge_before.shape);\r\n insertBetweenIntPoints(intersections.int_points2[int_point1_prev.id], intersections.int_points2[int_point1_curr.id], new_edge);\r\n newPoly.edges.add(new_edge);\r\n\r\n new_edge = new Flatten.Edge(new Flatten.Segment(int_point1_curr.pt, int_point1_prev.pt)); // (int_point1_curr.edge_before.shape.reverse());\r\n insertBetweenIntPoints(intersections.int_points2[int_point1_curr.id], intersections.int_points2[int_point1_prev.id], new_edge);\r\n newPoly.edges.add(new_edge);\r\n }\r\n int_point1_prev = int_point1_curr;\r\n }\r\n\r\n // Recreate faces\r\n newPoly.recreateFaces();\r\n return newPoly;\r\n }\r\n\r\n /**\r\n * Returns the first founded edge of polygon that contains given point\r\n * @param {Point} pt\r\n * @returns {Edge}\r\n */\r\n findEdgeByPoint(pt) {\r\n let edge;\r\n for (let face of this.faces) {\r\n edge = face.findEdgeByPoint(pt);\r\n if (edge !== undefined)\r\n break;\r\n }\r\n return edge;\r\n }\r\n\r\n /**\r\n * Split polygon into array of polygons, where each polygon is an island with all\r\n * hole that it contains\r\n * @returns {Flatten.Polygon[]}\r\n */\r\n splitToIslands() {\r\n if (this.isEmpty()) return []; // return empty array if polygon is empty\r\n let polygons = this.toArray(); // split into array of one-loop polygons\r\n /* Sort polygons by area in descending order */\r\n polygons.sort((polygon1, polygon2) => polygon2.area() - polygon1.area());\r\n /* define orientation of the island by orientation of the first polygon in array */\r\n let orientation = [...polygons[0].faces][0].orientation();\r\n /* Create output array from polygons with same orientation as a first polygon (array of islands) */\r\n let newPolygons = polygons.filter(polygon => [...polygon.faces][0].orientation() === orientation);\r\n for (let polygon of polygons) {\r\n let face = [...polygon.faces][0];\r\n if (face.orientation() === orientation) continue; // skip same orientation\r\n /* Proceed with opposite orientation */\r\n /* Look if any of island polygons contains tested polygon as a hole */\r\n for (let islandPolygon of newPolygons) {\r\n if (face.shapes.every(shape => islandPolygon.contains(shape))) {\r\n islandPolygon.addFace(face.shapes); // add polygon as a hole in islandPolygon\r\n break;\r\n }\r\n }\r\n }\r\n // TODO: assert if not all polygons added into output\r\n return newPolygons;\r\n }\r\n\r\n /**\r\n * Reverse orientation of all faces to opposite\r\n * @returns {Polygon}\r\n */\r\n reverse() {\r\n for (let face of this.faces) {\r\n face.reverse();\r\n }\r\n return this;\r\n }\r\n\r\n /**\r\n * Returns true if polygon contains shape: no point of shape lay outside of the polygon,\r\n * false otherwise\r\n * @param {Shape} shape - test shape\r\n * @returns {boolean}\r\n */\r\n contains(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n let rel = ray_shoot(this, shape);\r\n return rel === INSIDE || rel === BOUNDARY;\r\n } else {\r\n return cover(this, shape);\r\n }\r\n }\r\n\r\n /**\r\n * Return distance and shortest segment between polygon and other shape as array [distance, shortest_segment]\r\n * @param {Shape} shape Shape of one of the types Point, Circle, Line, Segment, Arc or Polygon\r\n * @returns {Number | Segment}\r\n */\r\n distanceTo(shape) {\r\n // let {Distance} = Flatten;\r\n\r\n if (shape instanceof Flatten.Point) {\r\n let [dist, shortest_segment] = Flatten.Distance.point2polygon(shape, this);\r\n shortest_segment = shortest_segment.reverse();\r\n return [dist, shortest_segment];\r\n }\r\n\r\n if (shape instanceof Flatten.Circle ||\r\n shape instanceof Flatten.Line ||\r\n shape instanceof Flatten.Segment ||\r\n shape instanceof Flatten.Arc) {\r\n let [dist, shortest_segment] = Flatten.Distance.shape2polygon(shape, this);\r\n shortest_segment = shortest_segment.reverse();\r\n return [dist, shortest_segment];\r\n }\r\n\r\n /* this method is bit faster */\r\n if (shape instanceof Flatten.Polygon) {\r\n let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Flatten.Segment()];\r\n let dist, shortest_segment;\r\n\r\n for (let edge of this.edges) {\r\n // let [dist, shortest_segment] = Distance.shape2polygon(edge.shape, shape);\r\n let min_stop = min_dist_and_segment[0];\r\n [dist, shortest_segment] = Flatten.Distance.shape2planarSet(edge.shape, shape.edges, min_stop);\r\n if (Flatten.Utils.LT(dist, min_stop)) {\r\n min_dist_and_segment = [dist, shortest_segment];\r\n }\r\n }\r\n return min_dist_and_segment;\r\n }\r\n }\r\n\r\n /**\r\n * Return array of intersection points between polygon and other shape\r\n * @param shape Shape of the one of supported types
\r\n * @returns {Point[]}\r\n */\r\n intersect(shape) {\r\n if (shape instanceof Flatten.Point) {\r\n return this.contains(shape) ? [shape] : [];\r\n }\r\n\r\n if (shape instanceof Flatten.Line) {\r\n return intersectLine2Polygon(shape, this);\r\n }\r\n\r\n if (shape instanceof Flatten.Circle) {\r\n return intersectCircle2Polygon(shape, this);\r\n }\r\n\r\n if (shape instanceof Flatten.Segment) {\r\n return intersectSegment2Polygon(shape, this);\r\n }\r\n\r\n if (shape instanceof Flatten.Arc) {\r\n return intersectArc2Polygon(shape, this);\r\n }\r\n\r\n if (shape instanceof Flatten.Polygon) {\r\n return intersectPolygon2Polygon(shape, this);\r\n }\r\n }\r\n\r\n /**\r\n * Returns new polygon translated by vector vec\r\n * @param {Vector} vec\r\n * @returns {Polygon}\r\n */\r\n translate(vec) {\r\n let newPolygon = new Polygon();\r\n for (let face of this.faces) {\r\n newPolygon.addFace(face.shapes.map(shape => shape.translate(vec)));\r\n }\r\n return newPolygon;\r\n }\r\n\r\n /**\r\n * Return new polygon rotated by given angle around given point\r\n * If point omitted, rotate around origin (0,0)\r\n * Positive value of angle defines rotation counter clockwise, negative - clockwise\r\n * @param {number} angle - rotation angle in radians\r\n * @param {Point} center - rotation center, default is (0,0)\r\n * @returns {Polygon} - new rotated polygon\r\n */\r\n rotate(angle = 0, center = new Flatten.Point()) {\r\n let newPolygon = new Polygon();\r\n for (let face of this.faces) {\r\n newPolygon.addFace(face.shapes.map(shape => shape.rotate(angle, center)));\r\n }\r\n return newPolygon;\r\n }\r\n\r\n /**\r\n * Return new polygon transformed using affine transformation matrix\r\n * @param {Matrix} matrix - affine transformation matrix\r\n * @returns {Polygon} - new polygon\r\n */\r\n transform(matrix = new Flatten.Matrix()) {\r\n let newPolygon = new Polygon();\r\n for (let face of this.faces) {\r\n newPolygon.addFace(face.shapes.map(shape => shape.transform(matrix)));\r\n }\r\n return newPolygon;\r\n }\r\n\r\n /**\r\n * This method returns an object that defines how data will be\r\n * serialized when called JSON.stringify() method\r\n * @returns {Object}\r\n */\r\n toJSON() {\r\n return [...this.faces].map(face => face.toJSON());\r\n }\r\n\r\n /**\r\n * Transform all faces into array of polygons\r\n * @returns {Flatten.Polygon[]}\r\n */\r\n toArray() {\r\n return [...this.faces].map(face => face.toPolygon());\r\n }\r\n\r\n /**\r\n * Return string to draw polygon in svg\r\n * @param attrs - an object with attributes for svg path element,\r\n * like \"stroke\", \"strokeWidth\", \"fill\", \"fillRule\", \"fillOpacity\"\r\n * Defaults are stroke:\"black\", strokeWidth:\"1\", fill:\"lightcyan\", fillRule:\"evenodd\", fillOpacity: \"1\"\r\n * @returns {string}\r\n */\r\n svg(attrs = {}) {\r\n let {stroke, strokeWidth, fill, fillRule, fillOpacity, id, className} = attrs;\r\n // let restStr = Object.keys(rest).reduce( (acc, key) => acc += ` ${key}=\"${rest[key]}\"`, \"\");\r\n let id_str = (id && id.length > 0) ? `id=\"${id}\"` : \"\";\r\n let class_str = (className && className.length > 0) ? `class=\"${className}\"` : \"\";\r\n\r\n let svgStr = `\\n\\n`;\r\n return svgStr;\r\n }\r\n}\r\n\r\nFlatten.Polygon = Polygon;\r\n\r\n/**\r\n * Shortcut method to create new polygon\r\n */\r\nconst polygon = (...args) => new Flatten.Polygon(...args);\r\nFlatten.polygon = polygon;\r\n\r\nconst {Circle: Circle$1, Line: Line$1, Point: Point$1, Vector: Vector$1, Utils: Utils$1} = Flatten;\r\n/**\r\n * Class Inversion represent operator of inversion in circle\r\n * Inversion is a transformation of the Euclidean plane that maps generalized circles\r\n * (where line is considered as a circle with infinite radius) into generalized circles\r\n * See also https://en.wikipedia.org/wiki/Inversive_geometry and\r\n * http://mathworld.wolfram.com/Inversion.html
\r\n * @type {Inversion}\r\n */\r\nclass Inversion {\r\n /**\r\n * Inversion constructor\r\n * @param {Circle} inversion_circle inversion circle\r\n */\r\n constructor(inversion_circle) {\r\n this.circle = inversion_circle;\r\n }\r\n\r\n\r\n get inversion_circle() {\r\n return this.circle;\r\n }\r\n\r\n static inversePoint(inversion_circle, point) {\r\n const v = new Vector$1(inversion_circle.pc, point);\r\n const k2 = inversion_circle.r * inversion_circle.r;\r\n const len2 = v.dot(v);\r\n const reflected_point = Utils$1.EQ_0(len2) ?\r\n new Point$1(Number.POSITIVE_INFINITY, Number.POSITIVE_INFINITY) :\r\n inversion_circle.pc.translate(v.multiply(k2 / len2));\r\n return reflected_point;\r\n }\r\n\r\n static inverseCircle(inversion_circle, circle) {\r\n const dist = inversion_circle.pc.distanceTo(circle.pc)[0];\r\n if (Utils$1.EQ(dist, circle.r)) { // Circle passing through inversion center mapped into line\r\n let d = (inversion_circle.r * inversion_circle.r) / (2 * circle.r);\r\n let v = new Vector$1(inversion_circle.pc, circle.pc);\r\n v = v.normalize();\r\n let pt = inversion_circle.pc.translate(v.multiply(d));\r\n\r\n return new Line$1(pt, v);\r\n } else { // Circle not passing through inversion center - map into another circle */\r\n /* Taken from http://mathworld.wolfram.com */\r\n let v = new Vector$1(inversion_circle.pc, circle.pc);\r\n let s = inversion_circle.r * inversion_circle.r / (v.dot(v) - circle.r * circle.r);\r\n let pc = inversion_circle.pc.translate(v.multiply(s));\r\n let r = Math.abs(s) * circle.r;\r\n\r\n return new Circle$1(pc, r);\r\n }\r\n }\r\n\r\n static inverseLine(inversion_circle, line) {\r\n const [dist, shortest_segment] = inversion_circle.pc.distanceTo(line);\r\n if (Utils$1.EQ_0(dist)) { // Line passing through inversion center, is mapping to itself\r\n return line.clone();\r\n } else { // Line not passing through inversion center is mapping into circle\r\n let r = inversion_circle.r * inversion_circle.r / (2 * dist);\r\n let v = new Vector$1(inversion_circle.pc, shortest_segment.end);\r\n v = v.multiply(r / dist);\r\n return new Circle$1(inversion_circle.pc.translate(v), r);\r\n }\r\n }\r\n\r\n inverse(shape) {\r\n if (shape instanceof Point$1) {\r\n return Inversion.inversePoint(this.circle, shape);\r\n }\r\n else if (shape instanceof Circle$1) {\r\n return Inversion.inverseCircle(this.circle, shape);\r\n }\r\n else if (shape instanceof Line$1) {\r\n return Inversion.inverseLine(this.circle, shape);\r\n }\r\n }\r\n}\r\nFlatten.Inversion = Inversion;\r\n\r\n/**\r\n * Shortcut to create inversion operator\r\n * @param circle\r\n * @returns {Inversion}\r\n */\r\nconst inversion = (circle) => new Flatten.Inversion(circle);\r\nFlatten.inversion = inversion;\r\n\r\nclass Distance {\r\n /**\r\n * Calculate distance and shortest segment between points\r\n * @param pt1\r\n * @param pt2\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static point2point(pt1, pt2) {\r\n return pt1.distanceTo(pt2);\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between point and line\r\n * @param pt\r\n * @param line\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static point2line(pt, line) {\r\n let closest_point = pt.projectionOn(line);\r\n let vec = new Flatten.Vector(pt, closest_point);\r\n return [vec.length, new Flatten.Segment(pt, closest_point)];\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between point and circle\r\n * @param pt\r\n * @param circle\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static point2circle(pt, circle) {\r\n let [dist2center, shortest_dist] = pt.distanceTo(circle.center);\r\n if (Flatten.Utils.EQ_0(dist2center)) {\r\n return [circle.r, new Flatten.Segment(pt, circle.toArc().start)];\r\n } else {\r\n let dist = Math.abs(dist2center - circle.r);\r\n let v = new Flatten.Vector(circle.pc, pt).normalize().multiply(circle.r);\r\n let closest_point = circle.pc.translate(v);\r\n return [dist, new Flatten.Segment(pt, closest_point)];\r\n }\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between point and segment\r\n * @param pt\r\n * @param segment\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static point2segment(pt, segment) {\r\n /* Degenerated case of zero-length segment */\r\n if (segment.start.equalTo(segment.end)) {\r\n return Distance.point2point(pt, segment.start);\r\n }\r\n\r\n let v_seg = new Flatten.Vector(segment.start, segment.end);\r\n let v_ps2pt = new Flatten.Vector(segment.start, pt);\r\n let v_pe2pt = new Flatten.Vector(segment.end, pt);\r\n let start_sp = v_seg.dot(v_ps2pt);\r\n /* dot product v_seg * v_ps2pt */\r\n let end_sp = -v_seg.dot(v_pe2pt);\r\n /* minus dot product v_seg * v_pe2pt */\r\n\r\n let dist;\r\n let closest_point;\r\n if (Flatten.Utils.GE(start_sp, 0) && Flatten.Utils.GE(end_sp, 0)) { /* point inside segment scope */\r\n let v_unit = segment.tangentInStart(); // new Flatten.Vector(v_seg.x / this.length, v_seg.y / this.length);\r\n /* unit vector ||v_unit|| = 1 */\r\n dist = Math.abs(v_unit.cross(v_ps2pt));\r\n /* dist = abs(v_unit x v_ps2pt) */\r\n closest_point = segment.start.translate(v_unit.multiply(v_unit.dot(v_ps2pt)));\r\n return [dist, new Flatten.Segment(pt, closest_point)];\r\n } else if (start_sp < 0) { /* point is out of scope closer to ps */\r\n return pt.distanceTo(segment.start);\r\n } else { /* point is out of scope closer to pe */\r\n return pt.distanceTo(segment.end);\r\n }\r\n };\r\n\r\n /**\r\n * Calculate distance and shortest segment between point and arc\r\n * @param pt\r\n * @param arc\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static point2arc(pt, arc) {\r\n let circle = new Flatten.Circle(arc.pc, arc.r);\r\n let dist_and_segment = [];\r\n let dist, shortest_segment;\r\n [dist, shortest_segment] = Distance.point2circle(pt, circle);\r\n if (shortest_segment.end.on(arc)) {\r\n dist_and_segment.push(Distance.point2circle(pt, circle));\r\n }\r\n dist_and_segment.push(Distance.point2point(pt, arc.start));\r\n dist_and_segment.push(Distance.point2point(pt, arc.end));\r\n\r\n Distance.sort(dist_and_segment);\r\n\r\n return dist_and_segment[0];\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between segment and line\r\n * @param seg\r\n * @param line\r\n * @returns {Number | Segment}\r\n */\r\n static segment2line(seg, line) {\r\n let ip = seg.intersect(line);\r\n if (ip.length > 0) {\r\n return [0, new Flatten.Segment(ip[0], ip[0])]; // distance = 0, closest point is the first point\r\n }\r\n let dist_and_segment = [];\r\n dist_and_segment.push(Distance.point2line(seg.start, line));\r\n dist_and_segment.push(Distance.point2line(seg.end, line));\r\n\r\n Distance.sort(dist_and_segment);\r\n return dist_and_segment[0];\r\n\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between two segments\r\n * @param seg1\r\n * @param seg2\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static segment2segment(seg1, seg2) {\r\n let ip = intersectSegment2Segment(seg1, seg2);\r\n if (ip.length > 0) {\r\n return [0, new Flatten.Segment(ip[0], ip[0])]; // distance = 0, closest point is the first point\r\n }\r\n\r\n // Seg1 and seg2 not intersected\r\n let dist_and_segment = [];\r\n let dist_tmp, shortest_segment_tmp;\r\n [dist_tmp, shortest_segment_tmp] = Distance.point2segment(seg2.start, seg1);\r\n dist_and_segment.push([dist_tmp, shortest_segment_tmp.reverse()]);\r\n [dist_tmp, shortest_segment_tmp] = Distance.point2segment(seg2.end, seg1);\r\n dist_and_segment.push([dist_tmp, shortest_segment_tmp.reverse()]);\r\n dist_and_segment.push(Distance.point2segment(seg1.start, seg2));\r\n dist_and_segment.push(Distance.point2segment(seg1.end, seg2));\r\n\r\n Distance.sort(dist_and_segment);\r\n return dist_and_segment[0];\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between segment and circle\r\n * @param seg\r\n * @param circle\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static segment2circle(seg, circle) {\r\n /* Case 1 Segment and circle intersected. Return the first point and zero distance */\r\n let ip = seg.intersect(circle);\r\n if (ip.length > 0) {\r\n return [0, new Flatten.Segment(ip[0], ip[0])];\r\n }\r\n\r\n // No intersection between segment and circle\r\n\r\n /* Case 2. Distance to projection of center point to line bigger than radius\r\n * And projection point belong to segment\r\n * Then measure again distance from projection to circle and return it */\r\n let line = new Flatten.Line(seg.ps, seg.pe);\r\n let [dist, shortest_segment] = Distance.point2line(circle.center, line);\r\n if (Flatten.Utils.GE(dist, circle.r) && shortest_segment.end.on(seg)) {\r\n return Distance.point2circle(shortest_segment.end, circle);\r\n }\r\n /* Case 3. Otherwise closest point is one of the end points of the segment */\r\n else {\r\n let [dist_from_start, shortest_segment_from_start] = Distance.point2circle(seg.start, circle);\r\n let [dist_from_end, shortest_segment_from_end] = Distance.point2circle(seg.end, circle);\r\n return Flatten.Utils.LT(dist_from_start, dist_from_end) ?\r\n [dist_from_start, shortest_segment_from_start] :\r\n [dist_from_end, shortest_segment_from_end];\r\n }\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between segment and arc\r\n * @param seg\r\n * @param arc\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static segment2arc(seg, arc) {\r\n /* Case 1 Segment and arc intersected. Return the first point and zero distance */\r\n let ip = seg.intersect(arc);\r\n if (ip.length > 0) {\r\n return [0, new Flatten.Segment(ip[0], ip[0])];\r\n }\r\n\r\n // No intersection between segment and arc\r\n let line = new Flatten.Line(seg.ps, seg.pe);\r\n let circle = new Flatten.Circle(arc.pc, arc.r);\r\n\r\n /* Case 2. Distance to projection of center point to line bigger than radius AND\r\n * projection point belongs to segment AND\r\n * distance from projection point to circle belongs to arc =>\r\n * return this distance from projection to circle */\r\n let [dist_from_center, shortest_segment_from_center] = Distance.point2line(circle.center, line);\r\n if (Flatten.Utils.GE(dist_from_center, circle.r) && shortest_segment_from_center.end.on(seg)) {\r\n let [dist_from_projection, shortest_segment_from_projection] =\r\n Distance.point2circle(shortest_segment_from_center.end, circle);\r\n if (shortest_segment_from_projection.end.on(arc)) {\r\n return [dist_from_projection, shortest_segment_from_projection];\r\n }\r\n }\r\n /* Case 3. Otherwise closest point is one of the end points of the segment */\r\n let dist_and_segment = [];\r\n dist_and_segment.push(Distance.point2arc(seg.start, arc));\r\n dist_and_segment.push(Distance.point2arc(seg.end, arc));\r\n\r\n let dist_tmp, segment_tmp;\r\n [dist_tmp, segment_tmp] = Distance.point2segment(arc.start, seg);\r\n dist_and_segment.push([dist_tmp, segment_tmp.reverse()]);\r\n\r\n [dist_tmp, segment_tmp] = Distance.point2segment(arc.end, seg);\r\n dist_and_segment.push([dist_tmp, segment_tmp.reverse()]);\r\n\r\n Distance.sort(dist_and_segment);\r\n return dist_and_segment[0];\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between two circles\r\n * @param circle1\r\n * @param circle2\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static circle2circle(circle1, circle2) {\r\n let ip = circle1.intersect(circle2);\r\n if (ip.length > 0) {\r\n return [0, new Flatten.Segment(ip[0], ip[0])];\r\n }\r\n\r\n // Case 1. Concentric circles. Convert to arcs and take distance between two arc starts\r\n if (circle1.center.equalTo(circle2.center)) {\r\n let arc1 = circle1.toArc();\r\n let arc2 = circle2.toArc();\r\n return Distance.point2point(arc1.start, arc2.start);\r\n } else {\r\n // Case 2. Not concentric circles\r\n let line = new Flatten.Line(circle1.center, circle2.center);\r\n let ip1 = line.intersect(circle1);\r\n let ip2 = line.intersect(circle2);\r\n\r\n let dist_and_segment = [];\r\n\r\n dist_and_segment.push(Distance.point2point(ip1[0], ip2[0]));\r\n dist_and_segment.push(Distance.point2point(ip1[0], ip2[1]));\r\n dist_and_segment.push(Distance.point2point(ip1[1], ip2[0]));\r\n dist_and_segment.push(Distance.point2point(ip1[1], ip2[1]));\r\n\r\n Distance.sort(dist_and_segment);\r\n return dist_and_segment[0];\r\n }\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between two circles\r\n * @param circle\r\n * @param line\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static circle2line(circle, line) {\r\n let ip = circle.intersect(line);\r\n if (ip.length > 0) {\r\n return [0, new Flatten.Segment(ip[0], ip[0])];\r\n }\r\n\r\n let [dist_from_center, shortest_segment_from_center] = Distance.point2line(circle.center, line);\r\n let [dist, shortest_segment] = Distance.point2circle(shortest_segment_from_center.end, circle);\r\n shortest_segment = shortest_segment.reverse();\r\n return [dist, shortest_segment];\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between arc and line\r\n * @param arc\r\n * @param line\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static arc2line(arc, line) {\r\n /* Case 1 Line and arc intersected. Return the first point and zero distance */\r\n let ip = line.intersect(arc);\r\n if (ip.length > 0) {\r\n return [0, new Flatten.Segment(ip[0], ip[0])];\r\n }\r\n\r\n let circle = new Flatten.Circle(arc.center, arc.r);\r\n\r\n /* Case 2. Distance to projection of center point to line bigger than radius AND\r\n * projection point belongs to segment AND\r\n * distance from projection point to circle belongs to arc =>\r\n * return this distance from projection to circle */\r\n let [dist_from_center, shortest_segment_from_center] = Distance.point2line(circle.center, line);\r\n if (Flatten.Utils.GE(dist_from_center, circle.r)) {\r\n let [dist_from_projection, shortest_segment_from_projection] =\r\n Distance.point2circle(shortest_segment_from_center.end, circle);\r\n if (shortest_segment_from_projection.end.on(arc)) {\r\n return [dist_from_projection, shortest_segment_from_projection];\r\n }\r\n } else {\r\n let dist_and_segment = [];\r\n dist_and_segment.push(Distance.point2line(arc.start, line));\r\n dist_and_segment.push(Distance.point2line(arc.end, line));\r\n\r\n Distance.sort(dist_and_segment);\r\n return dist_and_segment[0];\r\n }\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between arc and circle\r\n * @param arc\r\n * @param circle2\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static arc2circle(arc, circle2) {\r\n let ip = arc.intersect(circle2);\r\n if (ip.length > 0) {\r\n return [0, new Flatten.Segment(ip[0], ip[0])];\r\n }\r\n\r\n let circle1 = new Flatten.Circle(arc.center, arc.r);\r\n\r\n let [dist, shortest_segment] = Distance.circle2circle(circle1, circle2);\r\n if (shortest_segment.start.on(arc)) {\r\n return [dist, shortest_segment];\r\n } else {\r\n let dist_and_segment = [];\r\n\r\n dist_and_segment.push(Distance.point2circle(arc.start, circle2));\r\n dist_and_segment.push(Distance.point2circle(arc.end, circle2));\r\n\r\n Distance.sort(dist_and_segment);\r\n\r\n return dist_and_segment[0];\r\n }\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between two arcs\r\n * @param arc1\r\n * @param arc2\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static arc2arc(arc1, arc2) {\r\n let ip = arc1.intersect(arc2);\r\n if (ip.length > 0) {\r\n return [0, new Flatten.Segment(ip[0], ip[0])];\r\n }\r\n\r\n let circle1 = new Flatten.Circle(arc1.center, arc1.r);\r\n let circle2 = new Flatten.Circle(arc2.center, arc2.r);\r\n\r\n let [dist, shortest_segment] = Distance.circle2circle(circle1, circle2);\r\n if (shortest_segment.start.on(arc1) && shortest_segment.end.on(arc2)) {\r\n return [dist, shortest_segment];\r\n } else {\r\n let dist_and_segment = [];\r\n\r\n let dist_tmp, segment_tmp;\r\n\r\n [dist_tmp, segment_tmp] = Distance.point2arc(arc1.start, arc2);\r\n if (segment_tmp.end.on(arc2)) {\r\n dist_and_segment.push([dist_tmp, segment_tmp]);\r\n }\r\n\r\n [dist_tmp, segment_tmp] = Distance.point2arc(arc1.end, arc2);\r\n if (segment_tmp.end.on(arc2)) {\r\n dist_and_segment.push([dist_tmp, segment_tmp]);\r\n }\r\n\r\n [dist_tmp, segment_tmp] = Distance.point2arc(arc2.start, arc1);\r\n if (segment_tmp.end.on(arc1)) {\r\n dist_and_segment.push([dist_tmp, segment_tmp.reverse()]);\r\n }\r\n\r\n [dist_tmp, segment_tmp] = Distance.point2arc(arc2.end, arc1);\r\n if (segment_tmp.end.on(arc1)) {\r\n dist_and_segment.push([dist_tmp, segment_tmp.reverse()]);\r\n }\r\n\r\n [dist_tmp, segment_tmp] = Distance.point2point(arc1.start, arc2.start);\r\n dist_and_segment.push([dist_tmp, segment_tmp]);\r\n\r\n [dist_tmp, segment_tmp] = Distance.point2point(arc1.start, arc2.end);\r\n dist_and_segment.push([dist_tmp, segment_tmp]);\r\n\r\n [dist_tmp, segment_tmp] = Distance.point2point(arc1.end, arc2.start);\r\n dist_and_segment.push([dist_tmp, segment_tmp]);\r\n\r\n [dist_tmp, segment_tmp] = Distance.point2point(arc1.end, arc2.end);\r\n dist_and_segment.push([dist_tmp, segment_tmp]);\r\n\r\n Distance.sort(dist_and_segment);\r\n\r\n return dist_and_segment[0];\r\n }\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between point and polygon\r\n * @param point\r\n * @param polygon\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static point2polygon(point, polygon) {\r\n let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Flatten.Segment()];\r\n for (let edge of polygon.edges) {\r\n let [dist, shortest_segment] = (edge.shape instanceof Flatten.Segment) ?\r\n Distance.point2segment(point, edge.shape) : Distance.point2arc(point, edge.shape);\r\n if (Flatten.Utils.LT(dist, min_dist_and_segment[0])) {\r\n min_dist_and_segment = [dist, shortest_segment];\r\n }\r\n }\r\n return min_dist_and_segment;\r\n }\r\n\r\n static shape2polygon(shape, polygon) {\r\n let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Flatten.Segment()];\r\n for (let edge of polygon.edges) {\r\n let [dist, shortest_segment] = shape.distanceTo(edge.shape);\r\n if (Flatten.Utils.LT(dist, min_dist_and_segment[0])) {\r\n min_dist_and_segment = [dist, shortest_segment];\r\n }\r\n }\r\n return min_dist_and_segment;\r\n }\r\n\r\n /**\r\n * Calculate distance and shortest segment between two polygons\r\n * @param polygon1\r\n * @param polygon2\r\n * @returns {Number | Segment} - distance and shortest segment\r\n */\r\n static polygon2polygon(polygon1, polygon2) {\r\n let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Flatten.Segment()];\r\n for (let edge1 of polygon1.edges) {\r\n for (let edge2 of polygon2.edges) {\r\n let [dist, shortest_segment] = edge1.shape.distanceTo(edge2.shape);\r\n if (Flatten.Utils.LT(dist, min_dist_and_segment[0])) {\r\n min_dist_and_segment = [dist, shortest_segment];\r\n }\r\n }\r\n }\r\n return min_dist_and_segment;\r\n }\r\n\r\n /**\r\n * Returns [mindist, maxdist] array of squared minimal and maximal distance between boxes\r\n * Minimal distance by x is\r\n * (box2.xmin - box1.xmax), if box1 is left to box2\r\n * (box1.xmin - box2.xmax), if box2 is left to box1\r\n * 0, if box1 and box2 are intersected by x\r\n * Minimal distance by y is defined in the same way\r\n *\r\n * Maximal distance is estimated as a sum of squared dimensions of the merged box\r\n *\r\n * @param box1\r\n * @param box2\r\n * @returns {Number | Number} - minimal and maximal distance\r\n */\r\n static box2box_minmax(box1, box2) {\r\n let mindist_x = Math.max(Math.max(box1.xmin - box2.xmax, 0), Math.max(box2.xmin - box1.xmax, 0));\r\n let mindist_y = Math.max(Math.max(box1.ymin - box2.ymax, 0), Math.max(box2.ymin - box1.ymax, 0));\r\n let mindist = mindist_x * mindist_x + mindist_y * mindist_y;\r\n\r\n let box = box1.merge(box2);\r\n let dx = box.xmax - box.xmin;\r\n let dy = box.ymax - box.ymin;\r\n let maxdist = dx * dx + dy * dy;\r\n\r\n return [mindist, maxdist];\r\n }\r\n\r\n static minmax_tree_process_level(shape, level, min_stop, tree) {\r\n // Calculate minmax distance to each shape in current level\r\n // Insert result into the interval tree for further processing\r\n // update min_stop with maxdist, it will be the new stop distance\r\n let mindist, maxdist;\r\n for (let node of level) {\r\n\r\n // [mindist, maxdist] = Distance.box2box_minmax(shape.box, node.max);\r\n // if (Flatten.Utils.GT(mindist, min_stop))\r\n // continue;\r\n\r\n // Estimate min-max dist to the shape stored in the node.item, using node.item.key which is shape's box\r\n [mindist, maxdist] = Distance.box2box_minmax(shape.box, node.item.key);\r\n if (node.item.value instanceof Flatten.Edge) {\r\n tree.insert([mindist, maxdist], node.item.value.shape);\r\n } else {\r\n tree.insert([mindist, maxdist], node.item.value);\r\n }\r\n if (Flatten.Utils.LT(maxdist, min_stop)) {\r\n min_stop = maxdist; // this will be the new distance estimation\r\n }\r\n }\r\n\r\n if (level.length === 0)\r\n return min_stop;\r\n\r\n // Calculate new level from left and right children of the current\r\n let new_level_left = level.map(node => node.left.isNil() ? undefined : node.left).filter(node => node !== undefined);\r\n let new_level_right = level.map(node => node.right.isNil() ? undefined : node.right).filter(node => node !== undefined);\r\n // Merge left and right subtrees and leave only relevant subtrees\r\n let new_level = [...new_level_left, ...new_level_right].filter(node => {\r\n // Node subtree quick reject, node.max is a subtree box\r\n let [mindist, maxdist] = Distance.box2box_minmax(shape.box, node.max);\r\n return (Flatten.Utils.LE(mindist, min_stop));\r\n });\r\n\r\n min_stop = Distance.minmax_tree_process_level(shape, new_level, min_stop, tree);\r\n return min_stop;\r\n }\r\n\r\n /**\r\n * Calculates sorted tree of [mindist, maxdist] intervals between query shape\r\n * and shapes of the planar set.\r\n * @param shape\r\n * @param set\r\n */\r\n static minmax_tree(shape, set, min_stop) {\r\n let tree = new IntervalTree();\r\n let level = [set.index.root];\r\n let squared_min_stop = min_stop < Number.POSITIVE_INFINITY ? min_stop * min_stop : Number.POSITIVE_INFINITY;\r\n squared_min_stop = Distance.minmax_tree_process_level(shape, level, squared_min_stop, tree);\r\n return tree;\r\n }\r\n\r\n static minmax_tree_calc_distance(shape, node, min_dist_and_segment) {\r\n let min_dist_and_segment_new, stop;\r\n if (node != null && !node.isNil()) {\r\n [min_dist_and_segment_new, stop] = Distance.minmax_tree_calc_distance(shape, node.left, min_dist_and_segment);\r\n\r\n if (stop) {\r\n return [min_dist_and_segment_new, stop];\r\n }\r\n\r\n if (Flatten.Utils.LT(min_dist_and_segment_new[0], Math.sqrt(node.item.key.low))) {\r\n return [min_dist_and_segment_new, true]; // stop condition\r\n }\r\n\r\n let [dist, shortest_segment] = Distance.distance(shape, node.item.value);\r\n // console.log(dist)\r\n if (Flatten.Utils.LT(dist, min_dist_and_segment_new[0])) {\r\n min_dist_and_segment_new = [dist, shortest_segment];\r\n }\r\n\r\n [min_dist_and_segment_new, stop] = Distance.minmax_tree_calc_distance(shape, node.right, min_dist_and_segment_new);\r\n\r\n return [min_dist_and_segment_new, stop];\r\n }\r\n\r\n return [min_dist_and_segment, false];\r\n }\r\n\r\n /**\r\n * Calculates distance between shape and Planar Set of shapes\r\n * @param shape\r\n * @param {PlanarSet} set\r\n * @param {Number} min_stop\r\n * @returns {*}\r\n */\r\n static shape2planarSet(shape, set, min_stop = Number.POSITIVE_INFINITY) {\r\n let min_dist_and_segment = [min_stop, new Flatten.Segment()];\r\n let stop = false;\r\n if (set instanceof Flatten.PlanarSet) {\r\n let tree = Distance.minmax_tree(shape, set, min_stop);\r\n [min_dist_and_segment, stop] = Distance.minmax_tree_calc_distance(shape, tree.root, min_dist_and_segment);\r\n }\r\n return min_dist_and_segment;\r\n }\r\n\r\n static sort(dist_and_segment) {\r\n dist_and_segment.sort((d1, d2) => {\r\n if (Flatten.Utils.LT(d1[0], d2[0])) {\r\n return -1;\r\n }\r\n if (Flatten.Utils.GT(d1[0], d2[0])) {\r\n return 1;\r\n }\r\n return 0;\r\n });\r\n }\r\n\r\n static distance(shape1, shape2) {\r\n return shape1.distanceTo(shape2);\r\n }\r\n}\r\n\r\nFlatten.Distance = Distance;\r\n\r\n/**\r\n * Created by Alex Bol on 2/18/2017.\r\n */\r\n\r\nFlatten.BooleanOperations = BooleanOperations;\r\nFlatten.Relations = Relations;\r\n\r\nexport default Flatten;\r\nexport { Arc, BOUNDARY, BooleanOperations, Box, CCW, CW, Circle, Distance, Edge, errors as Errors, Face, INSIDE, Inversion, Line, Matrix, Multiline, ORIENTATION, OUTSIDE, PlanarSet, Point, Polygon, Ray, Relations, Segment, Utils, Vector, arc, box, circle, inversion, line, matrix, multiline, point, polygon, ray, ray_shoot, segment, vector };\r\n","(function(f){if(typeof exports===\"object\"&&typeof module!==\"undefined\"){module.exports=f()}else if(typeof define===\"function\"&&define.amd){define([],f)}else{var g;if(typeof window!==\"undefined\"){g=window}else if(typeof global!==\"undefined\"){g=global}else if(typeof self!==\"undefined\"){g=self}else{g=this}g.ELK = f()}})(function(){var define,module,exports;return (function(){function r(e,n,t){function o(i,f){if(!n[i]){if(!e[i]){var c=\"function\"==typeof require&&require;if(!f&&c)return c(i,!0);if(u)return u(i,!0);var a=new Error(\"Cannot find module '\"+i+\"'\");throw a.code=\"MODULE_NOT_FOUND\",a}var p=n[i]={exports:{}};e[i][0].call(p.exports,function(r){var n=e[i][1][r];return o(n||r)},p,p.exports,r,e,n,t)}return n[i].exports}for(var u=\"function\"==typeof require&&require,i=0;i 0 && arguments[0] !== undefined ? arguments[0] : {},\n _ref$defaultLayoutOpt = _ref.defaultLayoutOptions,\n defaultLayoutOptions = _ref$defaultLayoutOpt === undefined ? {} : _ref$defaultLayoutOpt,\n _ref$algorithms = _ref.algorithms,\n algorithms = _ref$algorithms === undefined ? ['layered', 'stress', 'mrtree', 'radial', 'force', 'disco', 'sporeOverlap', 'sporeCompaction', 'rectpacking'] : _ref$algorithms,\n workerFactory = _ref.workerFactory,\n workerUrl = _ref.workerUrl;\n\n _classCallCheck(this, ELK);\n\n this.defaultLayoutOptions = defaultLayoutOptions;\n this.initialized = false;\n\n // check valid worker construction possible\n if (typeof workerUrl === 'undefined' && typeof workerFactory === 'undefined') {\n throw new Error(\"Cannot construct an ELK without both 'workerUrl' and 'workerFactory'.\");\n }\n var factory = workerFactory;\n if (typeof workerUrl !== 'undefined' && typeof workerFactory === 'undefined') {\n // use default Web Worker\n factory = function factory(url) {\n return new Worker(url);\n };\n }\n\n // create the worker\n var worker = factory(workerUrl);\n if (typeof worker.postMessage !== 'function') {\n throw new TypeError(\"Created worker does not provide\" + \" the required 'postMessage' function.\");\n }\n\n // wrap the worker to 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b,c,d,e,f,g,h,i;g=0;f=a.f.e;for(d=0;d>5;if(e>=a.d){return a.e<0}c=a.a[e];b=1<<(b&31);if(a.e<0){d=Mgb(a);if(e>16)),15).Xc(f);if(h0){!(fad(a.a.c)&&b.n.d)&&!(gad(a.a.c)&&b.n.b)&&(b.g.d+=$wnd.Math.max(0,d/2-0.5));!(fad(a.a.c)&&b.n.a)&&!(gad(a.a.c)&&b.n.c)&&(b.g.a-=d-1)}}}\nfunction N3b(a){var b,c,d,e,f;e=new Rkb;f=O3b(a,e);b=BD(vNb(a,(wtc(),gtc)),10);if(b){for(d=new olb(b.j);d.a>b;f=a.m>>b|c<<22-b;e=a.l>>b|a.m<<22-b}else if(b<44){g=d?Fje:0;f=c>>b-22;e=a.m>>b-22|c<<44-b}else{g=d?Fje:0;f=d?Eje:0;e=c>>b-44}return TC(e&Eje,f&Eje,g&Fje)}\nfunction XOb(a){var b,c,d,e,f,g;this.c=new Rkb;this.d=a;d=Pje;e=Pje;b=Qje;c=Qje;for(g=Jsb(a,0);g.b!=g.d.c;){f=BD(Xsb(g),8);d=$wnd.Math.min(d,f.a);e=$wnd.Math.min(e,f.b);b=$wnd.Math.max(b,f.a);c=$wnd.Math.max(c,f.b)}this.a=new J6c(d,e,b-d,c-e)}\nfunction Dac(a,b){var c,d,e,f,g,h;for(f=new 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0}\nfunction aNc(a,b){var c,d,e,f,g;f=b.a;f.c.i==b.b?(g=f.d):(g=f.c);f.c.i==b.b?(d=f.c):(d=f.d);e=NLc(a.a,g,d);if(e>0&&e0}else if(e<0&&-e0}return false}\nfunction RZc(a,b,c,d){var e,f,g,h,i,j,k,l;e=(b-a.d)/a.c.c.length;f=0;a.a+=c;a.d=b;for(l=new olb(a.c);l.a>24}return g}\nfunction vdb(a){if(a.pe()){var b=a.c;b.qe()?(a.o='['+b.n):!b.pe()?(a.o='[L'+b.ne()+';'):(a.o='['+b.ne());a.b=b.me()+'[]';a.k=b.oe()+'[]';return}var c=a.j;var d=a.d;d=d.split('/');a.o=ydb('.',[c,ydb('$',d)]);a.b=ydb('.',[c,ydb('.',d)]);a.k=d[d.length-1]}\nfunction qGb(a,b){var c,d,e,f,g;g=null;for(f=new olb(a.e.a);f.a=0;b-=2){for(c=0;c<=b;c+=2){if(a.b[c]>a.b[c+2]||a.b[c]===a.b[c+2]&&a.b[c+1]>a.b[c+3]){d=a.b[c+2];a.b[c+2]=a.b[c];a.b[c]=d;d=a.b[c+3];a.b[c+3]=a.b[c+1];a.b[c+1]=d}}}a.c=true}\nfunction UUb(a,b){var c,d,e,f,g,h,i,j;g=b==1?KUb:JUb;for(f=g.a.ec().Kc();f.Ob();){e=BD(f.Pb(),103);for(i=BD(Qc(a.f.c,e),21).Kc();i.Ob();){h=BD(i.Pb(),46);d=BD(h.b,81);j=BD(h.a,189);c=j.c;switch(e.g){case 2:case 1:d.g.d+=c;break;case 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f,g;if((!OZb(b)&&b.c.i.c==b.d.i.c||!T6c(l7c(OC(GC(m1,1),nie,8,0,[e.i.n,e.n,e.a])),c))&&!OZb(b)){b.c==e?St(b.a,0,new g7c(c)):Dsb(b.a,new g7c(c));if(d&&!Rqb(a.a,c)){g=BD(vNb(b,(Nyc(),jxc)),74);if(!g){g=new s7c;yNb(b,jxc,g)}f=new g7c(c);Gsb(g,f,g.c.b,g.c);Qqb(a.a,f)}}}\nfunction Qac(a){var b,c;for(c=new Sr(ur(R_b(a).a.Kc(),new Sq));Qr(c);){b=BD(Rr(c),17);if(b.c.i.k!=(j0b(),f0b)){throw vbb(new y2c(Fne+P_b(a)+\"' has its layer constraint set to FIRST, but has at least one incoming edge that \"+' does not come from a FIRST_SEPARATE node. 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d,e,f,g,h,i,j,k;f=Edb(ED(a.b.Kc().Pb()));j=Edb(ED(Pq(b.b)));d=Y6c(R6c(a.a),j-c);e=Y6c(R6c(b.a),c-f);k=P6c(d,e);Y6c(k,1/(j-f));this.a=k;this.b=new Rkb;h=true;g=a.b.Kc();g.Pb();while(g.Ob()){i=Edb(ED(g.Pb()));if(h&&i-c>Oqe){this.b.Fc(c);h=false}this.b.Fc(i)}h&&this.b.Fc(c)}\nfunction vGb(a){var b,c,d,e;yGb(a,a.n);if(a.d.c.length>0){Blb(a.c);while(GGb(a,BD(mlb(new olb(a.e.a)),121))>5;b&=31;if(d>=a.d){return a.e<0?(Hgb(),Bgb):(Hgb(),Ggb)}f=a.d-d;e=KC(WD,oje,25,f+1,15,1);mhb(e,f,a.a,d,b);if(a.e<0){for(c=0;c0&&a.a[c]<<32-b!=0){for(c=0;c=0){return false}else{c=e1d((O6d(),M6d),e,b);if(!c){return true}else{d=c.Zj();return (d>1||d==-1)&&$1d(q1d(M6d,c))!=3}}}}else{return false}}\nfunction R1b(a,b,c,d){var e,f,g,h,i;h=atd(BD(qud((!b.b&&(b.b=new y5d(z2,b,4,7)),b.b),0),82));i=atd(BD(qud((!b.c&&(b.c=new y5d(z2,b,5,8)),b.c),0),82));if(Xod(h)==Xod(i)){return null}if(ntd(i,h)){return null}g=Mld(b);if(g==c){return d}else{f=BD(Ohb(a.a,g),10);if(f){e=f.e;if(e){return e}}}return null}\nfunction Cac(a,b){var 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