From c5eae2cf99c5f543c3f4fc6db88b8dee4a9e30d7 Mon Sep 17 00:00:00 2001 From: amandaghassaei Date: Sun, 26 Feb 2017 05:40:05 -0500 Subject: [PATCH] eod --- dependencies/earcut.js | 645 +++++++++++++++++++++++++++++++++++++++++ index.html | 7 +- js/globals.js | 2 +- js/pattern.js | 140 ++++++++- 4 files changed, 782 insertions(+), 12 deletions(-) create mode 100755 dependencies/earcut.js diff --git a/dependencies/earcut.js b/dependencies/earcut.js new file mode 100755 index 0000000..4b9dde7 --- /dev/null +++ b/dependencies/earcut.js @@ -0,0 +1,645 @@ +'use strict'; + +module.exports = earcut; + +function earcut(data, holeIndices, dim) { + + dim = dim || 2; + + var hasHoles = holeIndices && holeIndices.length, + outerLen = hasHoles ? holeIndices[0] * dim : data.length, + outerNode = linkedList(data, 0, outerLen, dim, true), + triangles = []; + + if (!outerNode) return triangles; + + var minX, minY, maxX, maxY, x, y, size; + + if (hasHoles) outerNode = eliminateHoles(data, holeIndices, outerNode, dim); + + // if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox + if (data.length > 80 * dim) { + minX = maxX = data[0]; + minY = maxY = data[1]; + + for (var i = dim; i < outerLen; i += dim) { + x = data[i]; + y = data[i + 1]; + if (x < minX) minX = x; + if (y < minY) minY = y; + if (x > maxX) maxX = x; + if (y > maxY) maxY = y; + } + + // minX, minY and size are later used to transform coords into integers for z-order calculation + size = Math.max(maxX - minX, maxY - minY); + } + + earcutLinked(outerNode, triangles, dim, minX, minY, size); + + return triangles; +} + +// create a circular doubly linked list from polygon points in the specified winding order +function linkedList(data, start, end, dim, clockwise) { + var i, last; + + if (clockwise === (signedArea(data, start, end, dim) > 0)) { + for (i = start; i < end; i += dim) last = insertNode(i, data[i], data[i + 1], last); + } else { + for (i = end - dim; i >= start; i -= dim) last = insertNode(i, data[i], data[i + 1], last); + } + + if (last && equals(last, last.next)) { + removeNode(last); + last = last.next; + } + + return last; +} + +// eliminate colinear or duplicate points +function filterPoints(start, end) { + if (!start) return start; + if (!end) end = start; + + var p = start, + again; + do { + again = false; + + if (!p.steiner && (equals(p, p.next) || area(p.prev, p, p.next) === 0)) { + removeNode(p); + p = end = p.prev; + if (p === p.next) return null; + again = true; + + } else { + p = p.next; + } + } while (again || p !== end); + + return end; +} + +// main ear slicing loop which triangulates a polygon (given as a linked list) +function earcutLinked(ear, triangles, dim, minX, minY, size, pass) { + if (!ear) return; + + // interlink polygon nodes in z-order + if (!pass && size) indexCurve(ear, minX, minY, size); + + var stop = ear, + prev, next; + + // iterate through ears, slicing them one by one + while (ear.prev !== ear.next) { + prev = ear.prev; + next = ear.next; + + if (size ? isEarHashed(ear, minX, minY, size) : isEar(ear)) { + // cut off the triangle + triangles.push(prev.i / dim); + triangles.push(ear.i / dim); + triangles.push(next.i / dim); + + removeNode(ear); + + // skipping the next vertice leads to less sliver triangles + ear = next.next; + stop = next.next; + + continue; + } + + ear = next; + + // if we looped through the whole remaining polygon and can't find any more ears + if (ear === stop) { + // try filtering points and slicing again + if (!pass) { + earcutLinked(filterPoints(ear), triangles, dim, minX, minY, size, 1); + + // if this didn't work, try curing all small self-intersections locally + } else if (pass === 1) { + ear = cureLocalIntersections(ear, triangles, dim); + earcutLinked(ear, triangles, dim, minX, minY, size, 2); + + // as a last resort, try splitting the remaining polygon into two + } else if (pass === 2) { + splitEarcut(ear, triangles, dim, minX, minY, size); + } + + break; + } + } +} + +// check whether a polygon node forms a valid ear with adjacent nodes +function isEar(ear) { + var a = ear.prev, + b = ear, + c = ear.next; + + if (area(a, b, c) >= 0) return false; // reflex, can't be an ear + + // now make sure we don't have other points inside the potential ear + var p = ear.next.next; + + while (p !== ear.prev) { + if (pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) && + area(p.prev, p, p.next) >= 0) return false; + p = p.next; + } + + return true; +} + +function isEarHashed(ear, minX, minY, size) { + var a = ear.prev, + b = ear, + c = ear.next; + + if (area(a, b, c) >= 0) return false; // reflex, can't be an ear + + // triangle bbox; min & max are calculated like this for speed + var minTX = a.x < b.x ? (a.x < c.x ? a.x : c.x) : (b.x < c.x ? b.x : c.x), + minTY = a.y < b.y ? (a.y < c.y ? a.y : c.y) : (b.y < c.y ? b.y : c.y), + maxTX = a.x > b.x ? (a.x > c.x ? a.x : c.x) : (b.x > c.x ? b.x : c.x), + maxTY = a.y > b.y ? (a.y > c.y ? a.y : c.y) : (b.y > c.y ? b.y : c.y); + + // z-order range for the current triangle bbox; + var minZ = zOrder(minTX, minTY, minX, minY, size), + maxZ = zOrder(maxTX, maxTY, minX, minY, size); + + // first look for points inside the triangle in increasing z-order + var p = ear.nextZ; + + while (p && p.z <= maxZ) { + if (p !== ear.prev && p !== ear.next && + pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) && + area(p.prev, p, p.next) >= 0) return false; + p = p.nextZ; + } + + // then look for points in decreasing z-order + p = ear.prevZ; + + while (p && p.z >= minZ) { + if (p !== ear.prev && p !== ear.next && + pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) && + area(p.prev, p, p.next) >= 0) return false; + p = p.prevZ; + } + + return true; +} + +// go through all polygon nodes and cure small local self-intersections +function cureLocalIntersections(start, triangles, dim) { + var p = start; + do { + var a = p.prev, + b = p.next.next; + + if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) { + + triangles.push(a.i / dim); + triangles.push(p.i / dim); + triangles.push(b.i / dim); + + // remove two nodes involved + removeNode(p); + removeNode(p.next); + + p = start = b; + } + p = p.next; + } while (p !== start); + + return p; +} + +// try splitting polygon into two and triangulate them independently +function splitEarcut(start, triangles, dim, minX, minY, size) { + // look for a valid diagonal that divides the polygon into two + var a = start; + do { + var b = a.next.next; + while (b !== a.prev) { + if (a.i !== b.i && isValidDiagonal(a, b)) { + // split the polygon in two by the diagonal + var c = splitPolygon(a, b); + + // filter colinear points around the cuts + a = filterPoints(a, a.next); + c = filterPoints(c, c.next); + + // run earcut on each half + earcutLinked(a, triangles, dim, minX, minY, size); + earcutLinked(c, triangles, dim, minX, minY, size); + return; + } + b = b.next; + } + a = a.next; + } while (a !== start); +} + +// link every hole into the outer loop, producing a single-ring polygon without holes +function eliminateHoles(data, holeIndices, outerNode, dim) { + var queue = [], + i, len, start, end, list; + + for (i = 0, len = holeIndices.length; i < len; i++) { + start = holeIndices[i] * dim; + end = i < len - 1 ? holeIndices[i + 1] * dim : data.length; + list = linkedList(data, start, end, dim, false); + if (list === list.next) list.steiner = true; + queue.push(getLeftmost(list)); + } + + queue.sort(compareX); + + // process holes from left to right + for (i = 0; i < queue.length; i++) { + eliminateHole(queue[i], outerNode); + outerNode = filterPoints(outerNode, outerNode.next); + } + + return outerNode; +} + +function compareX(a, b) { + return a.x - b.x; +} + +// find a bridge between vertices that connects hole with an outer ring and and link it +function eliminateHole(hole, outerNode) { + outerNode = findHoleBridge(hole, outerNode); + if (outerNode) { + var b = splitPolygon(outerNode, hole); + filterPoints(b, b.next); + } +} + +// David Eberly's algorithm for finding a bridge between hole and outer polygon +function findHoleBridge(hole, outerNode) { + var p = outerNode, + hx = hole.x, + hy = hole.y, + qx = -Infinity, + m; + + // find a segment intersected by a ray from the hole's leftmost point to the left; + // segment's endpoint with lesser x will be potential connection point + do { + if (hy <= p.y && hy >= p.next.y && p.next.y !== p.y) { + var x = p.x + (hy - p.y) * (p.next.x - p.x) / (p.next.y - p.y); + if (x <= hx && x > qx) { + qx = x; + if (x === hx) { + if (hy === p.y) return p; + if (hy === p.next.y) return p.next; + } + m = p.x < p.next.x ? p : p.next; + } + } + p = p.next; + } while (p !== outerNode); + + if (!m) return null; + + if (hx === qx) return m.prev; // hole touches outer segment; pick lower endpoint + + // look for points inside the triangle of hole point, segment intersection and endpoint; + // if there are no points found, we have a valid connection; + // otherwise choose the point of the minimum angle with the ray as connection point + + var stop = m, + mx = m.x, + my = m.y, + tanMin = Infinity, + tan; + + p = m.next; + + while (p !== stop) { + if (hx >= p.x && p.x >= mx && hx !== p.x && + pointInTriangle(hy < my ? hx : qx, hy, mx, my, hy < my ? qx : hx, hy, p.x, p.y)) { + + tan = Math.abs(hy - p.y) / (hx - p.x); // tangential + + if ((tan < tanMin || (tan === tanMin && p.x > m.x)) && locallyInside(p, hole)) { + m = p; + tanMin = tan; + } + } + + p = p.next; + } + + return m; +} + +// interlink polygon nodes in z-order +function indexCurve(start, minX, minY, size) { + var p = start; + do { + if (p.z === null) p.z = zOrder(p.x, p.y, minX, minY, size); + p.prevZ = p.prev; + p.nextZ = p.next; + p = p.next; + } while (p !== start); + + p.prevZ.nextZ = null; + p.prevZ = null; + + sortLinked(p); +} + +// Simon Tatham's linked list merge sort algorithm +// http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html +function sortLinked(list) { + var i, p, q, e, tail, numMerges, pSize, qSize, + inSize = 1; + + do { + p = list; + list = null; + tail = null; + numMerges = 0; + + while (p) { + numMerges++; + q = p; + pSize = 0; + for (i = 0; i < inSize; i++) { + pSize++; + q = q.nextZ; + if (!q) break; + } + + qSize = inSize; + + while (pSize > 0 || (qSize > 0 && q)) { + + if (pSize === 0) { + e = q; + q = q.nextZ; + qSize--; + } else if (qSize === 0 || !q) { + e = p; + p = p.nextZ; + pSize--; + } else if (p.z <= q.z) { + e = p; + p = p.nextZ; + pSize--; + } else { + e = q; + q = q.nextZ; + qSize--; + } + + if (tail) tail.nextZ = e; + else list = e; + + e.prevZ = tail; + tail = e; + } + + p = q; + } + + tail.nextZ = null; + inSize *= 2; + + } while (numMerges > 1); + + return list; +} + +// z-order of a point given coords and size of the data bounding box +function zOrder(x, y, minX, minY, size) { + // coords are transformed into non-negative 15-bit integer range + x = 32767 * (x - minX) / size; + y = 32767 * (y - minY) / size; + + x = (x | (x << 8)) & 0x00FF00FF; + x = (x | (x << 4)) & 0x0F0F0F0F; + x = (x | (x << 2)) & 0x33333333; + x = (x | (x << 1)) & 0x55555555; + + y = (y | (y << 8)) & 0x00FF00FF; + y = (y | (y << 4)) & 0x0F0F0F0F; + y = (y | (y << 2)) & 0x33333333; + y = (y | (y << 1)) & 0x55555555; + + return x | (y << 1); +} + +// find the leftmost node of a polygon ring +function getLeftmost(start) { + var p = start, + leftmost = start; + do { + if (p.x < leftmost.x) leftmost = p; + p = p.next; + } while (p !== start); + + return leftmost; +} + +// check if a point lies within a convex triangle +function pointInTriangle(ax, ay, bx, by, cx, cy, px, py) { + return (cx - px) * (ay - py) - (ax - px) * (cy - py) >= 0 && + (ax - px) * (by - py) - (bx - px) * (ay - py) >= 0 && + (bx - px) * (cy - py) - (cx - px) * (by - py) >= 0; +} + +// check if a diagonal between two polygon nodes is valid (lies in polygon interior) +function isValidDiagonal(a, b) { + return a.next.i !== b.i && a.prev.i !== b.i && !intersectsPolygon(a, b) && + locallyInside(a, b) && locallyInside(b, a) && middleInside(a, b); +} + +// signed area of a triangle +function area(p, q, r) { + return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y); +} + +// check if two points are equal +function equals(p1, p2) { + return p1.x === p2.x && p1.y === p2.y; +} + +// check if two segments intersect +function intersects(p1, q1, p2, q2) { + if ((equals(p1, q1) && equals(p2, q2)) || + (equals(p1, q2) && equals(p2, q1))) return true; + return area(p1, q1, p2) > 0 !== area(p1, q1, q2) > 0 && + area(p2, q2, p1) > 0 !== area(p2, q2, q1) > 0; +} + +// check if a polygon diagonal intersects any polygon segments +function intersectsPolygon(a, b) { + var p = a; + do { + if (p.i !== a.i && p.next.i !== a.i && p.i !== b.i && p.next.i !== b.i && + intersects(p, p.next, a, b)) return true; + p = p.next; + } while (p !== a); + + return false; +} + +// check if a polygon diagonal is locally inside the polygon +function locallyInside(a, b) { + return area(a.prev, a, a.next) < 0 ? + area(a, b, a.next) >= 0 && area(a, a.prev, b) >= 0 : + area(a, b, a.prev) < 0 || area(a, a.next, b) < 0; +} + +// check if the middle point of a polygon diagonal is inside the polygon +function middleInside(a, b) { + var p = a, + inside = false, + px = (a.x + b.x) / 2, + py = (a.y + b.y) / 2; + do { + if (((p.y > py) !== (p.next.y > py)) && p.next.y !== p.y && + (px < (p.next.x - p.x) * (py - p.y) / (p.next.y - p.y) + p.x)) + inside = !inside; + p = p.next; + } while (p !== a); + + return inside; +} + +// link two polygon vertices with a bridge; if the vertices belong to the same ring, it splits polygon into two; +// if one belongs to the outer ring and another to a hole, it merges it into a single ring +function splitPolygon(a, b) { + var a2 = new Node(a.i, a.x, a.y), + b2 = new Node(b.i, b.x, b.y), + an = a.next, + bp = b.prev; + + a.next = b; + b.prev = a; + + a2.next = an; + an.prev = a2; + + b2.next = a2; + a2.prev = b2; + + bp.next = b2; + b2.prev = bp; + + return b2; +} + +// create a node and optionally link it with previous one (in a circular doubly linked list) +function insertNode(i, x, y, last) { + var p = new Node(i, x, y); + + if (!last) { + p.prev = p; + p.next = p; + + } else { + p.next = last.next; + p.prev = last; + last.next.prev = p; + last.next = p; + } + return p; +} + +function removeNode(p) { + p.next.prev = p.prev; + p.prev.next = p.next; + + if (p.prevZ) p.prevZ.nextZ = p.nextZ; + if (p.nextZ) p.nextZ.prevZ = p.prevZ; +} + +function Node(i, x, y) { + // vertice index in coordinates array + this.i = i; + + // vertex coordinates + this.x = x; + this.y = y; + + // previous and next vertice nodes in a polygon ring + this.prev = null; + this.next = null; + + // z-order curve value + this.z = null; + + // previous and next nodes in z-order + this.prevZ = null; + this.nextZ = null; + + // indicates whether this is a steiner point + this.steiner = false; +} + +// return a percentage difference between the polygon area and its triangulation area; +// used to verify correctness of triangulation +earcut.deviation = function (data, holeIndices, dim, triangles) { + var hasHoles = holeIndices && holeIndices.length; + var outerLen = hasHoles ? holeIndices[0] * dim : data.length; + + var polygonArea = Math.abs(signedArea(data, 0, outerLen, dim)); + if (hasHoles) { + for (var i = 0, len = holeIndices.length; i < len; i++) { + var start = holeIndices[i] * dim; + var end = i < len - 1 ? holeIndices[i + 1] * dim : data.length; + polygonArea -= Math.abs(signedArea(data, start, end, dim)); + } + } + + var trianglesArea = 0; + for (i = 0; i < triangles.length; i += 3) { + var a = triangles[i] * dim; + var b = triangles[i + 1] * dim; + var c = triangles[i + 2] * dim; + trianglesArea += Math.abs( + (data[a] - data[c]) * (data[b + 1] - data[a + 1]) - + (data[a] - data[b]) * (data[c + 1] - data[a + 1])); + } + + return polygonArea === 0 && trianglesArea === 0 ? 0 : + Math.abs((trianglesArea - polygonArea) / polygonArea); +}; + +function signedArea(data, start, end, dim) { + var sum = 0; + for (var i = start, j = end - dim; i < end; i += dim) { + sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]); + j = i; + } + return sum; +} + +// turn a polygon in a multi-dimensional array form (e.g. as in GeoJSON) into a form Earcut accepts +earcut.flatten = function (data) { + var dim = data[0][0].length, + result = {vertices: [], holes: [], dimensions: dim}, + holeIndex = 0; + + for (var i = 0; i < data.length; i++) { + for (var j = 0; j < data[i].length; j++) { + for (var d = 0; d < dim; d++) result.vertices.push(data[i][j][d]); + } + if (i > 0) { + holeIndex += data[i - 1].length; + result.holes.push(holeIndex); + } + } + return result; +}; diff --git a/index.html b/index.html index bc6f1af..57498c0 100644 --- a/index.html +++ b/index.html @@ -353,8 +353,11 @@

Origami Simulator

- lakfjsdlkfjladskj -
+ http://www2.eng.cam.ac.uk/~sdg/preprint/5OSME.pdf + http://origami.c.u-tokyo.ac.jp/~tachi/cg/SimulationOfRigidOrigami_tachi_4OSME.pdf + https://github.com/mapbox/earcut + +

Built by Amanda Ghassaei as a homework assignment for Geometric Folding Algorithms. Code available on Github.

diff --git a/js/globals.js b/js/globals.js index bcc60d1..fc59acf 100644 --- a/js/globals.js +++ b/js/globals.js @@ -31,7 +31,7 @@ function initGlobals(){ density: 1, //import pattern settings - vertTol: 0.01,//vertex merge tolerange + vertTol: 0.01//vertex merge tolerange }; diff --git a/js/pattern.js b/js/pattern.js index 3012489..a40e90e 100644 --- a/js/pattern.js +++ b/js/pattern.js @@ -6,6 +6,8 @@ function initPattern(globals){ var object3D = new THREE.Object3D(); globals.threeView.sceneAddModel(object3D); + // var intersections = new THREE.Object3D(); + // object3D.add(intersections); var verticesRaw = [];//list of vertex3's //refs to vertex indices @@ -46,11 +48,13 @@ function initPattern(globals){ var stroke = $(this).attr("stroke").toLowerCase(); return stroke == "#ff0000" || stroke == "#f00"; }); + $mountains.css({'stroke-dasharray':'12, 6, 3, 6'}); var $valleys = $paths.filter(function(){ var stroke = $(this).attr("stroke").toLowerCase(); return stroke == "#0000ff" || stroke == "#00f"; }); + $valleys.css({'stroke-dasharray':'7, 6, 7, 6'}); var $cuts = $paths.filter(function(){ var stroke = $(this).attr("stroke").toLowerCase(); @@ -138,26 +142,144 @@ function initPattern(globals){ parsePath(_verticesRaw, _valleysRaw, $valleys); parsePath(_verticesRaw, _cutsRaw, $cuts); - findIntersections(_verticesRaw, _outlinesRaw, _mountainsRaw, _valleysRaw); + findIntersections(_verticesRaw, _outlinesRaw, _mountainsRaw, _valleysRaw, _cutsRaw); verticesRaw = _verticesRaw; outlinesRaw = _outlinesRaw; mountainsRaw = _mountainsRaw; valleysRaw = _valleysRaw; cutsRaw = _cutsRaw; - mergeVertices(globals.vertTol); + mergeVertices(); drawPattern(); } - function mergeVertices(tol){ - vertices = verticesRaw; - outlines = outlinesRaw; - mountains = mountainsRaw; - valleys = valleysRaw; - cuts = cutsRaw; + function mergeVertices(){ + + vertices = verticesRaw.slice(); + + var tolSq = globals.vertTol*globals.vertTol; + var combined = []; + var mergedVertices = []; + var diff = 1; + for (var i=vertices.length-1;i>=0;i--){ + var _combined = []; + for (var j=i-diff;j>=0;j--){ + if ((vertices[i].clone().sub(vertices[j])).lengthSq()0){ + _combined.push(i); + mergedVertices.push(vertices[i]); + combined.push(_combined); + for (var k=0;k= 0) set[j][0] = i; + if (combined[i].indexOf(set[j][1]) >= 0) set[j][1] = i; + } + } + } + + function findIntersections(_verticesRaw, _outlinesRaw, _mountainsRaw, _valleysRaw, _cutsRaw){ + findIntersectionsInSets(_verticesRaw, _outlinesRaw, _mountainsRaw); + findIntersectionsInSets(_verticesRaw, _outlinesRaw, _valleysRaw); + findIntersectionsInSets(_verticesRaw, _outlinesRaw, _cutsRaw); + findIntersectionsInSets(_verticesRaw, _mountainsRaw, _valleysRaw); + findIntersectionsInSets(_verticesRaw, _mountainsRaw, _cutsRaw); + findIntersectionsInSets(_verticesRaw, _valleysRaw, _cutsRaw); + } + + function findIntersectionsInSets(_verticesRaw, set1, set2){ + for (var i=set1.length-1;i>=0;i--){ + for (var j=set2.length-1;j>=0;j--){ + var v1 = _verticesRaw[set1[i][0]]; + var v2 = _verticesRaw[set1[i][1]]; + var v3 = _verticesRaw[set2[j][0]]; + var v4 = _verticesRaw[set2[j][1]]; + var data = line_intersect(v1, v2, v3, v4); + if (data) { + var d1 = getDistFromEnd(data.t1, v1, v2); + var d2 = getDistFromEnd(data.t2, v3, v4); + if (d1 === null || d2 === null) continue; + var seg1Int = d1>globals.vertTol; + var seg2Int = d2>globals.vertTol; + if (!seg1Int && !seg2Int) continue; + + var vertIndex = _verticesRaw.length; + _verticesRaw.push(data.intersection); + + if (seg1Int){ + set1.splice(i+1, 0, [vertIndex, set1[i][0]]); + set1.splice(i+1, 0, [vertIndex, set1[i][1]]); + set1.splice(i, 1); + i++; + if (j==0) i++; + } + if (seg2Int){ + set2.splice(j+1, 0, [vertIndex, set2[j][0]]); + set2.splice(j+1, 0, [vertIndex, set2[j][1]]); + set2.splice(j, 1); + j += 2; + } + } + } + } } - function findIntersections(_verticesRaw, _outlinesRaw, _mountainsRaw, _valleysRaw){ + function getDistFromEnd(t, v1, v2){ + if (t>0.5) t = 1-t; + var length = (v2.clone().sub(v1)).length(); + var dist = t*length; + if (dist < -globals.vertTol) return null; + if (dist > length+globals.vertTol) return null; + return dist; + } + + //http://paulbourke.net/geometry/pointlineplane/ + function line_intersect(v1, v2, v3, v4) { + var x1 = v1.x; + var y1 = v1.z; + var x2 = v2.x; + var y2 = v2.z; + var x3 = v3.x; + var y3 = v3.z; + var x4 = v4.x; + var y4 = v4.z; + + var ua, ub, denom = (y4 - y3)*(x2 - x1) - (x4 - x3)*(y2 - y1); + if (denom == 0) { + return null; + } + ua = ((x4 - x3)*(y1 - y3) - (y4 - y3)*(x1 - x3))/denom; + ub = ((x2 - x1)*(y1 - y3) - (y2 - y1)*(x1 - x3))/denom; + return { + intersection: new THREE.Vector3(x1 + ua*(x2 - x1), 0, y1 + ua*(y2 - y1)), + t1: ua, + t2: ub + }; } function drawPattern(){ -- GitLab