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<html lang="en">
<meta charset="utf-8"/>
<head><title>Test Voronoï</title></head>
<body>
<h1>A* on a Delaunay triangulation algorithm implemented with Quad-Edges</h1>
<p>This example uses a refinement algorithm where we compute a giant triangle
surrounding all the sites, then insert them one by one while keeping the
triangulation.</p>
<p>The geometric predicates (inCircle and isRightOf) have not been made robust. The envelope has been left gray. </p>
<p>Clicking on a triangle displays its circumscribed
circle, it should be respect the "Modified circle criterion".</p>
<div id="draw"></div>
<script src="svg.js"></script>
<script>
// http://www.cs.cmu.edu/afs/andrew/scs/cs/15-463/2001/pub/src/a2/cell/
// https://github.com/hastebrot/jsts-dist/blob/master/src/jsts
// https://github.com/savithru-j/cdt-js
// https://doc.cgal.org/latest/Triangulation_2/index.html
// GRAPH STUFF
class QuadEdge {
constructor () {
this.rot = null
this.vertex = null
this.next = null
}
get sym () {
return this.rot.rot
}
get org () {
return this.vertex
}
set org (o) {
this.vertex = o
}
get dest () {
return this.sym.org
}
set dest (d) {
this.sym.org = d
}
get invRot () {
return this.rot.sym
}
get left () {
return this.rot.vertex
}
get right () {
return this.invRot.vertex
}
get lNext () {
return this.invRot.oNext.rot
}
get lPrev () {
return this.next.sym
}
get rNext () {
return this.rot.oNext.invRot
}
get oNext () {
return this.next
}
get oPrev () {
return this.rot.next.rot
}
get dPrev () {
return this.invRot.oNext.invRot
}
get rPrev () {
return this.sym.oNext
}
}
const allEdges = []
function makeEdge (v1, v2) {
const q0 = new QuadEdge()
allEdges.push(q0)
const q1 = new QuadEdge()
const q2 = new QuadEdge()
const q3 = new QuadEdge()
q0.rot = q1
q1.rot = q2
q2.rot = q3
q3.rot = q0
q0.next = q0
q1.next = q3
q2.next = q2
q3.next = q1
q0.org = v1
q0.dest = v2
console.assert(q0.dest === v2)
console.assert(q0.org !== q0.dest, q0.org, q0.dest)
console.assert(q0.left === q0.right)
console.assert(q0.lNext === q0.rNext)
console.assert(q0.lNext === q0.sym)
console.assert(q0.oPrev === q0.oNext)
console.assert(q0.oPrev === q0)
q1.org = generateColor()
q3.org = generateColor()
return q0
}
function splice (a, b) {
const alpha = a.oNext.rot
const beta = b.oNext.rot
const t1 = b.oNext
const t2 = a.oNext
const t3 = beta.oNext
const t4 = alpha.oNext
a.next = t1
b.next = t2
alpha.next = t3
beta.next = t4
}
function connect (a, b) {
const e = makeEdge(a.dest, b.org)
splice(e, a.lNext)
splice(e.sym, b)
return e
}
function swap (e) {
const a = e.oPrev
const b = e.sym.oPrev
splice(e, a)
splice(e.sym, b)
splice(e, a.lNext)
splice(e.sym, b.lNext)
e.org = a.dest
e.dest = b.dest
}
</script>
<script>
// GEOMETRIC STUFF
function triArea (a, b, c) {
return (b.x - a.x) * (c.y - a.y) - (c.x - a.x) * (b.y - a.y)
}
function ccw (a, b, c) {
return triArea(a, b, c) > 0
}
function inCircle (a, b, c, p) {
const det = (a.x * a.x + a.y * a.y) * triArea(b, c, p) -
(b.x * b.x + b.y * b.y) * triArea(a, c, p) +
(c.x * c.x + c.y * c.y) * triArea(a, b, p) -
(p.x * p.x + p.y * p.y) * triArea(a, b, c)
return det > 0
}
// check the circle of the triangle this edge is in vs the point of the symmetric triangle
function inCircleEdge (edge) {
return inCircle(edge.org, edge.rPrev.dest, edge.dest, edge.sym.rPrev.dest)
}
function circumCenter (p0, p1, p2) {
const d = 2 * (p0.x * (p1.y - p2.y) + p1.x * (p2.y - p0.y) + p2.x * (p0.y - p1.y))
const p0_mag = p0.x * p0.x + p0.y * p0.y
const p1_mag = p1.x * p1.x + p1.y * p1.y
const p2_mag = p2.x * p2.x + p2.y * p2.y
const x = (p0_mag * (p1.y - p2.y) + p1_mag * (p2.y - p0.y) + p2_mag * (p0.y - p1.y)) / d
const y = (p0_mag * (p2.x - p1.x) + p1_mag * (p0.x - p2.x) + p2_mag * (p1.x - p0.x)) / d
return {x, y}
}
function circumCircleForEdge (edge) {
return circumCircle(edge.org, edge.dest, edge.rPrev.dest)
}
function distance (v1, v2) {
const sq = v => v * v
return Math.sqrt(sq(v1.x - v2.x) + sq(v1.y - v2.y))
}
function circumCircle (a, b, c) {
const {x, y} = circumCenter(a, b, c)
const center = {x, y}
return {...center, r: distance(a, center)}
}
console.assert(inCircle({x: 1, y: 2}, {x: 1, y: 1}, {x: 2, y: 1}, {x: 1.5, y: 1.5}))
console.assert(!inCircle({x: 1, y: 2}, {x: 1, y: 1}, {x: 2, y: 1}, {x: 15, y: 15}))
function edgeVector (e) {
const dx = e.dest.x - e.org.x
const dy = e.dest.y - e.org.y
return {x: dx, y: dy}
}
function edgeLength (e) {
return distance(e.dest, e.org)
}
function edgeOriginBisector (e) {
const prevVector = edgeVector(e.oNext)
const prevLength = edgeLength(e.oNext)
const vector = edgeVector(e)
const length = edgeLength(e)
return {
x: 20 * (vector.x / length + prevVector.x / prevLength),
y: 20 * (vector.y / length + prevVector.y / prevLength)
}
}
function edgeNormal (e, factor = 1) {
const vector = edgeVector(e)
const length = edgeLength(e)
// noinspection JSSuspiciousNameCombination
return {x: factor * -vector.y / length, y: factor * vector.x / length}
}
function edgeDirection (e, factor = 1) {
const vector = edgeVector(e)
const length = edgeLength(e)
return {x: factor * vector.x / length, y: factor * vector.y / length}
}
function isRightOf (point, edge) {
return ccw(point, edge.dest, edge.org)
}
// one edge and 2 points
function doesIntersect (edge, p1, p2) {
//https://stackoverflow.com/a/1968345/72637
const s1X = edge.dest.x - edge.org.x
const s1Y = edge.dest.y - edge.org.y
const s2X = p2.x - p1.x
const s2Y = p2.y - p1.y
let denominator = (-s2X * s1Y + s1X * s2Y)
let s = (-s1Y * (edge.org.x - p1.x) + s1X * (edge.org.y - p1.y)) / denominator
let t = (s2X * (edge.org.y - p1.y) - s2Y * (edge.org.x - p1.x)) / denominator
return (s >= 0 && s <= 1 && t >= 0 && t <= 1)
}
function edgeEndsAtPoint (edge, point) {
return edge.org === point || edge.dest === point
}
function isConvex (p1, p2, p3, p4) {
const arr = [p1, p2, p3, p4]
const nextPoint = index => arr[(index + 1) % arr.length]
const edgeVector = (fromP, toP) => ({x: toP.x - fromP.x, y: toP.y - fromP.y})
const crossProductZ = (v1, v2) => v1.x * v2.y - v1.y * v2.x
const edgesCrossProducts = arr.map((p, i) => crossProductZ(edgeVector(p, nextPoint(i)), edgeVector(nextPoint(i), nextPoint(i + 1))))
edgesCrossProducts.sort((a, b) => a - b)
return Math.sign(edgesCrossProducts.shift()) * Math.sign(edgesCrossProducts.pop()) === 1
}
function isQuadAroundEdgeConvex (edge) {
return isConvex(edge.rNext.org, edge.org, edge.oNext.dest, edge.dest)
}
function locateFromEdge (vertex, edge) {
let iter = 0
let e = edge
while (true) {
iter++
if (iter > 1000) {
throw new Error('lol')
}
if (vertex === e.org || vertex === e.dest) {
break
}
if (isRightOf(vertex, e)) {
e = e.sym
} else if (!isRightOf(vertex, e.oNext)) {
e = e.oNext
} else if (!isRightOf(vertex, e.dPrev)) {
e = e.dPrev
} else {
break
}
}
return e
}
</script>
<script>
// DELAUNAY
function makeTriangle (v1, v2, v3) {
const ea = makeEdge(v1, v2)
const eb = makeEdge(v2, v3)
splice(ea.sym, eb)
const ec = makeEdge(v3, v1)
splice(eb.sym, ec)
splice(ec.sym, ea)
return ea
}
const TAN_60 = Math.sqrt(3)
/***
* This is a triangle with an horizontal base and 2 60° sides.
* minX and maxX are the abscissa at y == 0
*/
class Envelope {
constructor () {
this.minY = NaN
this.minX = NaN
this.maxX = NaN
}
addPoint (x, y) {
this.minY = isNaN(this.minY) || y < this.minY ? y : this.minY
const limits = [x - y / TAN_60, x + y / TAN_60, this.minX, this.maxX].filter(e => !isNaN(e))
limits.sort((a, b) => a - b)
this.minX = limits[0]
this.maxX = limits[limits.length - 1]
}
get apex () {
const x = (this.minX + this.maxX) / 2
return {x: x, y: Math.abs(this.minX - x) * TAN_60 + 20}
}
get botLeft () {
const y = this.minY - 20
return {x: this.minX - 20 + (y / TAN_60), y}
}
get botRight () {
const y = this.minY - 20
return {x: this.maxX + 20 - (y / TAN_60), y}
}
}
function insertSite (edge, vertex) {
let e = locateFromEdge(vertex, edge)
if (e.org === vertex || e.dest === vertex) {
return e
}
//TODO: is on edge
let base = makeEdge(e.org, vertex)
splice(base, e)
const startEdge = base
let i = 10
const newEdgeGroup = svg.group().attr({stroke: 'green', 'stroke-width': 3})
const flippedEdges = newEdgeGroup.group().attr({stroke: 'red'})
newEdgeGroup.circle(10).move(vertex.x - 5, vertex.y - 5).attr({'stroke-width': 1, fill: 'none'})
displayEdge(base, newEdgeGroup)
do {
base = connect(e, base.sym)
displayEdge(base, newEdgeGroup)
e = base.oPrev
i--
if (i <= 0)
throw Error('error')
} while (e.lNext !== startEdge && i > 0)
i = 100
const suspectGroup = newEdgeGroup.group().attr({stroke: 'orange', 'stroke-width': 4, 'stroke-opacity': 4})
do {
const t = e.oPrev
const circleDef = circumCircle(e.org, t.dest, e.dest)
const localGroup = newEdgeGroup.group().attr({stroke: 'red', 'stroke-width': 1, fill: 'none'})
localGroup.circle(circleDef.r * 2).move(circleDef.x - circleDef.r, circleDef.y - circleDef.r)
displayEdge(e, localGroup)
//debugger
if (isRightOf(t.dest, e) && inCircle(e.org, t.dest, e.dest, vertex)) {
swap(e)
displayEdge(e, flippedEdges)
// go back and re-test the same edge with the new triangle
e = e.oPrev
} else {
if (e.oNext === startEdge) {
newEdgeGroup.remove()
return base
}
displayEdge(e, suspectGroup)
e = e.oNext.lPrev
}
localGroup.remove()
i--
if (i <= 0)
throw Error('error')
} while (true)
}
</script>
<script>
// A*
// yields arrays of 3 edges, grouped by face
function * iterateEdgesPerFace (startEdge, skippedVertices = new Set()) {
const markedEdges = new Set()
const edgeStack = [startEdge]
while (edgeStack.length) {
const e = edgeStack.pop()
if (markedEdges.has(e)) {
continue
}
if (e.left) {
let skipFace = false
let faceEdges = []
let faceEdge = e
do {
markedEdges.add(faceEdge)
edgeStack.push(faceEdge.sym)
if (skippedVertices.has(faceEdge.org))
skipFace = true
faceEdges.push(faceEdge)
faceEdge = faceEdge.lNext
} while (faceEdge !== e)
if (!skipFace)
yield faceEdges
}
}
}
function * iterateEdges (startEdge, skippedVertices = new Set()) {
for (let edgeArray of iterateEdgesPerFace(startEdge, skippedVertices))
for (let e of edgeArray)
yield e
}
function comparePoints (a, b) {
let xDiff = a.x - b.x
return xDiff !== 0 ? xDiff : a.y - b.y
}
const pointID = p => `${p.x},${p.y}`
const undirectedEdgeId = e => {
const vertices = [e.org, e.dest]
vertices.sort(comparePoints)
return `${pointID(vertices[0])}|${pointID(vertices[1])}`
}
function collectUndirectedEdges (startEdge, skippedVertices = new Set()) {
const markedEdges = {}
for (let e of iterateEdges(startEdge, skippedVertices)) {
let s = undirectedEdgeId(e)
markedEdges[s] = e
}
return markedEdges
}
function getNeighbors (edge) {
const res = []
let e = edge
do {
e = e.oNext
res.push(e)
} while (e !== edge)
return res
}
function createQueue () {
// the laziest queue implementation you'll see today
const queue = []
// some values might be inserted twice with varying priorities, so we just keep the list of who has been deleted
// it's forbidden to pass twice in the same node
const deleted = new Set()
const sortOrder = (elem1, elem2) => elem1.priority - elem2.priority
const res = {
deleted,
queue,
addToQueue: (v, priority) => {
queue.push({v, priority})
queue.sort(sortOrder)
},
getFromQueue: () => {
if (queue.length === 0)
return undefined
const val = queue.shift().v
if (deleted.has(val))
return res.getFromQueue()
deleted.add(val)
return val
},
isQueueEmpty: () => {
if (queue.length === 0)
return true
// the head of the queue could be some old deleted stuff
while (queue.length && deleted.has(queue[0]))
queue.shift()
return queue.length === 0
}
}
return res
}
function circlePoint (vertex, group) {
return group.circle(10).move(vertex.x - 5, vertex.y - 5).attr({'stroke-width': 1, fill: 'none'})
}
//https://en.wikipedia.org/wiki/A*_search_algorithm
//https://www.youtube.com/watch?v=ySN5Wnu88nE
//https://www.redblobgames.com/pathfinding/a-star/implementation.html
function aStar (oneEdge, startVertex, destinationVertex) {
circlePoint(startVertex, root).attr({'stroke': 'blue'})
circlePoint(destinationVertex, root).attr({'stroke': 'red'})
let startEdge = locateFromEdge(startVertex, oneEdge)
if (startEdge.org !== startVertex)
startEdge = startEdge.sym
const heuristic = distance
const queue = createQueue()
queue.addToQueue(startEdge, 0)
const cameFrom = {[pointID(startEdge.org)]: null}
const costSoFar = {[pointID(startEdge.org)]: 0}
while (!queue.isQueueEmpty()) {
const current = queue.getFromQueue()
console.log('current', current)
const currentVertexID = pointID(current.org)
if (current.org === destinationVertex)
break
let neighbors = getNeighbors(current)
let nGroup = root.group()
for (let n of neighbors) {
if (n === current)
continue
displayEdge(n, nGroup)
const neighborVertexID = pointID(n.dest)
const newCost = costSoFar[currentVertexID] + distance(current.org, n.dest)
if (costSoFar[neighborVertexID] === undefined || newCost < costSoFar[neighborVertexID]) {
costSoFar[neighborVertexID] = newCost
const priority = newCost + heuristic(destinationVertex, n.dest)
queue.addToQueue(n.lNext, priority)
cameFrom[neighborVertexID] = n
}
}
nGroup.remove()
}
console.log('costSoFar', costSoFar)
console.log('cameFrom', cameFrom)
let currentPoint = destinationVertex
while (currentPoint !== startVertex) {
const vID = pointID(currentPoint)
const edge = cameFrom[vID]
displayEdge(edge, edgeGroup)
currentPoint = edge.org
}
}
</script>
<script>
// google: octilinear metric
function generatePoints (count, xMin, xSize, yMin, ySize) {
const getNumber = (size) => Math.floor(Math.random() * size / 25) * 25
const points = {}
while (Object.keys(points).length < count) {
const point = {x: xMin + getNumber(xSize), y: yMin + getNumber(ySize)}
points[`${point.x}|${point.y}`] = point
}
return Object.values(points)
}
const generateColor = () => '#' + ('000000' + ((1 << 24) * Math.random() | 0).toString(16)).substr(-6)
function displayEdge (e, group) {
const o = e.org
const d = e.dest
return group.line(o.x, o.y, d.x, d.y)
}
function displayPolygon (edges, group) {
group.polygon(edges.map(e => [e.org.x, e.org.y]))
}
function displayEdgeCircumCircle (edge, group) {
const circleDef = circumCircleForEdge(edge)
return group.circle(circleDef.r * 2).move(circleDef.x - circleDef.r, circleDef.y - circleDef.r)
}
function * iteratePolygons (startEdge, skippedVertices = new Set()) {
for (let edgeArray of iterateEdgesPerFace(startEdge, skippedVertices)) {
yield edgeArray.map(e => e.org)
}
}
let svg = SVG(document.querySelector('#draw')[0])
const points = generatePoints(30, 30, 400, 30, 300)
const envelopeGroup = svg.group().attr({
stroke: 'lightgray',
'stroke-width': 10,
'stroke-linejoin': 'arcs',
'fill': 'none'
})
const background = svg.group()
const root = svg.group().attr({stroke: 'red', fill: 'none', class: 'root', 'vector-effect': 'non-scaling-stroke'})
const arrowMarker = svg.marker(10, 10, function (g) {
g.path('M0,0 L10,5 0,10').attr('fill', 'green')
})
const blueGroup = svg.group().attr({stroke: 'blue', fill: 'blue'})
const edgeGroup = svg.group().attr({class: 'edges', 'vector-effect': 'non-scaling-stroke'})
edgeGroup.attr({stroke: 'green', 'stroke-width': 1.5, 'marker-end': arrowMarker})
const envelope = new Envelope()
points.forEach(({x, y}) => envelope.addPoint(x, y))
function displayPoint (p, name) {
root.line(p.x - 10, p.y - 10, p.x + 10, p.y + 10)
root.line(p.x - 10, p.y + 10, p.x + 10, p.y - 10)
root.plain(name).move(p.x, p.y)
}
let botLeft = envelope.botLeft
let botRight = envelope.botRight
let apex = envelope.apex
const ea = makeTriangle(apex, botRight, botLeft)
ea.rot.vertex = generateColor()
displayPolygon([ea, ea.lNext, ea.lNext.lNext], envelopeGroup)
let i = 0
for (let vertex of points) {
displayPoint(vertex, 'V' + i)
const polygons = background.group()
for (let polygon of iteratePolygons(ea)) {
polygons.polygon(polygon.map(point => [point.x, point.y])).attr({
fill: 'blue',
'fill-opacity': 0.2,
stroke: 'white',
'stroke-width': 2,
'stroke-linejoin': 'round'
})
}
insertSite(ea, vertex)
polygons.remove()
i++
}
let currentCircle = null
let skippedVertices = new Set([apex, botRight, botLeft])
for (let polygon of iteratePolygons(ea, skippedVertices)) {
background.polygon(polygon.map(point => [point.x, point.y])).attr({
fill: 'blue',
'fill-opacity': 0.4,
stroke: 'white',
'stroke-width': 4,
'stroke-linejoin': 'round'
}).click(() => {
if (currentCircle)
currentCircle.remove()
const circleDef = circumCircle(...polygon)
currentCircle = root.group()
currentCircle.polygon(polygon.map(point => [point.x, point.y])).attr({
fill: 'red',
stroke: 'white',
'stroke-width': 4,
'stroke-linejoin': 'round'
})
currentCircle.circle(circleDef.r * 2).move(circleDef.x - circleDef.r, circleDef.y - circleDef.r)
})
}
aStar(ea, points[27], points[20])
</script>
</body>
</html>