[orx-triangulation] Improve triangulation, add kotlin/js support
This commit is contained in:
Edwin Jakobs
597
orx-triangulation/src/commonMain/kotlin/Delaunator.kt
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597
orx-triangulation/src/commonMain/kotlin/Delaunator.kt
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package org.openrndr.extra.triangulation
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import kotlin.math.*
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private val EPSILON: Double = 2.0.pow(-52)
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/**
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* A Kotlin port of Mapbox's Delaunator incredibly fast JavaScript library for Delaunay triangulation of 2D points.
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*
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* @description Port of Mapbox's Delaunator (JavaScript) library - https://github.com/mapbox/delaunator
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* @property coords flat positions' array - [x0, y0, x1, y1..]
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*
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* @since f0ed80d - commit
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* @author Ricardo Matias
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*/
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@Suppress("unused")
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internal class Delaunator(val coords: DoubleArray) {
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private val EDGE_STACK = IntArray(512)
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private var count = coords.size shr 1
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// arrays that will store the triangulation graph
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val maxTriangles = (2 * count - 5).coerceAtLeast(0)
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private val _triangles = IntArray(maxTriangles * 3)
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private val _halfedges = IntArray(maxTriangles * 3)
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lateinit var triangles: IntArray
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lateinit var halfedges: IntArray
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// temporary arrays for tracking the edges of the advancing convex hull
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private var hashSize = ceil(sqrt(count * 1.0)).toInt()
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private var hullPrev = IntArray(count) // edge to prev edge
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private var hullNext = IntArray(count) // edge to next edge
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private var hullTri = IntArray(count) // edge to adjacent triangle
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private var hullHash = IntArray(hashSize) // angular edge hash
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private var hullStart: Int = -1
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// temporary arrays for sorting points
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private var ids = IntArray(count)
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private var dists = DoubleArray(count)
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private var cx: Double = Double.NaN
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private var cy: Double = Double.NaN
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private var trianglesLen: Int = -1
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lateinit var hull: IntArray
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init {
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update()
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}
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fun update() {
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if (coords.size <= 2) {
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halfedges = IntArray(0)
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triangles = IntArray(0)
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hull = IntArray(0)
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return
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}
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// populate an array of point indices calculate input data bbox
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var minX = Double.POSITIVE_INFINITY
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var minY = Double.POSITIVE_INFINITY
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var maxX = Double.NEGATIVE_INFINITY
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var maxY = Double.NEGATIVE_INFINITY
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// points -> points
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// minX, minY, maxX, maxY
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for (i in 0 until count) {
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val x = coords[2 * i]
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val y = coords[2 * i + 1]
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if (x < minX) minX = x
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if (y < minY) minY = y
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if (x > maxX) maxX = x
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if (y > maxY) maxY = y
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ids[i] = i
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}
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val cx = (minX + maxX) / 2
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val cy = (minY + maxY) / 2
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var minDist = Double.POSITIVE_INFINITY
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var i0: Int = -1
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var i1: Int = -1
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var i2: Int = -1
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// pick a seed point close to the center
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for (i in 0 until count) {
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val d = dist(cx, cy, coords[2 * i], coords[2 * i + 1])
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if (d < minDist) {
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i0 = i
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minDist = d
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}
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}
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val i0x = coords[2 * i0]
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val i0y = coords[2 * i0 + 1]
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minDist = Double.POSITIVE_INFINITY
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// Find the point closest to the seed
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for(i in 0 until count) {
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if (i == i0) continue
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val d = dist(i0x, i0y, coords[2 * i], coords[2 * i + 1])
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if (d < minDist && d > 0) {
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i1 = i
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minDist = d
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}
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}
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var i1x = coords[2 * i1]
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var i1y = coords[2 * i1 + 1]
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var minRadius = Double.POSITIVE_INFINITY
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// Find the third point which forms the smallest circumcircle with the first two
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for (i in 0 until count) {
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if(i == i0 || i == i1) continue
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val r = circumradius(i0x, i0y, i1x, i1y, coords[2 * i], coords[2 * i + 1])
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if(r < minRadius) {
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i2 = i
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minRadius = r
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}
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}
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if (minRadius == Double.POSITIVE_INFINITY) {
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// order collinear points by dx (or dy if all x are identical)
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// and return the list as a hull
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for (i in 0 until count) {
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val a = (coords[2 * i] - coords[0])
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val b = (coords[2 * i + 1] - coords[1])
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dists[i] = if (a == 0.0) b else a
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}
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quicksort(ids, dists, 0, count - 1)
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val nhull = IntArray(count)
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var j = 0
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var d0 = Double.NEGATIVE_INFINITY
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for (i in 0 until count) {
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val id = ids[i]
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if (dists[id] > d0) {
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nhull[j++] = id
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d0 = dists[id]
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}
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}
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hull = nhull.copyOf(j)
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triangles = IntArray(0)
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halfedges = IntArray(0)
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return
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}
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var i2x = coords[2 * i2]
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var i2y = coords[2 * i2 + 1]
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// swap the order of the seed points for counter-clockwise orientation
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if (orient2d(i0x, i0y, i1x, i1y, i2x, i2y) < 0.0) {
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val i = i1
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val x = i1x
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val y = i1y
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i1 = i2
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i1x = i2x
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i1y = i2y
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i2 = i
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i2x = x
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i2y = y
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}
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val center = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y)
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this.cx = center[0]
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this.cy = center[1]
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for (i in 0 until count) {
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dists[i] = dist(coords[2 * i], coords[2 * i + 1], center[0], center[1])
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}
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// sort the points by distance from the seed triangle circumcenter
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quicksort(ids, dists, 0, count - 1)
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// set up the seed triangle as the starting hull
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hullStart = i0
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var hullSize = 3
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hullNext[i0] = i1
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hullNext[i1] = i2
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hullNext[i2] = i0
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hullPrev[i2] = i1
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hullPrev[i0] = i2
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hullPrev[i1] = i0
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hullTri[i0] = 0
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hullTri[i1] = 1
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hullTri[i2] = 2
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hullHash.fill(-1)
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hullHash[hashKey(i0x, i0y)] = i0
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hullHash[hashKey(i1x, i1y)] = i1
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hullHash[hashKey(i2x, i2y)] = i2
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trianglesLen = 0
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addTriangle(i0, i1, i2, -1, -1, -1)
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var xp = 0.0
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var yp = 0.0
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for (k in ids.indices) {
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val i = ids[k]
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val x = coords[2 * i]
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val y = coords[2 * i + 1]
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// skip near-duplicate points
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if (k > 0 && abs(x - xp) <= EPSILON && abs(y - yp) <= EPSILON) continue
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xp = x
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yp = y
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// skip seed triangle points
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if (i == i0 || i == i1 || i == i2) continue
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// find a visible edge on the convex hull using edge hash
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var start = 0
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val key = hashKey(x, y)
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for (j in 0 until hashSize) {
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start = hullHash[(key + j) % hashSize]
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if (start != -1 && start != hullNext[start]) break
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}
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start = hullPrev[start]
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var e = start
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var q = hullNext[e]
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while (orient2d(x, y, coords[2 * e], coords[2 * e + 1], coords[2 * q], coords[2 * q + 1]) >= 0) {
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e = q
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if (e == start) {
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e = -1
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break
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}
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q = hullNext[e]
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}
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if (e == -1) continue // likely a near-duplicate point skip it
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// add the first triangle from the point
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var t = addTriangle(e, i, hullNext[e], -1, -1, hullTri[e])
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// recursively flip triangles from the point until they satisfy the Delaunay condition
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hullTri[i] = legalize(t + 2)
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hullTri[e] = t // keep track of boundary triangles on the hull
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hullSize++
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// walk forward through the hull, adding more triangles and flipping recursively
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var next = hullNext[e]
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q = hullNext[next]
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while (orient2d(x, y, coords[2 * next], coords[2 * next + 1], coords[2 * q], coords[2 * q + 1]) < 0) {
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t = addTriangle(next, i, q, hullTri[i], -1, hullTri[next])
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hullTri[i] = legalize(t + 2)
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hullNext[next] = next // mark as removed
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hullSize--
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next = q
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q = hullNext[next]
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}
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// walk backward from the other side, adding more triangles and flipping
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if (e == start) {
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q = hullPrev[e]
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while (orient2d(x, y, coords[2 * q], coords[2 * q + 1], coords[2 * e], coords[2 * e + 1]) < 0) {
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t = addTriangle(q, i, e, -1, hullTri[e], hullTri[q])
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legalize(t + 2)
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hullTri[q] = t
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hullNext[e] = e // mark as removed
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hullSize--
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e = q
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q = hullPrev[e]
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}
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}
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// update the hull indices
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hullStart = e
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hullPrev[i] = e
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hullNext[e] = i
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hullPrev[next] = i
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hullNext[i] = next
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// save the two new edges in the hash table
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hullHash[hashKey(x, y)] = i
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hullHash[hashKey(coords[2 * e], coords[2 * e + 1])] = e
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}
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hull = IntArray(hullSize)
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var e = hullStart
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for (i in 0 until hullSize) {
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hull[i] = e
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e = hullNext[e]
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}
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// trim typed triangle mesh arrays
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triangles = _triangles.copyOf(trianglesLen)
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halfedges = _halfedges.copyOf(trianglesLen)
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}
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private fun legalize(a: Int): Int {
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var i = 0
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var na = a
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var ar: Int
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// recursion eliminated with a fixed-size stack
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while (true) {
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val b = _halfedges[na]
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/* if the pair of triangles doesn't satisfy the Delaunay condition
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* (p1 is inside the circumcircle of [p0, pl, pr]), flip them,
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* then do the same check/flip recursively for the new pair of triangles
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*
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* pl pl
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* /||\ / \
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* al/ || \bl al/ \a
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* / || \ / \
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* / a||b \ flip /___ar___\
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* p0\ || /p1 => p0\---bl---/p1
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* \ || / \ /
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* ar\ || /br b\ /br
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* \||/ \ /
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* pr pr
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*/
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val a0 = na - na % 3
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ar = a0 + (na + 2) % 3
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if (b == -1) { // convex hull edge
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if (i == 0) break
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na = EDGE_STACK[--i]
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continue
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}
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val b0 = b - b % 3
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val al = a0 + (na + 1) % 3
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val bl = b0 + (b + 2) % 3
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val p0 = _triangles[ar]
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val pr = _triangles[na]
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val pl = _triangles[al]
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val p1 = _triangles[bl]
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val illegal = inCircle(
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coords[2 * p0], coords[2 * p0 + 1],
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coords[2 * pr], coords[2 * pr + 1],
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coords[2 * pl], coords[2 * pl + 1],
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coords[2 * p1], coords[2 * p1 + 1])
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if (illegal) {
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_triangles[na] = p1
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_triangles[b] = p0
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val hbl = _halfedges[bl]
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// edge swapped on the other side of the hull (rare) fix the halfedge reference
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if (hbl == -1) {
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var e = hullStart
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do {
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if (hullTri[e] == bl) {
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hullTri[e] = na
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break
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}
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e = hullPrev[e]
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} while (e != hullStart)
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}
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link(na, hbl)
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link(b, _halfedges[ar])
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link(ar, bl)
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val br = b0 + (b + 1) % 3
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// don't worry about hitting the cap: it can only happen on extremely degenerate input
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if (i < EDGE_STACK.size) {
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EDGE_STACK[i++] = br
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}
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} else {
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if (i == 0) break
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na = EDGE_STACK[--i]
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}
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}
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return ar
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}
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private fun link(a:Int, b:Int) {
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_halfedges[a] = b
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if (b != -1) _halfedges[b] = a
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}
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// add a new triangle given vertex indices and adjacent half-edge ids
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private fun addTriangle(i0: Int, i1: Int, i2: Int, a: Int, b: Int, c: Int): Int {
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val t = trianglesLen
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_triangles[t] = i0
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_triangles[t + 1] = i1
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_triangles[t + 2] = i2
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link(t, a)
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link(t + 1, b)
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link(t + 2, c)
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trianglesLen += 3
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return t
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}
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private fun hashKey(x: Double, y: Double): Int {
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return (floor(pseudoAngle(x - cx, y - cy) * hashSize) % hashSize).toInt()
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}
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}
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fun circumradius(ax: Double, ay: Double,
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bx: Double, by: Double,
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cx: Double, cy: Double): Double {
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val dx = bx - ax
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val dy = by - ay
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val ex = cx - ax
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val ey = cy - ay
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val bl = dx * dx + dy * dy
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val cl = ex * ex + ey * ey
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val d = 0.5 / (dx * ey - dy * ex)
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val x = (ey * bl - dy * cl) * d
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val y = (dx * cl - ex * bl) * d
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return x * x + y * y
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}
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fun circumcenter(ax: Double, ay: Double,
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bx: Double, by: Double,
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cx: Double, cy: Double): DoubleArray {
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val dx = bx - ax
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val dy = by - ay
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val ex = cx - ax
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val ey = cy - ay
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val bl = dx * dx + dy * dy
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val cl = ex * ex + ey * ey
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val d = 0.5 / (dx * ey - dy * ex)
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val x = ax + (ey * bl - dy * cl) * d
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val y = ay + (dx * cl - ex * bl) * d
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return doubleArrayOf(x, y)
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}
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fun quicksort(ids: IntArray, dists: DoubleArray, left: Int, right: Int) {
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if (right - left <= 20) {
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for (i in (left + 1)..right) {
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val temp = ids[i]
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val tempDist = dists[temp]
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var j = i - 1
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while (j >= left && dists[ids[j]] > tempDist) ids[j + 1] = ids[j--]
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ids[j + 1] = temp
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}
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} else {
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val median = (left + right) shr 1
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var i = left + 1
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var j = right
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swap(ids, median, i)
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if (dists[ids[left]] > dists[ids[right]]) swap(ids, left, right)
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if (dists[ids[i]] > dists[ids[right]]) swap(ids, i, right)
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if (dists[ids[left]] > dists[ids[i]]) swap(ids, left, i)
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val temp = ids[i]
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val tempDist = dists[temp]
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while (true) {
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do i++ while (dists[ids[i]] < tempDist)
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do j-- while (dists[ids[j]] > tempDist)
|
||||
if (j < i) break
|
||||
swap(ids, i, j)
|
||||
}
|
||||
|
||||
ids[left + 1] = ids[j]
|
||||
ids[j] = temp
|
||||
|
||||
if (right - i + 1 >= j - left) {
|
||||
quicksort(ids, dists, i, right)
|
||||
quicksort(ids, dists, left, j - 1)
|
||||
} else {
|
||||
quicksort(ids, dists, left, j - 1)
|
||||
quicksort(ids, dists, i, right)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
private fun swap(arr: IntArray, i: Int, j: Int) {
|
||||
val tmp = arr[i]
|
||||
arr[i] = arr[j]
|
||||
arr[j] = tmp
|
||||
}
|
||||
|
||||
// monotonically increases with real angle, but doesn't need expensive trigonometry
|
||||
private fun pseudoAngle(dx: Double, dy: Double): Double {
|
||||
val p = dx / (abs(dx) + abs(dy))
|
||||
val a = if (dy > 0.0) 3.0 - p else 1.0 + p
|
||||
|
||||
return a / 4.0 // [0..1]
|
||||
}
|
||||
/*
|
||||
private fun inCircle(ax: Double, ay: Double,
|
||||
bx: Double, by: Double,
|
||||
cx: Double, cy: Double,
|
||||
px: Double, py: Double): Boolean {
|
||||
val dx = ax - px
|
||||
val dy = ay - py
|
||||
val ex = bx - px
|
||||
val ey = by - py
|
||||
val fx = cx - px
|
||||
val fy = cy - py
|
||||
|
||||
val ap = dx * dx + dy * dy
|
||||
val bp = ex * ex + ey * ey
|
||||
val cp = fx * fx + fy * fy
|
||||
|
||||
return dx * (ey * cp - bp * fy) -
|
||||
dy * (ex * cp - bp * fx) +
|
||||
ap * (ex * fy - ey * fx) < 0
|
||||
}*/
|
||||
|
||||
private fun inCircle(
|
||||
ax: Double, ay: Double,
|
||||
bx: Double, by: Double,
|
||||
cx: Double, cy: Double,
|
||||
px: Double, py: Double
|
||||
): Boolean {
|
||||
|
||||
val dx = twoDiff(ax, px)
|
||||
val dy = twoDiff(ay, py)
|
||||
val ex = twoDiff(bx, px)
|
||||
val ey = twoDiff(by, py)
|
||||
val fx = twoDiff(cx, px)
|
||||
val fy = twoDiff(cy, py)
|
||||
|
||||
val ap = ddAddDd(ddMultDd(dx, dx), ddMultDd(dy, dy))
|
||||
val bp = ddAddDd(ddMultDd(ex, ex), ddMultDd(ey, ey))
|
||||
val cp = ddAddDd(ddMultDd(fx, fx), ddMultDd(fy, fy))
|
||||
|
||||
val dd = ddAddDd(
|
||||
ddDiffDd(
|
||||
ddMultDd(dx, ddDiffDd(ddMultDd(ey, cp), ddMultDd(bp, fy))),
|
||||
ddMultDd(dy, ddDiffDd(ddMultDd(ex, cp), ddMultDd(bp, fx)))
|
||||
),
|
||||
ddMultDd(ap, ddDiffDd(ddMultDd(ex, fy), ddMultDd(ey, fx)))
|
||||
)
|
||||
// add a small bias here, it seems to help
|
||||
return (dd[1]) <= 1E-8
|
||||
}
|
||||
|
||||
|
||||
private fun dist(ax: Double, ay: Double, bx: Double, by: Double): Double {
|
||||
//val dx = ax - bx
|
||||
//val dy = ay - by
|
||||
//return dx * dx + dy * dy
|
||||
|
||||
// double-double implementation but I think it is overkill.
|
||||
|
||||
val dx = twoDiff(ax, bx)
|
||||
val dy = twoDiff(ay, by)
|
||||
val dx2 = ddMultDd(dx, dx)
|
||||
val dy2 = ddMultDd(dy, dy)
|
||||
val d2 = ddAddDd(dx2, dy2)
|
||||
|
||||
return d2[0] + d2[1]
|
||||
|
||||
}
|
||||
Reference in New Issue
Block a user