initial commit
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1
icegps-triangulation/.gitignore
vendored
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1
icegps-triangulation/.gitignore
vendored
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@@ -0,0 +1 @@
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/build
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16
icegps-triangulation/build.gradle.kts
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16
icegps-triangulation/build.gradle.kts
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plugins {
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id("java-library")
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alias(libs.plugins.kotlin.jvm)
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}
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java {
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sourceCompatibility = JavaVersion.VERSION_17
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targetCompatibility = JavaVersion.VERSION_17
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}
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kotlin {
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compilerOptions {
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jvmTarget = org.jetbrains.kotlin.gradle.dsl.JvmTarget.JVM_17
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}
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}
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dependencies {
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implementation(project(":math"))
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}
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@@ -0,0 +1,596 @@
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package com.icegps.triangulation
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import kotlin.math.*
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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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class Delaunator(val coords: DoubleArray) {
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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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||||
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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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||||
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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 = inCircleRobust(
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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],
|
||||
coords[2 * p1], coords[2 * p1 + 1])
|
||||
|
||||
if (illegal) {
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||||
_triangles[na] = p1
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||||
_triangles[b] = p0
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||||
|
||||
val hbl = _halfedges[bl]
|
||||
|
||||
// edge swapped on the other side of the hull (rare) fix the halfedge reference
|
||||
if (hbl == -1) {
|
||||
var e = hullStart
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||||
do {
|
||||
if (hullTri[e] == bl) {
|
||||
hullTri[e] = na
|
||||
break
|
||||
}
|
||||
e = hullPrev[e]
|
||||
} while (e != hullStart)
|
||||
}
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||||
link(na, hbl)
|
||||
link(b, _halfedges[ar])
|
||||
link(ar, bl)
|
||||
|
||||
val br = b0 + (b + 1) % 3
|
||||
|
||||
// don't worry about hitting the cap: it can only happen on extremely degenerate input
|
||||
if (i < EDGE_STACK.size) {
|
||||
EDGE_STACK[i++] = br
|
||||
}
|
||||
} else {
|
||||
if (i == 0) break
|
||||
na = EDGE_STACK[--i]
|
||||
}
|
||||
}
|
||||
|
||||
return ar
|
||||
|
||||
}
|
||||
|
||||
private fun link(a:Int, b:Int) {
|
||||
_halfedges[a] = b
|
||||
if (b != -1) _halfedges[b] = a
|
||||
}
|
||||
|
||||
// add a new triangle given vertex indices and adjacent half-edge ids
|
||||
private fun addTriangle(i0: Int, i1: Int, i2: Int, a: Int, b: Int, c: Int): Int {
|
||||
val t = trianglesLen
|
||||
|
||||
_triangles[t] = i0
|
||||
_triangles[t + 1] = i1
|
||||
_triangles[t + 2] = i2
|
||||
|
||||
link(t, a)
|
||||
link(t + 1, b)
|
||||
link(t + 2, c)
|
||||
|
||||
trianglesLen += 3
|
||||
|
||||
return t
|
||||
}
|
||||
|
||||
private fun hashKey(x: Double, y: Double): Int {
|
||||
return (floor(pseudoAngle(x - cx, y - cy) * hashSize) % hashSize).toInt()
|
||||
}
|
||||
}
|
||||
|
||||
fun circumradius(ax: Double, ay: Double,
|
||||
bx: Double, by: Double,
|
||||
cx: Double, cy: Double): Double {
|
||||
val dx = bx - ax
|
||||
val dy = by - ay
|
||||
val ex = cx - ax
|
||||
val ey = cy - ay
|
||||
|
||||
val bl = dx * dx + dy * dy
|
||||
val cl = ex * ex + ey * ey
|
||||
val d = 0.5 / (dx * ey - dy * ex)
|
||||
|
||||
val x = (ey * bl - dy * cl) * d
|
||||
val y = (dx * cl - ex * bl) * d
|
||||
|
||||
return x * x + y * y
|
||||
}
|
||||
|
||||
fun circumcenter(ax: Double, ay: Double,
|
||||
bx: Double, by: Double,
|
||||
cx: Double, cy: Double): DoubleArray {
|
||||
val dx = bx - ax
|
||||
val dy = by - ay
|
||||
val ex = cx - ax
|
||||
val ey = cy - ay
|
||||
|
||||
val bl = dx * dx + dy * dy
|
||||
val cl = ex * ex + ey * ey
|
||||
val d = 0.5 / (dx * ey - dy * ex)
|
||||
|
||||
val x = ax + (ey * bl - dy * cl) * d
|
||||
val y = ay + (dx * cl - ex * bl) * d
|
||||
|
||||
return doubleArrayOf(x, y)
|
||||
}
|
||||
|
||||
fun quicksort(ids: IntArray, dists: DoubleArray, left: Int, right: Int) {
|
||||
if (right - left <= 20) {
|
||||
for (i in (left + 1)..right) {
|
||||
val temp = ids[i]
|
||||
val tempDist = dists[temp]
|
||||
var j = i - 1
|
||||
while (j >= left && dists[ids[j]] > tempDist) ids[j + 1] = ids[j--]
|
||||
ids[j + 1] = temp
|
||||
}
|
||||
} else {
|
||||
val median = (left + right) shr 1
|
||||
var i = left + 1
|
||||
var j = right
|
||||
|
||||
swap(ids, median, i)
|
||||
|
||||
if (dists[ids[left]] > dists[ids[right]]) swap(ids, left, right)
|
||||
if (dists[ids[i]] > dists[ids[right]]) swap(ids, i, right)
|
||||
if (dists[ids[left]] > dists[ids[i]]) swap(ids, left, i)
|
||||
|
||||
val temp = ids[i]
|
||||
val tempDist = dists[temp]
|
||||
|
||||
while (true) {
|
||||
do i++ while (dists[ids[i]] < tempDist)
|
||||
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 inCircleRobust(
|
||||
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)))
|
||||
)
|
||||
return (dd[1]) <= 0
|
||||
}
|
||||
|
||||
|
||||
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]
|
||||
|
||||
}
|
||||
@@ -0,0 +1,225 @@
|
||||
package com.icegps.triangulation
|
||||
|
||||
import com.icegps.math.geometry.Vector2D
|
||||
import com.icegps.triangulation.Delaunay.Companion.from
|
||||
import kotlin.math.cos
|
||||
import kotlin.math.pow
|
||||
import kotlin.math.sin
|
||||
|
||||
/*
|
||||
ISC License
|
||||
|
||||
Copyright 2021 Ricardo Matias.
|
||||
|
||||
Permission to use, copy, modify, and/or distribute this software for any purpose
|
||||
with or without fee is hereby granted, provided that the above copyright notice
|
||||
and this permission notice appear in all copies.
|
||||
|
||||
THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
|
||||
REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
|
||||
FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
|
||||
INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
|
||||
OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
|
||||
TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
|
||||
THIS SOFTWARE.
|
||||
*/
|
||||
|
||||
/**
|
||||
* Use [from] static method to use the delaunay triangulation
|
||||
*
|
||||
* @description Port of d3-delaunay (JavaScript) library - https://github.com/d3/d3-delaunay
|
||||
* @property points flat positions' array - [x0, y0, x1, y1..]
|
||||
*
|
||||
* @since 9258fa3 - commit
|
||||
* @author Ricardo Matias
|
||||
*/
|
||||
@Suppress("unused")
|
||||
class Delaunay(val points: DoubleArray) {
|
||||
companion object {
|
||||
/**
|
||||
* Entry point for the delaunay triangulation
|
||||
*
|
||||
* @property points a list of 2D points
|
||||
*/
|
||||
fun from(points: List<Vector2D>): Delaunay {
|
||||
val n = points.size
|
||||
val coords = DoubleArray(n * 2)
|
||||
|
||||
for (i in points.indices) {
|
||||
val p = points[i]
|
||||
coords[2 * i] = p.x
|
||||
coords[2 * i + 1] = p.y
|
||||
}
|
||||
|
||||
return Delaunay(coords)
|
||||
}
|
||||
}
|
||||
|
||||
private var delaunator: Delaunator = Delaunator(points)
|
||||
|
||||
val inedges = IntArray(points.size / 2)
|
||||
private val hullIndex = IntArray(points.size / 2)
|
||||
|
||||
var halfedges: IntArray = delaunator.halfedges
|
||||
var hull: IntArray = delaunator.hull
|
||||
var triangles: IntArray = delaunator.triangles
|
||||
|
||||
init {
|
||||
init()
|
||||
}
|
||||
|
||||
fun update() {
|
||||
delaunator.update()
|
||||
init()
|
||||
}
|
||||
|
||||
fun neighbors(i: Int) = sequence<Int> {
|
||||
val e0 = inedges[i]
|
||||
if (e0 != -1) {
|
||||
var e = e0
|
||||
var p0 = -1
|
||||
|
||||
loop@ do {
|
||||
p0 = triangles[e]
|
||||
yield(p0)
|
||||
e = if (e % 3 == 2) e - 2 else e + 1
|
||||
if (e == -1) {
|
||||
break@loop
|
||||
}
|
||||
|
||||
if (triangles[e] != i) {
|
||||
break@loop
|
||||
//error("bad triangulation")
|
||||
}
|
||||
e = halfedges[e]
|
||||
|
||||
if (e == -1) {
|
||||
val p = hull[(hullIndex[i] + 1) % hull.size]
|
||||
if (p != p0) {
|
||||
yield(p)
|
||||
}
|
||||
break@loop
|
||||
}
|
||||
} while (e != e0)
|
||||
}
|
||||
}
|
||||
|
||||
fun collinear(): Boolean {
|
||||
for (i in 0 until triangles.size step 3) {
|
||||
val a = 2 * triangles[i]
|
||||
val b = 2 * triangles[i + 1]
|
||||
val c = 2 * triangles[i + 2]
|
||||
val coords = points
|
||||
val cross = (coords[c] - coords[a]) * (coords[b + 1] - coords[a + 1])
|
||||
-(coords[b] - coords[a]) * (coords[c + 1] - coords[a + 1])
|
||||
if (cross > 1e-10) return false;
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
private fun jitter(x: Double, y: Double, r: Double): DoubleArray {
|
||||
return doubleArrayOf(x + sin(x + y) * r, y + cos(x - y) * r)
|
||||
}
|
||||
|
||||
fun init() {
|
||||
|
||||
if (hull.size > 2 && collinear()) {
|
||||
println("warning: triangulation is collinear")
|
||||
val r = 1E-8
|
||||
for (i in 0 until points.size step 2) {
|
||||
val p = jitter(points[i], points[i + 1], r)
|
||||
points[i] = p[0]
|
||||
points[i + 1] = p[1]
|
||||
}
|
||||
|
||||
delaunator = Delaunator(points)
|
||||
halfedges = delaunator.halfedges
|
||||
hull = delaunator.hull
|
||||
triangles = delaunator.triangles
|
||||
|
||||
}
|
||||
|
||||
|
||||
|
||||
inedges.fill(-1)
|
||||
hullIndex.fill(-1)
|
||||
|
||||
// Compute an index from each point to an (arbitrary) incoming halfedge
|
||||
// Used to give the first neighbor of each point for this reason,
|
||||
// on the hull we give priority to exterior halfedges
|
||||
for (e in halfedges.indices) {
|
||||
val p = triangles[nextHalfedge(e)]
|
||||
|
||||
if (halfedges[e] == -1 || inedges[p] == -1) inedges[p] = e
|
||||
}
|
||||
|
||||
for (i in hull.indices) {
|
||||
hullIndex[hull[i]] = i
|
||||
}
|
||||
|
||||
// degenerate case: 1 or 2 (distinct) points
|
||||
if (hull.size in 1..2) {
|
||||
triangles = IntArray(3) { -1 }
|
||||
halfedges = IntArray(3) { -1 }
|
||||
triangles[0] = hull[0]
|
||||
inedges[hull[0]] = 1
|
||||
if (hull.size == 2) {
|
||||
inedges[hull[1]] = 0
|
||||
triangles[1] = hull[1]
|
||||
triangles[2] = hull[1]
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
fun find(x: Double, y: Double, i: Int = 0): Int {
|
||||
var i1 = i
|
||||
var c = step(i, x, y)
|
||||
|
||||
while (c >= 0 && c != i && c != i1) {
|
||||
i1 = c
|
||||
c = step(i1, x, y)
|
||||
}
|
||||
return c
|
||||
}
|
||||
|
||||
fun nextHalfedge(e: Int) = if (e % 3 == 2) e - 2 else e + 1
|
||||
fun prevHalfedge(e: Int) = if (e % 3 == 0) e + 2 else e - 1
|
||||
|
||||
fun step(i: Int, x: Double, y: Double): Int {
|
||||
if (inedges[i] == -1 || points.isEmpty()) return (i + 1) % (points.size shr 1)
|
||||
|
||||
var c = i
|
||||
var dc = (x - points[i * 2]).pow(2) + (y - points[i * 2 + 1]).pow(2)
|
||||
val e0 = inedges[i]
|
||||
var e = e0
|
||||
do {
|
||||
val t = triangles[e]
|
||||
val dt = (x - points[t * 2]).pow(2) + (y - points[t * 2 + 1]).pow(2)
|
||||
|
||||
if (dt < dc) {
|
||||
dc = dt
|
||||
c = t
|
||||
}
|
||||
|
||||
e = if (e % 3 == 2) e - 2 else e + 1
|
||||
|
||||
if (triangles[e] != i) {
|
||||
//error("bad triangulation")
|
||||
break
|
||||
} // bad triangulation
|
||||
|
||||
e = halfedges[e]
|
||||
|
||||
if (e == -1) {
|
||||
e = hull[(hullIndex[i] + 1) % hull.size]
|
||||
if (e != t) {
|
||||
if ((x - points[e * 2]).pow(2) + (y - points[e * 2 + 1]).pow(2) < dc) return e
|
||||
}
|
||||
break
|
||||
}
|
||||
} while (e != e0)
|
||||
|
||||
return c
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,69 @@
|
||||
package com.icegps.triangulation
|
||||
|
||||
import com.icegps.math.geometry.Vector3D
|
||||
import com.icegps.math.geometry.toVector2D
|
||||
|
||||
/**
|
||||
* Kotlin/OPENRNDR idiomatic interface to `Delaunay`
|
||||
*/
|
||||
class DelaunayTriangulation(val points: List<Vector3D>) {
|
||||
val delaunay: Delaunay = Delaunay.from(points.map { it.toVector2D() })
|
||||
|
||||
fun neighbors(pointIndex: Int): Sequence<Int> {
|
||||
return delaunay.neighbors(pointIndex)
|
||||
}
|
||||
|
||||
fun neighborPoints(pointIndex: Int): List<Vector3D> {
|
||||
return neighbors(pointIndex).map { points[it] }.toList()
|
||||
}
|
||||
|
||||
fun triangleIndices(): List<IntArray> {
|
||||
val list = mutableListOf<IntArray>()
|
||||
for (i in delaunay.triangles.indices step 3) {
|
||||
list.add(
|
||||
intArrayOf(
|
||||
delaunay.triangles[i],
|
||||
delaunay.triangles[i + 1],
|
||||
delaunay.triangles[i + 2]
|
||||
)
|
||||
)
|
||||
}
|
||||
return list
|
||||
}
|
||||
|
||||
fun triangles(filterPredicate: (Int, Int, Int) -> Boolean = { _, _, _ -> true }): List<Triangle> {
|
||||
val list = mutableListOf<Triangle>()
|
||||
|
||||
for (i in delaunay.triangles.indices step 3) {
|
||||
val t0 = delaunay.triangles[i]
|
||||
val t1 = delaunay.triangles[i + 1]
|
||||
val t2 = delaunay.triangles[i + 2]
|
||||
|
||||
// originally they are defined *counterclockwise*
|
||||
if (filterPredicate(t2, t1, t0)) {
|
||||
val p1 = points[t0]
|
||||
val p2 = points[t1]
|
||||
val p3 = points[t2]
|
||||
list.add(Triangle(p3, p2, p1))
|
||||
}
|
||||
}
|
||||
return list
|
||||
}
|
||||
|
||||
fun nearest(query: Vector3D): Int = delaunay.find(query.x, query.y)
|
||||
|
||||
fun nearestPoint(query: Vector3D): Vector3D = points[nearest(query)]
|
||||
}
|
||||
|
||||
/**
|
||||
* Computes the Delaunay triangulation for the list of 2D points.
|
||||
*
|
||||
* The Delaunay triangulation is a triangulation of a set of points such that
|
||||
* no point is inside the circumcircle of any triangle. It maximizes the minimum
|
||||
* angle of all the angles in the triangles, avoiding skinny triangles.
|
||||
*
|
||||
* @return A DelaunayTriangulation object representing the triangulation of the given points.
|
||||
*/
|
||||
fun List<Vector3D>.delaunayTriangulation(): DelaunayTriangulation {
|
||||
return DelaunayTriangulation(this)
|
||||
}
|
||||
@@ -0,0 +1,340 @@
|
||||
package com.icegps.triangulation
|
||||
|
||||
import kotlin.math.pow
|
||||
|
||||
// original code: https://github.com/FlorisSteenkamp/double-double/
|
||||
|
||||
|
||||
/**
|
||||
* Returns the difference and exact error of subtracting two floating point
|
||||
* numbers.
|
||||
* Uses an EFT (error-free transformation), i.e. `a-b === x+y` exactly.
|
||||
* The returned result is a non-overlapping expansion (smallest value first!).
|
||||
*
|
||||
* * **precondition:** `abs(a) >= abs(b)` - A fast test that can be used is
|
||||
* `(a > b) === (a > -b)`
|
||||
*
|
||||
* See https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf
|
||||
*/
|
||||
fun fastTwoDiff(a: Double, b: Double): DoubleArray {
|
||||
val x = a - b;
|
||||
val y = (a - x) - b;
|
||||
|
||||
return doubleArrayOf(y, x)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the sum and exact error of adding two floating point numbers.
|
||||
* Uses an EFT (error-free transformation), i.e. a+b === x+y exactly.
|
||||
* The returned sum is a non-overlapping expansion (smallest value first!).
|
||||
*
|
||||
* Precondition: abs(a) >= abs(b) - A fast test that can be used is
|
||||
* (a > b) === (a > -b)
|
||||
*
|
||||
* See https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf
|
||||
*/
|
||||
fun fastTwoSum(a: Double, b: Double): DoubleArray {
|
||||
val x = a + b;
|
||||
|
||||
return doubleArrayOf(b - (x - a), x)
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Truncates a floating point value's significand and returns the result.
|
||||
* Similar to split, but with the ability to specify the number of bits to keep.
|
||||
*
|
||||
* **Theorem 17 (Veltkamp-Dekker)**: Let a be a p-bit floating-point number, where
|
||||
* p >= 3. Choose a splitting point s such that p/2 <= s <= p-1. Then the
|
||||
* following algorithm will produce a (p-s)-bit value a_hi and a
|
||||
* nonoverlapping (s-1)-bit value a_lo such that abs(a_hi) >= abs(a_lo) and
|
||||
* a = a_hi + a_lo.
|
||||
*
|
||||
* * see [Shewchuk](https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf)
|
||||
*
|
||||
* @param a a double
|
||||
* @param bits the number of significand bits to leave intact
|
||||
*/
|
||||
fun reduceSignificand(
|
||||
a: Double,
|
||||
bits: Int
|
||||
): Double {
|
||||
|
||||
val s = 53 - bits;
|
||||
val f = 2.0.pow(s) + 1;
|
||||
|
||||
val c = f * a;
|
||||
val r = c - (c - a);
|
||||
|
||||
return r;
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* === 2^Math.ceil(p/2) + 1 where p is the # of significand bits in a double === 53.
|
||||
* @internal
|
||||
*/
|
||||
const val f = 134217729; // 2**27 + 1;
|
||||
|
||||
|
||||
/**
|
||||
* Returns the result of splitting a double into 2 26-bit doubles.
|
||||
*
|
||||
* Theorem 17 (Veltkamp-Dekker): Let a be a p-bit floating-point number, where
|
||||
* p >= 3. Choose a splitting point s such that p/2 <= s <= p-1. Then the
|
||||
* following algorithm will produce a (p-s)-bit value a_hi and a
|
||||
* nonoverlapping (s-1)-bit value a_lo such that abs(a_hi) >= abs(a_lo) and
|
||||
* a = a_hi + a_lo.
|
||||
*
|
||||
* see e.g. [Shewchuk](https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf)
|
||||
* @param a A double floating point number
|
||||
*/
|
||||
fun split(a: Double): DoubleArray {
|
||||
val c = f * a;
|
||||
val a_h = c - (c - a);
|
||||
val a_l = a - a_h;
|
||||
|
||||
return doubleArrayOf(a_h, a_l)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the exact result of subtracting b from a.
|
||||
*
|
||||
* @param a minuend - a double-double precision floating point number
|
||||
* @param b subtrahend - a double-double precision floating point number
|
||||
*/
|
||||
fun twoDiff(a: Double, b: Double): DoubleArray {
|
||||
val x = a - b;
|
||||
val bvirt = a - x;
|
||||
val y = (a - (x + bvirt)) + (bvirt - b);
|
||||
|
||||
return doubleArrayOf(y, x)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the exact result of multiplying two doubles.
|
||||
*
|
||||
* * the resulting array is the reverse of the standard twoSum in the literature.
|
||||
*
|
||||
* Theorem 18 (Shewchuk): Let a and b be p-bit floating-point numbers, where
|
||||
* p >= 6. Then the following algorithm will produce a nonoverlapping expansion
|
||||
* x + y such that ab = x + y, where x is an approximation to ab and y
|
||||
* represents the roundoff error in the calculation of x. Furthermore, if
|
||||
* round-to-even tiebreaking is used, x and y are non-adjacent.
|
||||
*
|
||||
* See https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf
|
||||
* @param a A double
|
||||
* @param b Another double
|
||||
*/
|
||||
fun twoProduct(a: Double, b: Double): DoubleArray {
|
||||
val x = a * b;
|
||||
|
||||
//const [ah, al] = split(a);
|
||||
val c = f * a;
|
||||
val ah = c - (c - a);
|
||||
val al = a - ah;
|
||||
//const [bh, bl] = split(b);
|
||||
val d = f * b;
|
||||
val bh = d - (d - b);
|
||||
val bl = b - bh;
|
||||
|
||||
val y = (al * bl) - ((x - (ah * bh)) - (al * bh) - (ah * bl));
|
||||
|
||||
//const err1 = x - (ah * bh);
|
||||
//const err2 = err1 - (al * bh);
|
||||
//const err3 = err2 - (ah * bl);
|
||||
//const y = (al * bl) - err3;
|
||||
|
||||
return doubleArrayOf(y, x)
|
||||
}
|
||||
|
||||
fun twoSquare(a: Double): DoubleArray {
|
||||
val x = a * a;
|
||||
|
||||
//const [ah, al] = split(a);
|
||||
val c = f * a;
|
||||
val ah = c - (c - a);
|
||||
val al = a - ah;
|
||||
|
||||
val y = (al * al) - ((x - (ah * ah)) - 2 * (ah * al));
|
||||
|
||||
return doubleArrayOf(y, x)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the exact result of adding two doubles.
|
||||
*
|
||||
* * the resulting array is the reverse of the standard twoSum in the literature.
|
||||
*
|
||||
* Theorem 7 (Knuth): Let a and b be p-bit floating-point numbers. Then the
|
||||
* following algorithm will produce a nonoverlapping expansion x + y such that
|
||||
* a + b = x + y, where x is an approximation to a + b and y is the roundoff
|
||||
* error in the calculation of x.
|
||||
*
|
||||
* See https://people.eecs.berkeley.edu/~jrs/papers/robustr.pdf
|
||||
*/
|
||||
fun twoSum(a: Double, b: Double): DoubleArray {
|
||||
val x = a + b;
|
||||
val bv = x - a;
|
||||
|
||||
return doubleArrayOf((a - (x - bv)) + (b - bv), x)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the result of subtracting the second given double-double-precision
|
||||
* floating point number from the first.
|
||||
*
|
||||
* * relative error bound: 3u^2 + 13u^3, i.e. fl(a-b) = (a-b)(1+ϵ),
|
||||
* where ϵ <= 3u^2 + 13u^3, u = 0.5 * Number.EPSILON
|
||||
* * the error bound is not sharp - the worst case that could be found by the
|
||||
* authors were 2.25u^2
|
||||
*
|
||||
* ALGORITHM 6 of https://hal.archives-ouvertes.fr/hal-01351529v3/document
|
||||
* @param x a double-double precision floating point number
|
||||
* @param y another double-double precision floating point number
|
||||
*/
|
||||
fun ddDiffDd(x: DoubleArray, y: DoubleArray): DoubleArray {
|
||||
val xl = x[0];
|
||||
val xh = x[1];
|
||||
val yl = y[0];
|
||||
val yh = y[1];
|
||||
|
||||
//const [sl,sh] = twoSum(xh,yh);
|
||||
val sh = xh - yh;
|
||||
val _1 = sh - xh;
|
||||
val sl = (xh - (sh - _1)) + (-yh - _1);
|
||||
//const [tl,th] = twoSum(xl,yl);
|
||||
val th = xl - yl;
|
||||
val _2 = th - xl;
|
||||
val tl = (xl - (th - _2)) + (-yl - _2);
|
||||
val c = sl + th;
|
||||
//const [vl,vh] = fastTwoSum(sh,c)
|
||||
val vh = sh + c;
|
||||
val vl = c - (vh - sh);
|
||||
val w = tl + vl
|
||||
//const [zl,zh] = fastTwoSum(vh,w)
|
||||
val zh = vh + w;
|
||||
val zl = w - (zh - vh);
|
||||
|
||||
return doubleArrayOf(zl, zh)
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns the product of two double-double-precision floating point numbers.
|
||||
*
|
||||
* * relative error bound: 7u^2, i.e. fl(a+b) = (a+b)(1+ϵ),
|
||||
* where ϵ <= 7u^2, u = 0.5 * Number.EPSILON
|
||||
* the error bound is not sharp - the worst case that could be found by the
|
||||
* authors were 5u^2
|
||||
*
|
||||
* * ALGORITHM 10 of https://hal.archives-ouvertes.fr/hal-01351529v3/document
|
||||
* @param x a double-double precision floating point number
|
||||
* @param y another double-double precision floating point number
|
||||
*/
|
||||
fun ddMultDd(x: DoubleArray, y: DoubleArray): DoubleArray {
|
||||
|
||||
|
||||
//const xl = x[0];
|
||||
val xh = x[1];
|
||||
//const yl = y[0];
|
||||
val yh = y[1];
|
||||
|
||||
//const [cl1,ch] = twoProduct(xh,yh);
|
||||
val ch = xh * yh;
|
||||
val c = f * xh;
|
||||
val ah = c - (c - xh);
|
||||
val al = xh - ah;
|
||||
val d = f * yh;
|
||||
val bh = d - (d - yh);
|
||||
val bl = yh - bh;
|
||||
val cl1 = (al * bl) - ((ch - (ah * bh)) - (al * bh) - (ah * bl));
|
||||
|
||||
//return fastTwoSum(ch,cl1 + (xh*yl + xl*yh));
|
||||
val b = cl1 + (xh * y[0] + x[0] * yh);
|
||||
val xx = ch + b;
|
||||
|
||||
return doubleArrayOf(b - (xx - ch), xx)
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Returns the result of adding two double-double-precision floating point
|
||||
* numbers.
|
||||
*
|
||||
* * relative error bound: 3u^2 + 13u^3, i.e. fl(a+b) = (a+b)(1+ϵ),
|
||||
* where ϵ <= 3u^2 + 13u^3, u = 0.5 * Number.EPSILON
|
||||
* * the error bound is not sharp - the worst case that could be found by the
|
||||
* authors were 2.25u^2
|
||||
*
|
||||
* ALGORITHM 6 of https://hal.archives-ouvertes.fr/hal-01351529v3/document
|
||||
* @param x a double-double precision floating point number
|
||||
* @param y another double-double precision floating point number
|
||||
*/
|
||||
fun ddAddDd(x: DoubleArray, y: DoubleArray): DoubleArray {
|
||||
val xl = x[0];
|
||||
val xh = x[1];
|
||||
val yl = y[0];
|
||||
val yh = y[1];
|
||||
|
||||
//const [sl,sh] = twoSum(xh,yh);
|
||||
val sh = xh + yh;
|
||||
val _1 = sh - xh;
|
||||
val sl = (xh - (sh - _1)) + (yh - _1);
|
||||
//val [tl,th] = twoSum(xl,yl);
|
||||
val th = xl + yl;
|
||||
val _2 = th - xl;
|
||||
val tl = (xl - (th - _2)) + (yl - _2);
|
||||
val c = sl + th;
|
||||
//val [vl,vh] = fastTwoSum(sh,c)
|
||||
val vh = sh + c;
|
||||
val vl = c - (vh - sh);
|
||||
val w = tl + vl
|
||||
//val [zl,zh] = fastTwoSum(vh,w)
|
||||
val zh = vh + w;
|
||||
val zl = w - (zh - vh);
|
||||
|
||||
return doubleArrayOf(zl, zh)
|
||||
}
|
||||
|
||||
|
||||
/**
|
||||
* Returns the product of a double-double-precision floating point number and a
|
||||
* double.
|
||||
*
|
||||
* * slower than ALGORITHM 8 (one call to fastTwoSum more) but about 2x more
|
||||
* accurate
|
||||
* * relative error bound: 1.5u^2 + 4u^3, i.e. fl(a+b) = (a+b)(1+ϵ),
|
||||
* where ϵ <= 1.5u^2 + 4u^3, u = 0.5 * Number.EPSILON
|
||||
* * the bound is very sharp
|
||||
* * probably prefer `ddMultDouble2` due to extra speed
|
||||
*
|
||||
* * ALGORITHM 7 of https://hal.archives-ouvertes.fr/hal-01351529v3/document
|
||||
* @param y a double
|
||||
* @param x a double-double precision floating point number
|
||||
*/
|
||||
fun ddMultDouble1(y: Double, x: DoubleArray): DoubleArray {
|
||||
val xl = x[0];
|
||||
val xh = x[1];
|
||||
|
||||
//val [cl1,ch] = twoProduct(xh,y);
|
||||
val ch = xh * y;
|
||||
val c = f * xh;
|
||||
val ah = c - (c - xh);
|
||||
val al = xh - ah;
|
||||
val d = f * y;
|
||||
val bh = d - (d - y);
|
||||
val bl = y - bh;
|
||||
val cl1 = (al * bl) - ((ch - (ah * bh)) - (al * bh) - (ah * bl));
|
||||
|
||||
val cl2 = xl * y;
|
||||
//val [tl1,th] = fastTwoSum(ch,cl2);
|
||||
val th = ch + cl2;
|
||||
val tl1 = cl2 - (th - ch);
|
||||
|
||||
val tl2 = tl1 + cl1;
|
||||
//val [zl,zh] = fastTwoSum(th,tl2);
|
||||
val zh = th + tl2;
|
||||
val zl = tl2 - (zh - th);
|
||||
|
||||
return doubleArrayOf(zl, zh);
|
||||
}
|
||||
@@ -0,0 +1,19 @@
|
||||
package com.icegps.triangulation
|
||||
|
||||
fun orient2d(bx: Double, by: Double, ax: Double, ay: Double, cx: Double, cy: Double): Double {
|
||||
// (ax,ay) (bx,by) are swapped such that the sign of the determinant is flipped. which is what Delaunator.kt expects.
|
||||
|
||||
/*
|
||||
| a b | = | ax - cx ay - cy |
|
||||
| c d | | bx - cx by - cy |
|
||||
*/
|
||||
|
||||
val a = twoDiff(ax, cx)
|
||||
val b = twoDiff(ay, cy)
|
||||
val c = twoDiff(bx, cx)
|
||||
val d = twoDiff(by, cy)
|
||||
|
||||
val determinant = ddDiffDd(ddMultDd(a, d), ddMultDd(b, c))
|
||||
|
||||
return determinant[1]
|
||||
}
|
||||
@@ -0,0 +1,13 @@
|
||||
package com.icegps.triangulation
|
||||
|
||||
import com.icegps.math.geometry.Vector3D
|
||||
|
||||
/**
|
||||
* @author tabidachinokaze
|
||||
* @date 2025/11/26
|
||||
*/
|
||||
data class Triangle(
|
||||
val x1: Vector3D,
|
||||
val x2: Vector3D,
|
||||
val x3: Vector3D,
|
||||
)
|
||||
Reference in New Issue
Block a user