package org.openrndr.extra.triangulation import org.openrndr.math.Vector2 import org.openrndr.shape.Rectangle import org.openrndr.shape.Triangle import org.openrndr.shape.contour import org.openrndr.shape.contours import kotlin.js.JsName 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): 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 { val e0 = inedges.getOrNull(i) ?: return@sequence 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 } fun voronoi(bounds: Rectangle): Voronoi = Voronoi(this, bounds) }