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package org.openrndr.extra.triangulation
import kotlin.math.*
val EPSILON: Double = 2.0.pow(-52)
/**
* A Kotlin port of Mapbox's Delaunator incredibly fast JavaScript library for Delaunay triangulation of 2D points.
*
* @description Port of Mapbox's Delaunator (JavaScript) library - https://github.com/mapbox/delaunator
* @property coords flat positions' array - [x0, y0, x1, y1..]
*
* @since f0ed80d - commit
* @author Ricardo Matias
*/
@Suppress("unused")
class Delaunator(val coords: DoubleArray) {
val EDGE_STACK = IntArray(512)
private var count = coords.size shr 1
// arrays that will store the triangulation graph
val maxTriangles = (2 * count - 5).coerceAtLeast(0)
private val _triangles = IntArray(maxTriangles * 3)
private val _halfedges = IntArray(maxTriangles * 3)
lateinit var triangles: IntArray
lateinit var halfedges: IntArray
// temporary arrays for tracking the edges of the advancing convex hull
private var hashSize = ceil(sqrt(count * 1.0)).toInt()
private var hullPrev = IntArray(count) // edge to prev edge
private var hullNext = IntArray(count) // edge to next edge
private var hullTri = IntArray(count) // edge to adjacent triangle
private var hullHash = IntArray(hashSize) // angular edge hash
private var hullStart: Int = -1
// temporary arrays for sorting points
private var ids = IntArray(count)
private var dists = DoubleArray(count)
private var cx: Double = Double.NaN
private var cy: Double = Double.NaN
private var trianglesLen: Int = -1
lateinit var hull: IntArray
init {
update()
}
fun update() {
if (coords.size <= 2) {
halfedges = IntArray(0)
triangles = IntArray(0)
hull = IntArray(0)
return
}
// populate an array of point indices calculate input data bbox
var minX = Double.POSITIVE_INFINITY
var minY = Double.POSITIVE_INFINITY
var maxX = Double.NEGATIVE_INFINITY
var maxY = Double.NEGATIVE_INFINITY
// points -> points
// minX, minY, maxX, maxY
for (i in 0 until count) {
val x = coords[2 * i]
val y = coords[2 * i + 1]
if (x < minX) minX = x
if (y < minY) minY = y
if (x > maxX) maxX = x
if (y > maxY) maxY = y
ids[i] = i
}
val cx = (minX + maxX) / 2
val cy = (minY + maxY) / 2
var minDist = Double.POSITIVE_INFINITY
var i0: Int = -1
var i1: Int = -1
var i2: Int = -1
// pick a seed point close to the center
for (i in 0 until count) {
val d = dist(cx, cy, coords[2 * i], coords[2 * i + 1])
if (d < minDist) {
i0 = i
minDist = d
}
}
val i0x = coords[2 * i0]
val i0y = coords[2 * i0 + 1]
minDist = Double.POSITIVE_INFINITY
// Find the point closest to the seed
for(i in 0 until count) {
if (i == i0) continue
val d = dist(i0x, i0y, coords[2 * i], coords[2 * i + 1])
if (d < minDist && d > 0) {
i1 = i
minDist = d
}
}
var i1x = coords[2 * i1]
var i1y = coords[2 * i1 + 1]
var minRadius = Double.POSITIVE_INFINITY
// Find the third point which forms the smallest circumcircle with the first two
for (i in 0 until count) {
if(i == i0 || i == i1) continue
val r = circumradius(i0x, i0y, i1x, i1y, coords[2 * i], coords[2 * i + 1])
if(r < minRadius) {
i2 = i
minRadius = r
}
}
if (minRadius == Double.POSITIVE_INFINITY) {
// order collinear points by dx (or dy if all x are identical)
// and return the list as a hull
for (i in 0 until count) {
val a = (coords[2 * i] - coords[0])
val b = (coords[2 * i + 1] - coords[1])
dists[i] = if (a == 0.0) b else a
}
quicksort(ids, dists, 0, count - 1)
val nhull = IntArray(count)
var j = 0
var d0 = Double.NEGATIVE_INFINITY
for (i in 0 until count) {
val id = ids[i]
if (dists[id] > d0) {
nhull[j++] = id
d0 = dists[id]
}
}
hull = nhull.copyOf(j)
triangles = IntArray(0)
halfedges = IntArray(0)
return
}
var i2x = coords[2 * i2]
var i2y = coords[2 * i2 + 1]
// swap the order of the seed points for counter-clockwise orientation
if (orient2d(i0x, i0y, i1x, i1y, i2x, i2y) < 0.0) {
val i = i1
val x = i1x
val y = i1y
i1 = i2
i1x = i2x
i1y = i2y
i2 = i
i2x = x
i2y = y
}
val center = circumcenter(i0x, i0y, i1x, i1y, i2x, i2y)
this.cx = center[0]
this.cy = center[1]
for (i in 0 until count) {
dists[i] = dist(coords[2 * i], coords[2 * i + 1], center[0], center[1])
}
// sort the points by distance from the seed triangle circumcenter
quicksort(ids, dists, 0, count - 1)
// set up the seed triangle as the starting hull
hullStart = i0
var hullSize = 3
hullNext[i0] = i1
hullNext[i1] = i2
hullNext[i2] = i0
hullPrev[i2] = i1
hullPrev[i0] = i2
hullPrev[i1] = i0
hullTri[i0] = 0
hullTri[i1] = 1
hullTri[i2] = 2
hullHash.fill(-1)
hullHash[hashKey(i0x, i0y)] = i0
hullHash[hashKey(i1x, i1y)] = i1
hullHash[hashKey(i2x, i2y)] = i2
trianglesLen = 0
addTriangle(i0, i1, i2, -1, -1, -1)
var xp = 0.0
var yp = 0.0
for (k in ids.indices) {
val i = ids[k]
val x = coords[2 * i]
val y = coords[2 * i + 1]
// skip near-duplicate points
if (k > 0 && abs(x - xp) <= EPSILON && abs(y - yp) <= EPSILON) continue
xp = x
yp = y
// skip seed triangle points
if (i == i0 || i == i1 || i == i2) continue
// find a visible edge on the convex hull using edge hash
var start = 0
val key = hashKey(x, y)
for (j in 0 until hashSize) {
start = hullHash[(key + j) % hashSize]
if (start != -1 && start != hullNext[start]) break
}
start = hullPrev[start]
var e = start
var q = hullNext[e]
while (orient2d(x, y, coords[2 * e], coords[2 * e + 1], coords[2 * q], coords[2 * q + 1]) >= 0) {
e = q
if (e == start) {
e = -1
break
}
q = hullNext[e]
}
if (e == -1) continue // likely a near-duplicate point skip it
// add the first triangle from the point
var t = addTriangle(e, i, hullNext[e], -1, -1, hullTri[e])
// recursively flip triangles from the point until they satisfy the Delaunay condition
hullTri[i] = legalize(t + 2)
hullTri[e] = t // keep track of boundary triangles on the hull
hullSize++
// walk forward through the hull, adding more triangles and flipping recursively
var next = hullNext[e]
q = hullNext[next]
while (orient2d(x, y, coords[2 * next], coords[2 * next + 1], coords[2 * q], coords[2 * q + 1]) < 0) {
t = addTriangle(next, i, q, hullTri[i], -1, hullTri[next])
hullTri[i] = legalize(t + 2)
hullNext[next] = next // mark as removed
hullSize--
next = q
q = hullNext[next]
}
// walk backward from the other side, adding more triangles and flipping
if (e == start) {
q = hullPrev[e]
while (orient2d(x, y, coords[2 * q], coords[2 * q + 1], coords[2 * e], coords[2 * e + 1]) < 0) {
t = addTriangle(q, i, e, -1, hullTri[e], hullTri[q])
legalize(t + 2)
hullTri[q] = t
hullNext[e] = e // mark as removed
hullSize--
e = q
q = hullPrev[e]
}
}
// update the hull indices
hullStart = e
hullPrev[i] = e
hullNext[e] = i
hullPrev[next] = i
hullNext[i] = next
// save the two new edges in the hash table
hullHash[hashKey(x, y)] = i
hullHash[hashKey(coords[2 * e], coords[2 * e + 1])] = e
}
hull = IntArray(hullSize)
var e = hullStart
for (i in 0 until hullSize) {
hull[i] = e
e = hullNext[e]
}
// trim typed triangle mesh arrays
triangles = _triangles.copyOf(trianglesLen)
halfedges = _halfedges.copyOf(trianglesLen)
}
private fun legalize(a: Int): Int {
var i = 0
var na = a
var ar: Int
// recursion eliminated with a fixed-size stack
while (true) {
val b = _halfedges[na]
/* if the pair of triangles doesn't satisfy the Delaunay condition
* (p1 is inside the circumcircle of [p0, pl, pr]), flip them,
* then do the same check/flip recursively for the new pair of triangles
*
* pl pl
* /||\ / \
* al/ || \bl al/ \a
* / || \ / \
* / a||b \ flip /___ar___\
* p0\ || /p1 => p0\---bl---/p1
* \ || / \ /
* ar\ || /br b\ /br
* \||/ \ /
* pr pr
*/
val a0 = na - na % 3
ar = a0 + (na + 2) % 3
if (b == -1) { // convex hull edge
if (i == 0) break
na = EDGE_STACK[--i]
continue
}
val b0 = b - b % 3
val al = a0 + (na + 1) % 3
val bl = b0 + (b + 2) % 3
val p0 = _triangles[ar]
val pr = _triangles[na]
val pl = _triangles[al]
val p1 = _triangles[bl]
val illegal = inCircleRobust(
coords[2 * p0], coords[2 * p0 + 1],
coords[2 * pr], coords[2 * pr + 1],
coords[2 * pl], coords[2 * pl + 1],
coords[2 * p1], coords[2 * p1 + 1])
if (illegal) {
_triangles[na] = p1
_triangles[b] = p0
val hbl = _halfedges[bl]
// edge swapped on the other side of the hull (rare) fix the halfedge reference
if (hbl == -1) {
var e = hullStart
do {
if (hullTri[e] == bl) {
hullTri[e] = na
break
}
e = hullPrev[e]
} while (e != hullStart)
}
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]
}
