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[orx-shapes] Add alpha shapes (#203)

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This commit is contained in:
Steven van den Broek
2021-10-24 20:41:40 +02:00
committed by GitHub
parent af524b8e42
commit ee3a3603c0
7 changed files with 186 additions and 2 deletions
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7
orx-shapes/build.gradle.kts
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@@ -26,6 +26,7 @@ kotlin {
dependencies {
implementation(project(":orx-camera"))
implementation(project(":orx-color"))
implementation(project(":orx-jvm:orx-triangulation"))
implementation("org.openrndr:openrndr-application:$openrndrVersion")
implementation("org.openrndr:openrndr-extensions:$openrndrVersion")
runtimeOnly("org.openrndr:openrndr-gl3:$openrndrVersion")
@@ -67,6 +68,12 @@ kotlin {
}
}
@Suppress("UNUSED_VARIABLE")
val jvmMain by getting {
dependencies {
implementation(project(":orx-jvm:orx-triangulation"))
}
}
@Suppress("UNUSED_VARIABLE")
val commonTest by getting {
dependencies {
implementation(kotlin("test-common"))

24
orx-shapes/src/demo/kotlin/DemoAlphaShape.kt Normal file
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@@ -0,0 +1,24 @@
import org.openrndr.application
import org.openrndr.color.ColorRGBa
import org.openrndr.extra.shapes.AlphaShape
import org.openrndr.math.Vector2
import kotlin.random.Random
fun main() = application {
program {
val points = List(20) {
Vector2(
Random.nextDouble(width*0.25, width*0.75),
Random.nextDouble(height*0.25, height*0.75)
)
}
val alphaShape = AlphaShape(points)
val c = alphaShape.create()
extend {
drawer.fill = ColorRGBa.PINK
drawer.contour(c)
drawer.fill = ColorRGBa.WHITE
drawer.circles(points, 4.0)
}
}
}

2
orx-shapes/src/demo/kotlin/DemoBezierPatchDrawer02.kt
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@@ -2,9 +2,9 @@ import org.openrndr.application
import org.openrndr.color.ColorRGBa
import org.openrndr.draw.loadFont
import org.openrndr.extensions.SingleScreenshot
import org.openrndr.extra.color.spaces.toOKLABa
import org.openrndr.extra.shapes.bezierPatch
import org.openrndr.extra.shapes.drawers.bezierPatch
import org.openrndr.extras.color.spaces.toOKLABa
import org.openrndr.shape.Circle
fun main() {

2
orx-shapes/src/demo/kotlin/DemoBezierPatchDrawer03.kt
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@@ -6,7 +6,7 @@ import org.openrndr.extensions.SingleScreenshot
import org.openrndr.extra.shapes.bezierPatch
import org.openrndr.extra.shapes.drawers.bezierPatch
import org.openrndr.extra.shapes.grid
import org.openrndr.extras.color.spaces.toOKLABa
import org.openrndr.extra.color.spaces.toOKLABa
import org.openrndr.math.Vector2
import org.openrndr.math.Vector3
import org.openrndr.math.min

2
orx-shapes/src/demo/kotlin/DemoHobbyCurve.kt → orx-shapes/src/demo/kotlin/DemoHobbyCurve01.kt
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@@ -10,6 +10,8 @@ fun main() = application {
drawer.stroke = ColorRGBa.BLACK
drawer.fill = ColorRGBa.PINK
drawer.contour(hobbyCurve(points, closed=true))
drawer.fill = ColorRGBa.WHITE
drawer.circles(points, 4.0)
}
}
}

26
orx-shapes/src/demo/kotlin/DemoHobbyCurve02.kt Normal file
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@@ -0,0 +1,26 @@
import org.openrndr.application
import org.openrndr.color.ColorRGBa
import org.openrndr.extra.shapes.AlphaShape
import org.openrndr.extra.shapes.hobbyCurve
import org.openrndr.math.Vector2
import kotlin.random.Random
fun main() = application {
program {
val points = List(20) {
Vector2(
Random.nextDouble(width*0.25, width*0.75),
Random.nextDouble(height*0.25, height*0.75)
)
}
val alphaShape = AlphaShape(points)
val c = alphaShape.create()
val hobby = hobbyCurve(c.segments.map { it.start }, closed=true)
extend {
drawer.fill = ColorRGBa.PINK
drawer.contour(hobby)
drawer.fill = ColorRGBa.WHITE
drawer.circles(points, 4.0)
}
}
}

125
orx-shapes/src/jvmMain/kotlin/AlphaShape.kt Normal file
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@@ -0,0 +1,125 @@
package org.openrndr.extra.shapes
import org.openrndr.extra.triangulation.Delaunay
import org.openrndr.math.Vector2
import org.openrndr.shape.Segment
import org.openrndr.shape.ShapeContour
import org.openrndr.shape.contains
import kotlin.math.max
import kotlin.math.min
import kotlin.math.pow
import kotlin.math.sqrt
private fun circumradius(p1: Vector2, p2: Vector2, p3: Vector2): Double {
val a = (p2 - p1).length
val b = (p3 - p2).length
val c = (p1 - p3).length
return (a*b*c) / sqrt((a+b+c)*(b+c-a)*(c+a-b)*(a+b-c))
}
/**
* Class for creating alpha shapes.
* Use the [create] method to create an alpha shape.
* @param points The points for which an alpha shape is calculated.
*/
class AlphaShape(val points: List<Vector2>) {
val delaunay = Delaunay.from(points)
private fun <A, B> Pair<A, B>.flip() = Pair(second, first)
/**
* Creates an alpha shape.
* @param alpha The alpha parameter from the mathematical definition of an alpha shape.
* If alpha is 0.0 the alpha shape consists only of the set of input points, yielding [ShapeContour.EMPTY].
* As alpha goes to infinity, the alpha shape becomes equal to the convex hull of the input points.
* @return A closed [ShapeContour] representing the outer boundary of the alpha shape.
*/
fun create(alpha: Double): ShapeContour {
if (delaunay.points.size < 9) return ShapeContour.EMPTY
val triangles = delaunay.triangles
var allEdges = mutableSetOf<Pair<Int, Int>>()
var perimeterEdges = mutableSetOf<Pair<Int, Int>>()
for (i in triangles.indices step 3){
val t0 = triangles[i] * 2
val t1 = triangles[i + 1] * 2
val t2 = triangles[i + 2] * 2
val p1 = getVec(t0)
val p2 = getVec(t1)
val p3 = getVec(t2)
val r = circumradius(p1, p2, p3)
if (r < alpha){
val edges = listOf(Pair(t0, t1), Pair(t1, t2), Pair(t2, t0))
for (edge in edges){
val fEdge = edge.flip()
if (edge !in allEdges && fEdge !in allEdges){
allEdges.add(edge)
perimeterEdges.add(edge)
} else {
perimeterEdges.remove(edge)
perimeterEdges.remove(fEdge)
}
}
}
}
return edgesToShapeContour(perimeterEdges.toList())
}
/**
* Returns the alpha shape with the smallest alpha such that all input points are contained in the alpha shape.
*/
fun create(): ShapeContour = create(determineAlpha())
private fun getVec(i: Int) = Vector2(delaunay.points[i], delaunay.points[i + 1])
private fun edgesToShapeContour(edges: List<Pair<Int, Int>>): ShapeContour {
if (edges.isEmpty()) return ShapeContour.EMPTY
val mapping = edges.toMap()
val segments = mutableListOf<Segment>()
val start = edges.first().first
var current = start
repeat(edges.size) {
val next = mapping[current]!!
segments.add(Segment(getVec(current), getVec(next)))
current = next
}
return if (current == start) {
ShapeContour(segments, closed = true)
} else {
ShapeContour.EMPTY
}
}
/**
* Performs binary search to find the smallest alpha such that all points are inside the alpha shape.
*/
fun determineAlpha(): Double {
// Compute bounding box to find an upper bound for the binary search
var minX = Double.POSITIVE_INFINITY
var minY = Double.POSITIVE_INFINITY
var maxX = Double.NEGATIVE_INFINITY
var maxY = Double.NEGATIVE_INFINITY
for (i in delaunay.points.indices step 2){
val x = delaunay.points[i]
val y = delaunay.points[i+1]
minX = min(minX, x)
maxX = max(maxX, x)
minY = min(minY, y)
maxY = max(maxY, y)
}
// Perform binary search
var lower = 0.0
var upper = (maxX - minX).pow(2) + (maxY - minY).pow(2)
val precision = 0.001
while(lower < upper - precision){
val mid = (lower + upper)/2
val polygon = create(mid)
if (points.all { it in polygon }) upper = mid else lower = mid
}
return upper
}
}