Add 3D Bézier patch (#190)
This commit is contained in:
Steven van den Broek
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GitHub
GitHub
parent
941d5020db
commit
a6d08467fa
274
orx-shapes/src/commonMain/kotlin/BezierPatch3D.kt
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274
orx-shapes/src/commonMain/kotlin/BezierPatch3D.kt
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@@ -0,0 +1,274 @@
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package org.openrndr.extra.shapes
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import org.openrndr.color.AlgebraicColor
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import org.openrndr.color.ColorRGBa
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import org.openrndr.color.ConvertibleToColorRGBa
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import org.openrndr.math.Matrix44
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import org.openrndr.math.Vector3
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import org.openrndr.shape.Path3D
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import org.openrndr.shape.Segment3D
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import kotlin.random.Random
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open class BezierPatch3DBase<C>(
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val points: List<List<Vector3>>,
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val colors: List<List<C>> = emptyList()
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)
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where C : AlgebraicColor<C>, C : ConvertibleToColorRGBa {
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init {
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require(points.size == 4 && points.all { it.size == 4 })
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require(colors.isEmpty() || colors.size == 4 && colors.all { it.size == 4 })
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}
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/**
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* Return a transposed version of the bezier path by transposing the [points] matrix
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*/
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val transposed
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get() = BezierPatch3DBase(
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listOf(
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listOf(points[0][0], points[1][0], points[2][0], points[3][0]),
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listOf(points[0][1], points[1][1], points[2][1], points[3][1]),
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listOf(points[0][2], points[1][2], points[2][2], points[3][2]),
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listOf(points[0][3], points[1][3], points[2][3], points[3][3]),
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),
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if (colors.isEmpty()) emptyList() else {
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listOf(
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listOf(colors[0][0], colors[1][0], colors[2][0], colors[3][0]),
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listOf(colors[0][1], colors[1][1], colors[2][1], colors[3][1]),
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listOf(colors[0][2], colors[1][2], colors[2][2], colors[3][2]),
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listOf(colors[0][3], colors[1][3], colors[2][3], colors[3][3]),
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)
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}
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)
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fun transform(transform: Matrix44) = BezierPatch3DBase(points.map { r ->
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r.map { (transform * it.xyz1).div }
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}, colors)
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private fun coeffs2(t: Double): DoubleArray {
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val it = 1.0 - t
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val it2 = it * it
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val t2 = t * t
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return doubleArrayOf(it2, 2 * it * t, t2)
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}
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private fun coeffs3(t: Double): DoubleArray {
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val it = 1.0 - t
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val it2 = it * it
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val it3 = it2 * it
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val t2 = t * t
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val t3 = t2 * t
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return doubleArrayOf(it3, 3 * it2 * t, 3 * it * t2, t3)
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}
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/**
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* Return a point on the patch by using its u,v parameterization
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* @param u a value between 0 and 1
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* @param v a value between 0 and 1
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*/
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fun position(u: Double, v: Double): Vector3 {
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val csu = coeffs3(u)
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val csv = coeffs3(v)
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var result = Vector3.ZERO
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for (j in 0 until 4) {
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for (i in 0 until 4) {
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result += points[j][i] * csu[i] * csv[j]
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}
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}
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return result
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}
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/**
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* Return a gradient vector on the patch by using its u,v parameterization
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* @param u a value between 0 and 1
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* @param v a value between 0 and 1
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*/
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fun gradient(u: Double, v: Double): Vector3 {
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val f0 = List(4) { MutableList(3) { Vector3.ZERO } }
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for (j in 0 until 4) {
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for (i in 0 until 3) {
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f0[j][i] = points[j][i + 1] - points[j][i]
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}
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}
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val f1 = List(3) { MutableList(3) { Vector3.ZERO } }
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for (j in 0 until 3) {
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for (i in 0 until 3) {
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f1[j][i] = f0[j + 1][i] - f0[j][i]
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}
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}
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val csu = coeffs2(u)
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val csv = coeffs2(v)
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var result = Vector3.ZERO
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for (j in 0 until 3) {
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for (i in 0 until 3) {
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result += f1[j][i] * csu[i] * csv[j]
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}
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}
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return result
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}
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/**
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* Generate a random point on the path
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* @return a point that is uniformly distributed in uv space
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*/
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fun randomPoint(random: Random = Random.Default) = position(random.nextDouble(), random.nextDouble())
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fun horizontal(v: Double): Path3D {
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val cs = coeffs3(v)
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val cps = Array(4) { Vector3.ZERO }
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for (j in 0 until 4) {
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for (i in 0 until 4) {
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cps[j] += points[i][j] * cs[i]
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}
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}
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return Path3D(listOf(Segment3D(cps[0], cps[1], cps[2], cps[3])), false)
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}
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fun vertical(u: Double): Path3D {
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val cs = coeffs3(u)
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val cps = Array(4) { Vector3.ZERO }
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for (j in 0 until 4) {
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for (i in 0 until 4) {
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cps[j] += points[j][i] * cs[i]
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}
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}
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return Path3D(listOf(Segment3D(cps[0], cps[1], cps[2], cps[3])), false)
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}
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/**
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* Extract a sub-patch based on uv parameterization
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*/
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fun sub(u0: Double, v0: Double, u1: Double, v1: Double): BezierPatch3DBase<C> {
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val c0 = Segment3D(points[0][0], points[0][1], points[0][2], points[0][3]).sub(u0, u1)
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val c1 = Segment3D(points[1][0], points[1][1], points[1][2], points[1][3]).sub(u0, u1)
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val c2 = Segment3D(points[2][0], points[2][1], points[2][2], points[2][3]).sub(u0, u1)
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val c3 = Segment3D(points[3][0], points[3][1], points[3][2], points[3][3]).sub(u0, u1)
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val sub0 = bezierPatch(c0, c1, c2, c3)
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val d0 = Segment3D(sub0.points[0][0], sub0.points[1][0], sub0.points[2][0], sub0.points[3][0]).sub(v0, v1)
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val d1 = Segment3D(sub0.points[0][1], sub0.points[1][1], sub0.points[2][1], sub0.points[3][1]).sub(v0, v1)
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val d2 = Segment3D(sub0.points[0][2], sub0.points[1][2], sub0.points[2][2], sub0.points[3][2]).sub(v0, v1)
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val d3 = Segment3D(sub0.points[0][3], sub0.points[1][3], sub0.points[2][3], sub0.points[3][3]).sub(v0, v1)
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return fromSegments<C>(d0, d1, d2, d3).transposed
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}
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val path: Path3D = Path3D(
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listOf(
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Segment3D(points[0][0], points[0][1], points[0][2], points[0][3]),
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Segment3D(points[0][3], points[1][3], points[2][3], points[3][3]),
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Segment3D(points[3][3], points[3][2], points[3][1], points[3][0]),
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Segment3D(points[3][0], points[2][0], points[1][0], points[0][0]),
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), true
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)
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operator fun times(scale: Double) =
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BezierPatch3DBase(
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points.map { j -> j.map { i -> i * scale } },
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if (colors.isEmpty()) colors else colors.map { j -> j.map { i -> i * scale } }
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)
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operator fun div(scale: Double) =
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BezierPatch3DBase(points.map { j -> j.map { i -> i / scale } },
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if (colors.isEmpty()) colors else colors.map { j -> j.map { i -> i / scale } }
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)
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operator fun plus(right: BezierPatch3DBase<C>) =
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BezierPatch3DBase(List(4) { j -> List(4) { i -> points[j][i] + right.points[j][i] } },
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if (colors.isEmpty() && right.colors.isEmpty()) { colors }
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else if (colors.isEmpty() && right.colors.isNotEmpty()) { right.colors }
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else if (colors.isNotEmpty() && right.colors.isEmpty()) { colors }
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else { List(4) { j -> List(4) { i -> colors[j][i] + right.colors[j][i] } } }
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)
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operator fun minus(right: BezierPatch3DBase<C>) =
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BezierPatch3DBase(List(4) { j -> List(4) { i -> points[j][i] - right.points[j][i] } },
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if (colors.isEmpty() && right.colors.isEmpty()) { colors }
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else if (colors.isEmpty() && right.colors.isNotEmpty()) { right.colors }
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else if (colors.isNotEmpty() && right.colors.isEmpty()) { colors }
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else { List(4) { j -> List(4) { i -> colors[j][i] - right.colors[j][i] } } }
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)
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fun <K> withColors(colors: List<List<K>>): BezierPatch3DBase<K>
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where K : AlgebraicColor<K>, K : ConvertibleToColorRGBa {
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return BezierPatch3DBase(points, colors)
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}
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companion object {
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fun <C> fromSegments(c0: Segment3D, c1: Segment3D, c2: Segment3D, c3: Segment3D): BezierPatch3DBase<C>
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where C : AlgebraicColor<C>, C : ConvertibleToColorRGBa {
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val c0c = c0.cubic
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val c1c = c1.cubic
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val c2c = c2.cubic
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val c3c = c3.cubic
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val c0l = listOf(c0c.start, c0c.control[0], c0c.control[1], c0c.end)
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val c1l = listOf(c1c.start, c1c.control[0], c1c.control[1], c1c.end)
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val c2l = listOf(c2c.start, c2c.control[0], c2c.control[1], c2c.end)
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val c3l = listOf(c3c.start, c3c.control[0], c3c.control[1], c3c.end)
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return BezierPatch3DBase(listOf(c0l, c1l, c2l, c3l))
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}
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}
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}
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class BezierPatch3D(points: List<List<Vector3>>, colors: List<List<ColorRGBa>> = emptyList()) :
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BezierPatch3DBase<ColorRGBa>(points, colors)
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/**
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* Create a cubic bezier patch from 4 segments. The control points of the segments are used in row-wise fashion
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*/
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fun bezierPatch(c0: Segment3D, c1: Segment3D, c2: Segment3D, c3: Segment3D): BezierPatch3D {
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val c0c = c0.cubic
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val c1c = c1.cubic
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val c2c = c2.cubic
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val c3c = c3.cubic
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val c0l = listOf(c0c.start, c0c.control[0], c0c.control[1], c0c.end)
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val c1l = listOf(c1c.start, c1c.control[0], c1c.control[1], c1c.end)
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val c2l = listOf(c2c.start, c2c.control[0], c2c.control[1], c2c.end)
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val c3l = listOf(c3c.start, c3c.control[0], c3c.control[1], c3c.end)
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return BezierPatch3D(listOf(c0l, c1l, c2l, c3l))
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}
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/**
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* Create a bezier patch from a closed shape contour (with 4 segments).
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* @param alpha control for linearity, default is `1.0/3.0`
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*/
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fun bezierPatch(path: Path3D, alpha: Double = 1.0 / 3.0): BezierPatch3D {
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require(path.segments.size == 4) {
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"""contour needs exactly 4 segments (has ${path.segments.size})"""
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}
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val c0 = path.segments[0].cubic
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val c1 = path.segments[1].cubic
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val c2 = path.segments[2].cubic
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val c3 = path.segments[3].cubic
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val fa = 1.0 - alpha
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val fb = alpha
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val x00 = (c0.control[0] * fa + c2.control[1] * fb + c3.control[1] * fa + c1.control[0] * fb) / 2.0
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val x01 = (c0.control[1] * fa + c2.control[0] * fb + c3.control[1] * fb + c1.control[0] * fa) / 2.0
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val x10 = (c0.control[0] * fb + c2.control[1] * fa + c3.control[0] * fa + c1.control[1] * fb) / 2.0
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val x11 = (c0.control[1] * fb + c2.control[0] * fa + c3.control[0] * fb + c1.control[1] * fa) / 2.0
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val cps = listOf(
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listOf(c0.start, c0.control[0], c0.control[1], c0.end),
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listOf(c3.control[1], x00, x01, c1.control[0]),
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listOf(c3.control[0], x10, x11, c1.control[1]),
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listOf(c2.end, c2.control[1], c2.control[0], c2.start),
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)
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return BezierPatch3D(cps)
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}
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/**
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* Create a bezier patch from 4 corners
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* @param corners a list of corners from which to create the patch
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* @param alpha control for linearity, default is `1.0/3.0`
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*/
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fun bezierPatch(corners: List<Vector3>, alpha: Double = 1.0 / 3.0): BezierPatch3D {
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require(corners.size == 4) {
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"""need exactly 4 corners (got ${corners.size}"""
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}
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return bezierPatch(Path3D.fromPoints(corners, true), alpha)
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}
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@@ -3,6 +3,7 @@ package org.openrndr.extra.shapes.drawers
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import org.openrndr.color.ColorRGBa
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import org.openrndr.color.ColorRGBa
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import org.openrndr.draw.*
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import org.openrndr.draw.*
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import org.openrndr.extra.shapes.BezierPatchBase
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import org.openrndr.extra.shapes.BezierPatchBase
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import org.openrndr.extra.shapes.BezierPatch3DBase
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import org.openrndr.internal.Driver
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import org.openrndr.internal.Driver
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import org.openrndr.math.Vector2
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import org.openrndr.math.Vector2
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@@ -258,6 +259,97 @@ class BezierPatchDrawer {
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)
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)
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shader.end()
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shader.end()
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}
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}
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@JvmName("drawBezierPatch3D")
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fun drawBezierPatches(
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context: DrawContext,
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drawStyle: DrawStyle,
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bezierPatches: List<BezierPatch3DBase<ColorRGBa>>,
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subdivisions: Int = 32
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) {
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ensureVertexCount(bezierPatches.size * 16)
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val shader = shadeStyleManager.shader(
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drawStyle.shadeStyle,
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listOf(vertices.vertexFormat),
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emptyList()
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)
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vertices.put {
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for (bezierPatch in bezierPatches) {
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for (j in 0 until 4) {
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for (i in 0 until 4) {
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write(bezierPatch.points[j][i])
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if (bezierPatch.colors.isEmpty()) {
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write(ColorRGBa.WHITE)
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} else {
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write(bezierPatch.colors[j][i])
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}
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write(Vector2(i / 3.0, j / 3.0))
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}
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}
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}
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}
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shader.begin()
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||||||
|
shader.uniform("u_subdivisions", subdivisions)
|
||||||
|
context.applyToShader(shader)
|
||||||
|
drawStyle.applyToShader(shader)
|
||||||
|
Driver.instance.setState(drawStyle)
|
||||||
|
Driver.instance.drawVertexBuffer(
|
||||||
|
shader,
|
||||||
|
listOf(vertices),
|
||||||
|
DrawPrimitive.PATCHES,
|
||||||
|
0,
|
||||||
|
16 * bezierPatches.size,
|
||||||
|
16
|
||||||
|
)
|
||||||
|
shader.end()
|
||||||
|
}
|
||||||
|
|
||||||
|
@JvmName("drawBezierPatch3DOKLab")
|
||||||
|
fun drawBezierPatches(
|
||||||
|
context: DrawContext,
|
||||||
|
drawStyle: DrawStyle,
|
||||||
|
bezierPatches: List<BezierPatch3DBase<ColorOKLABa>>,
|
||||||
|
subdivisions: Int = 32
|
||||||
|
) {
|
||||||
|
ensureVertexCount(bezierPatches.size * 16)
|
||||||
|
val shader = shadeStyleManagerOKLab.shader(
|
||||||
|
drawStyle.shadeStyle,
|
||||||
|
listOf(vertices.vertexFormat),
|
||||||
|
emptyList()
|
||||||
|
)
|
||||||
|
|
||||||
|
vertices.put {
|
||||||
|
for(bezierPatch in bezierPatches) {
|
||||||
|
for (j in 0 until 4) {
|
||||||
|
for (i in 0 until 4) {
|
||||||
|
write(bezierPatch.points[j][i])
|
||||||
|
if (bezierPatch.colors.isEmpty()) {
|
||||||
|
write(ColorRGBa.WHITE)
|
||||||
|
} else {
|
||||||
|
write(bezierPatch.colors[j][i].let {
|
||||||
|
Vector4(it.l, it.a, it.b, it.alpha)
|
||||||
|
})
|
||||||
|
}
|
||||||
|
write(Vector2(i / 3.0, j / 3.0))
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
shader.begin()
|
||||||
|
shader.uniform("u_subdivisions", subdivisions)
|
||||||
|
context.applyToShader(shader)
|
||||||
|
drawStyle.applyToShader(shader)
|
||||||
|
Driver.instance.setState(drawStyle)
|
||||||
|
Driver.instance.drawVertexBuffer(
|
||||||
|
shader,
|
||||||
|
listOf(vertices),
|
||||||
|
DrawPrimitive.PATCHES,
|
||||||
|
0,
|
||||||
|
16 * bezierPatches.size,
|
||||||
|
16
|
||||||
|
)
|
||||||
|
shader.end()
|
||||||
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
private val Drawer.bezierPatchDrawer: BezierPatchDrawer by lazy { BezierPatchDrawer() }
|
private val Drawer.bezierPatchDrawer: BezierPatchDrawer by lazy { BezierPatchDrawer() }
|
||||||
@@ -281,3 +373,23 @@ fun Drawer.bezierPatch(bezierPatch: BezierPatchBase<ColorOKLABa>, subdivisions:
|
|||||||
fun Drawer.bezierPatches(bezierPatch: List<BezierPatchBase<ColorOKLABa>>, subdivisions: Int = 32) {
|
fun Drawer.bezierPatches(bezierPatch: List<BezierPatchBase<ColorOKLABa>>, subdivisions: Int = 32) {
|
||||||
bezierPatchDrawer.drawBezierPatches(context, drawStyle, bezierPatch, subdivisions)
|
bezierPatchDrawer.drawBezierPatches(context, drawStyle, bezierPatch, subdivisions)
|
||||||
}
|
}
|
||||||
|
|
||||||
|
@JvmName("bezierPatch3DRGBa")
|
||||||
|
fun Drawer.bezierPatch(bezierPatch: BezierPatch3DBase<ColorRGBa>, subdivisions: Int = 32) {
|
||||||
|
bezierPatchDrawer.drawBezierPatches(context, drawStyle, listOf(bezierPatch), subdivisions)
|
||||||
|
}
|
||||||
|
|
||||||
|
@JvmName("bezierPatches3DRGBa")
|
||||||
|
fun Drawer.bezierPatches(bezierPatch: List<BezierPatch3DBase<ColorRGBa>>, subdivisions: Int = 32) {
|
||||||
|
bezierPatchDrawer.drawBezierPatches(context, drawStyle, bezierPatch, subdivisions)
|
||||||
|
}
|
||||||
|
|
||||||
|
@JvmName("bezierPatch3DOKLAB")
|
||||||
|
fun Drawer.bezierPatch(bezierPatch: BezierPatch3DBase<ColorOKLABa>, subdivisions: Int = 32) {
|
||||||
|
bezierPatchDrawer.drawBezierPatches(context, drawStyle, listOf(bezierPatch), subdivisions)
|
||||||
|
}
|
||||||
|
|
||||||
|
@JvmName("bezierPatches3DOKLAB")
|
||||||
|
fun Drawer.bezierPatches(bezierPatch: List<BezierPatch3DBase<ColorOKLABa>>, subdivisions: Int = 32) {
|
||||||
|
bezierPatchDrawer.drawBezierPatches(context, drawStyle, bezierPatch, subdivisions)
|
||||||
|
}
|
||||||
|
|||||||
82
orx-shapes/src/demo/kotlin/DemoBezierPatch05.kt
Normal file
82
orx-shapes/src/demo/kotlin/DemoBezierPatch05.kt
Normal file
@@ -0,0 +1,82 @@
|
|||||||
|
import org.openrndr.WindowMultisample
|
||||||
|
import org.openrndr.application
|
||||||
|
import org.openrndr.color.ColorRGBa
|
||||||
|
import org.openrndr.draw.BufferMultisample
|
||||||
|
import org.openrndr.extensions.SingleScreenshot
|
||||||
|
import org.openrndr.extra.shapes.bezierPatch
|
||||||
|
import org.openrndr.extra.shapes.drawers.bezierPatch
|
||||||
|
import org.openrndr.extras.camera.Orbital
|
||||||
|
import org.openrndr.math.Vector3
|
||||||
|
import org.openrndr.shape.Segment3D
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Shows how to
|
||||||
|
* - create a [bezierPatch] out of 4 [Segment3D]
|
||||||
|
* - create a sub-patch out of a [bezierPatch]
|
||||||
|
* - create horizontal and vertical [Path3D]s out of [bezierPatch]es
|
||||||
|
* - add colors to a [bezierPatch]
|
||||||
|
* - draw a [bezierPatch] surface
|
||||||
|
*
|
||||||
|
* The created contours are horizontal and vertical in "bezier-patch space" but
|
||||||
|
* are rendered deformed following the shape of the bezier patch.
|
||||||
|
*/
|
||||||
|
suspend fun main() {
|
||||||
|
application {
|
||||||
|
configure {
|
||||||
|
width = 800
|
||||||
|
height = 800
|
||||||
|
multisample = WindowMultisample.SampleCount(8)
|
||||||
|
}
|
||||||
|
program {
|
||||||
|
if (System.getProperty("takeScreenshot") == "true") {
|
||||||
|
extend(SingleScreenshot()) {
|
||||||
|
this.outputFile = System.getProperty("screenshotPath")
|
||||||
|
multisample = BufferMultisample.SampleCount(8)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
val c0 = Segment3D(Vector3(-5.0, 0.0, -9.0), Vector3(5.0, 0.0, -9.0))
|
||||||
|
val c1 = Segment3D(Vector3(-5.0, -5.0, -3.0), Vector3(5.0, -5.0, -3.0))
|
||||||
|
val c2 = Segment3D(Vector3(-5.0, 5.0, 3.0), Vector3(5.0, 5.0, 3.0))
|
||||||
|
val c3 = Segment3D(Vector3(-5.0, 0.0, 9.0), Vector3(5.0, 0.0, 9.0))
|
||||||
|
|
||||||
|
val col = listOf(ColorRGBa.PINK, ColorRGBa.RED, ColorRGBa.BLUE, ColorRGBa.PINK)
|
||||||
|
val cols = listOf(col, col, col, col)
|
||||||
|
val bp = bezierPatch(c0, c1, c2, c3).withColors(cols)
|
||||||
|
val bpSub = bp.sub(0.1, 0.1, 0.6, 0.6)
|
||||||
|
|
||||||
|
val cam = Orbital()
|
||||||
|
extend(cam){
|
||||||
|
eye = Vector3(x=9.9, y=12.8, z=6.9)
|
||||||
|
lookAt = Vector3(x=1.6, y=-1.9, z=1.2)
|
||||||
|
}
|
||||||
|
|
||||||
|
extend {
|
||||||
|
drawer.clear(ColorRGBa.PINK)
|
||||||
|
|
||||||
|
drawer.translate(-5.0, 0.0, 0.0)
|
||||||
|
// Show the segments that form the bezier patch
|
||||||
|
drawer.stroke = ColorRGBa.YELLOW
|
||||||
|
drawer.strokeWeight = 50.0
|
||||||
|
drawer.segments(listOf(c0, c1, c2, c3))
|
||||||
|
|
||||||
|
// Show the grid
|
||||||
|
drawer.strokeWeight = 1.0
|
||||||
|
val n = 10
|
||||||
|
for (i in 0..n) {
|
||||||
|
drawer.stroke = ColorRGBa.BLACK
|
||||||
|
drawer.lineStrip(bp.horizontal(i / n.toDouble()).adaptivePositions(0.01))
|
||||||
|
drawer.lineStrip(bp.vertical(i / n.toDouble()).adaptivePositions(0.01))
|
||||||
|
|
||||||
|
drawer.stroke = ColorRGBa.RED
|
||||||
|
drawer.lineStrip(bpSub.horizontal(i / n.toDouble()).adaptivePositions(0.01))
|
||||||
|
drawer.lineStrip(bpSub.vertical(i / n.toDouble()).adaptivePositions(0.01))
|
||||||
|
}
|
||||||
|
|
||||||
|
// Draw the colored Bezier surface
|
||||||
|
drawer.translate(10.0, 0.0, 0.0)
|
||||||
|
drawer.bezierPatch(bp)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
Reference in New Issue
Block a user