82 lines
2.8 KiB
Kotlin
82 lines
2.8 KiB
Kotlin
package matrix
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import org.openrndr.application
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import org.openrndr.color.ColorRGBa
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import org.openrndr.extra.math.matrix.Matrix
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import org.openrndr.extra.math.matrix.invertMatrixCholesky
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import org.openrndr.extra.noise.uniform
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import org.openrndr.extra.noise.uniformRing
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import org.openrndr.math.Vector2
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import org.openrndr.shape.Circle
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import org.openrndr.shape.Segment2D
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import kotlin.math.pow
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import kotlin.random.Random
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/**
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* Demonstrate least squares method to fit a cubic bezier to noisy points
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*/
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fun main() {
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application {
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configure {
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width = 720
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height = 720
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}
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program {
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val r = Random(0)
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fun factorial(n: Int): Int = if (n <= 1) 1 else n * factorial(n - 1)
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fun comb(a: Int, b: Int): Int {
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return factorial(a) / (factorial(b) * factorial(a - b))
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}
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fun bernstein(n: Int, i: Int, t: Double): Double {
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return comb(n, i) * t.pow(i) * (1.0 - t).pow(n - i)
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}
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extend {
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for (z in 0 until 10) {
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val c = Circle(drawer.bounds.center, 300.0- z*30.0).contour
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for (ls in c.segments) {
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val pointCount = 5
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val A = Matrix(pointCount, 4)
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val b = Matrix(pointCount, 2)
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for (i in 0 until pointCount) {
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val t = when (i) {
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0 -> 0.0
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pointCount - 1 -> 1.0
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else -> Double.uniform(0.0, 1.0, r)
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}
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val p = ls.position(t)
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val pr = p + Vector2.uniformRing(0.0, 0.5, r)
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A[i, 0] = bernstein(3, 0, t)
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A[i, 1] = bernstein(3, 1, t)
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A[i, 2] = bernstein(3, 2, t)
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A[i, 3] = bernstein(3, 3, t)
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b[i, 0] = pr.x
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b[i, 1] = pr.y
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}
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val At = A.transposed()
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val AtA = At * A
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val Atb = At * b
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val AtAI = invertMatrixCholesky(AtA)
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val x = AtAI * Atb
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val segment = Segment2D(
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//ls.start,
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Vector2(x[0, 0], x[0, 1]),
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Vector2(x[1, 0], x[1, 1]),
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Vector2(x[2, 0], x[2, 1]),
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//ls.end
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Vector2(x[3, 0], x[3, 1])
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)
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drawer.stroke = ColorRGBa.PINK
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drawer.segment(segment)
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}
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}
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}
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}
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}
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} |