[orx-math] Add cubic Bezier least squares fitting demo to matrix package

2025-08-17 02:02:46 +02:00
parent 2a50589f73
commit db29f07aa3
1 changed files with 82 additions and 0 deletions
--- a/orx-math/src/jvmDemo/kotlin/matrix/DemoLeastSquares02.kt
+++ b/orx-math/src/jvmDemo/kotlin/matrix/DemoLeastSquares02.kt
@@ -0,0 +1,82 @@
+package matrix
+
+import org.openrndr.application
+import org.openrndr.color.ColorRGBa
+import org.openrndr.extra.math.matrix.Matrix
+import org.openrndr.extra.math.matrix.invertMatrixCholesky
+import org.openrndr.extra.noise.uniform
+import org.openrndr.extra.noise.uniformRing
+import org.openrndr.math.Vector2
+import org.openrndr.shape.Circle
+import org.openrndr.shape.Segment2D
+import kotlin.math.pow
+import kotlin.random.Random
+
+/**
+ * Demonstrate least squares method to fit a cubic bezier to noisy points
+ */
+fun main() {
+    application {
+        configure {
+            width = 720
+            height = 720
+        }
+        program {
+            val r = Random(0)
+            fun factorial(n: Int): Int = if (n <= 1) 1 else n * factorial(n - 1)
+
+            fun comb(a: Int, b: Int): Int {
+                return factorial(a) / (factorial(b) * factorial(a - b))
+            }
+
+            fun bernstein(n: Int, i: Int, t: Double): Double {
+                return comb(n, i) * t.pow(i) * (1.0 - t).pow(n - i)
+            }
+            extend {
+                for (z in 0 until 10) {
+                    val c = Circle(drawer.bounds.center, 300.0- z*30.0).contour
+                    for (ls in c.segments) {
+
+                        val pointCount = 5
+                        val A = Matrix(pointCount, 4)
+                        val b = Matrix(pointCount, 2)
+                        for (i in 0 until pointCount) {
+                            val t = when (i) {
+                                0 -> 0.0
+                                pointCount - 1 -> 1.0
+                                else -> Double.uniform(0.0, 1.0, r)
+                            }
+                            val p = ls.position(t)
+                            val pr = p + Vector2.uniformRing(0.0, 0.5, r)
+
+                            A[i, 0] = bernstein(3, 0, t)
+                            A[i, 1] = bernstein(3, 1, t)
+                            A[i, 2] = bernstein(3, 2, t)
+                            A[i, 3] = bernstein(3, 3, t)
+                            b[i, 0] = pr.x
+                            b[i, 1] = pr.y
+                        }
+                        val At = A.transposed()
+                        val AtA = At * A
+                        val Atb = At * b
+
+                        val AtAI = invertMatrixCholesky(AtA)
+                        val x = AtAI * Atb
+
+                        val segment = Segment2D(
+                            //ls.start,
+                            Vector2(x[0, 0], x[0, 1]),
+                            Vector2(x[1, 0], x[1, 1]),
+                            Vector2(x[2, 0], x[2, 1]),
+                            //ls.end
+                            Vector2(x[3, 0], x[3, 1])
+                        )
+
+                        drawer.stroke = ColorRGBa.PINK
+                        drawer.segment(segment)
+                    }
+                }
+            }
+        }
+    }
+}