[orx-shapes] Add custom tensions to HobbyCurve and related 2D/3D demos and tests

orx-shapes/src/commonMain/kotlin/hobbycurve/HobbyCurve.kt

@@ -38,23 +38,39 @@ private fun Vector3.atan22(other: Vector3): Double {
 
 
 /**
- * Uses Hobby's algorithm to construct a [ShapeContour] through a given list of points.
+ * Generates a smooth contour passing through a set of points based on Hobby's algorithm.
- * @param points The list of points through which the curve should go.
+ *
- * @param closed Whether to construct a closed or open curve.
+ * @param points A list of 2D points through which the curve should pass.
- * @param curl The 'curl' at the endpoints of the curve; this is only applicable when [closed] is false. Best results for values in [-1, 1], where a higher value makes segments closer to circular arcs.
+ * @param closed A boolean value indicating whether the curve is closed (true)
- * @return A [ShapeContour] through [points].
+ *               forming a loop, or open (false). The default is false.
+ * @param curl A parameter that controls the curvature of the open-ended curve. Only
+ *             applicable if the curve is not closed. The default is 0.0.
+ * @param tensions A lambda function that accepts the chord index (an integer) and returns
+ *                 a pair of tension values (Double) for the curve's control points. These
+ *                 tensions influence how tightly the curve conforms to the points.
+ *                 The default lambda assigns both values as 1.0.
+ * @return A ShapeContour object representing the smoothed curve based on Hobby's algorithm.
  */
-fun hobbyCurve(points: List<Vector2>, closed: Boolean = false, curl: Double = 0.0): ShapeContour {
+fun hobbyCurve(
+    points: List<Vector2>, closed: Boolean = false, curl: Double = 0.0,
+    tensions: (chordIndex: Int, inAngleDegrees:Double, outAngleDegrees:Double) -> Pair<Double, Double> = { _, _, _ -> Pair(1.0, 1.0) },
+): ShapeContour {
     if (points.size <= 1) return ShapeContour.EMPTY
 
     val m = points.size
+
+    /** Chord count */
     val n = if (closed) m else m - 1
 
+    /** Chords array stores vectors representing line segments between consecutive points
+    Each chord is calculated as the vector difference between the next point and current point */
     val chords = Array(n) { points[(it + 1) % m] - points[it] }
     val distances = Array(n) { chords[it].length }
 
     require(distances.all { it > 0.0 })
 
+    /** Array storing turning angles (in radians) between adjacent chords at each point
+    For each point i, gamma[i] represents the angle between chord[i-1] and chord[i] */
     val gamma = DoubleArray(m)
     for (i in (if (closed) 0 else 1) until n) {
         gamma[i] = chords[(i - 1).mod(m)].atan22(chords[(i).mod(m)])
@@ -67,13 +83,12 @@ fun hobbyCurve(points: List<Vector2>, closed: Boolean = false, curl: Double = 0.
     val d = DoubleArray(m) { 0.0 }
 
     for (i in (if (closed) 0 else 1) until n) {
-        val j = (i + 1).mod(m)
+        val next = (i + 1).mod(m)
-        val k = (i - 1).mod(m)
+        val prev = (i - 1).mod(m)
-
+        a[i] = 1 / distances[prev]
-        a[i] = 1 / distances[k]
+        b[i] = (2 * distances[prev] + 2 * distances[i]) / (distances[prev] * distances[i])
-        b[i] = (2 * distances[k] + 2 * distances[i]) / (distances[k] * distances[i])
         c[i] = 1 / distances[i]
-        d[i] = -(2 * gamma[i] * distances[i] + gamma[j] * distances[k]) / (distances[k] * distances[i])
+        d[i] = -(2 * gamma[i] * distances[i] + gamma[next] * distances[prev]) / (distances[prev] * distances[i])
     }
 
     val alpha: DoubleArray
@@ -102,7 +117,7 @@ fun hobbyCurve(points: List<Vector2>, closed: Boolean = false, curl: Double = 0.
         val t = c[n - 1]
         c[n - 1] = 0.0
         alpha = sherman(a, b, c, d, s, t)
-        beta = DoubleArray(n) { 0.0 }
+        beta = DoubleArray(n)
         for (i in 0 until n) {
             val j = (i + 1) % n
             beta[i] = -gamma[j] - alpha[j]
@@ -114,8 +129,9 @@ fun hobbyCurve(points: List<Vector2>, closed: Boolean = false, curl: Double = 0.
     for (i in 0 until n) {
         val v1 = rotateAngle(chords[i], alpha[i]).normalized
         val v2 = rotateAngle(chords[i], -beta[i]).normalized
-        c1s.add(points[i % m] + v1 * rho(alpha[i], beta[i]) * distances[i] / 3.0)
+        val t = tensions(i, gamma[i].asDegrees, gamma[(i + 1).mod(m)].asDegrees)
-        c2s.add(points[(i + 1) % m] - v2 * rho(beta[i], alpha[i]) * distances[i] / 3.0)
+        c1s.add(points[i % m] + v1 * rho(alpha[i], beta[i]) * t.first * distances[i] / 3.0)
+        c2s.add(points[(i + 1) % m] - v2 * rho(beta[i], alpha[i]) * t.second * distances[i] / 3.0)
     }
     return ShapeContour(List(n) { Segment2D(points[it], c1s[it], c2s[it], points[(it + 1) % m]) }, closed = closed)
 }
@@ -132,7 +148,7 @@ fun hobbyCurve(
     points: List<Vector3>,
     closed: Boolean = false,
     curl: Double = 0.0,
-    tensions: (chordIndex: Int) -> Pair<Double, Double> = { _ -> Pair(1.0, 1.0) }
+    tensions: (chordIndex: Int, inAngleDegrees:Double, outAngleDegrees:Double) -> Pair<Double, Double> = { _, _, _ -> Pair(1.0, 1.0) },
 ): Path3D {
     if (points.size <= 1) return Path3D.EMPTY
 
@@ -212,7 +228,7 @@ fun hobbyCurve(
         val r2 = buildTransform { rotate(normals[(i + 1).mod(normals.size)], -beta[i].asDegrees) }
         val v1 = (r1 * chords[i].xyz0).xyz.normalized
         val v2 = (r2 * chords[i].xyz0).xyz.normalized
-        val t = tensions(i)
+        val t = tensions(i, gamma[i].asDegrees, gamma[(i + 1).mod(m)].asDegrees)
         c1s.add(points[i % m] + v1 * rho(alpha[i], beta[i]) * distances[i] * t.first / 3.0)
         c2s.add(points[(i + 1) % m] - v2 * rho(beta[i], alpha[i]) * distances[i] * t.second / 3.0)
     }
@@ -222,9 +238,14 @@ fun hobbyCurve(
     }, closed = closed)
 }
 
-
+/**
-/** The Thomas algorithm: solve a system of linear equations encoded in a tridiagonal matrix.
+ * Solves a tridiagonal system of equations using the Thomas algorithm.
-https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm
+ * [Wikipedia](https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm)
+ * @param a The subdiagonal elements of the tridiagonal matrix.
+ * @param b The diagonal elements of the tridiagonal matrix.
+ * @param c The superdiagonal elements of the tridiagonal matrix.
+ * @param d The right-hand side vector of the system.
+ * @return A double array representing the solution to the tridiagonal system.
  */
 private fun thomas(a: DoubleArray, b: DoubleArray, c: DoubleArray, d: DoubleArray): DoubleArray {
     val n = a.size
@@ -283,11 +304,11 @@ private fun sherman(
 }
 
 /**
- * Calculates a parameter used in Hobby's algorithm for constructing smooth curves.
+ * Calculates a ratio used in Hobby's curve construction based on the angles between curve segments.
  *
- * @param a The first angle in radians, representing the direction of the tangent vector at the start of the segment.
+ * @param a The angle (in radians) at the current point on the curve.
- * @param b The second angle in radians, representing the direction of the tangent vector at the end of the segment.
+ * @param b The angle (in radians) at the neighboring point on the curve.
- * @return A computed value used to adjust the control points for the curve segment.
+ * @return A calculated ratio used to control the curve's shape.
  */
 private fun rho(a: Double, b: Double): Double {
     val sa = sin(a)
@@ -301,4 +322,4 @@ private fun rho(a: Double, b: Double): Double {
 }
 
 private fun rotate(v: Vector2, s: Double, c: Double) = Vector2(v.x * c - v.y * s, v.x * s + v.y * c)
-private fun rotateAngle(v: Vector2, alpha: Double) = rotate(v, sin(alpha), cos(alpha))
+private fun rotateAngle(v: Vector2, alpha: Double) = rotate(v, sin(alpha), cos(alpha))

orx-shapes/src/commonTest/kotlin/TestHobbyCurve.kt

@@ -0,0 +1,19 @@
+import org.openrndr.extra.shapes.hobbycurve.hobbyCurve
+import org.openrndr.shape.Rectangle
+import kotlin.test.Test
+import kotlin.test.assertEquals
+import kotlin.test.assertTrue
+
+class TestHobbyCurve {
+
+    @Test
+    fun testSymmetric() {
+        val rectangle = Rectangle(0.0, 0.0, 100.0, 100.0).contour
+        val h = rectangle.hobbyCurve()
+        assertTrue(h.closed)
+        assertEquals(4, h.segments.size)
+        assertEquals(-1.0, h.direction(0.25).dot(h.direction(0.75)), 1e-6)
+        assertEquals(-1.0, h.direction(0.125).dot(h.direction(0.625)), 1e-6)
+        assertEquals(-1.0, h.direction(0.375).dot(h.direction(0.875)), 1e-6)
+    }
+}

orx-shapes/src/jvmDemo/kotlin/hobbycurve/DemoHobbyCurve02.kt

@@ -8,6 +8,10 @@ import org.openrndr.math.Vector2
 import kotlin.random.Random
 
 fun main() = application {
+    configure {
+        width = 720
+        height = 720
+    }
     program {
         val points = List(40) {
             Vector2(

orx-shapes/src/jvmDemo/kotlin/hobbycurve/DemoHobbyCurve03.kt

@@ -0,0 +1,28 @@
+package hobbycurve
+
+import org.openrndr.application
+import org.openrndr.color.ColorRGBa
+import org.openrndr.extra.noise.scatter
+import org.openrndr.extra.shapes.hobbycurve.hobbyCurve
+import org.openrndr.extra.shapes.ordering.hilbertOrder
+import kotlin.random.Random
+
+fun main() = application {
+    configure {
+        width = 720
+        height = 720
+    }
+    program {
+        extend {
+            for (i in -20..20) {
+                val t = i / 10.0
+                val points = drawer.bounds.offsetEdges(-50.0).scatter(25.0, random = Random(0)).hilbertOrder()
+                drawer.stroke = ColorRGBa.WHITE.opacify(0.5)
+                drawer.fill = null
+                drawer.contour(hobbyCurve(points, closed = false, tensions = { i, inAngle, outAngle ->
+                    Pair(t, t)
+                }))
+            }
+        }
+    }
+}

orx-shapes/src/jvmDemo/kotlin/hobbycurve/DemoHobbyCurve3D01.kt

@@ -29,7 +29,7 @@ fun main() = application {
             val hobby3D = hobbyCurve(
                 pts.map { it.xy0 + Vector3(0.0, 0.0, Double.uniform(-360.0, 360.0, r)) },
                 true,
-                tensions = { chordIndex: Int ->
+                tensions = { chordIndex, inAngle, outAngle ->
                     Pair(
                         cos(seconds + chordIndex * 0.1) * 0.5 + 0.5,
                         cos(seconds + (1.0 + chordIndex) * 0.1) * 0.5 + 0.5