[orx-noise] Add Rseq and Hammersley sequences

orx-noise/build.gradle.kts

@@ -37,6 +37,8 @@ kotlin {
                 implementation(project(":orx-hash-grid"))
                 implementation(project(":orx-noise"))
                 implementation(project(":orx-jvm:orx-gui"))
+                implementation(project(":orx-mesh-generators"))
+                implementation(project(":orx-camera"))
             }
         }
     }

orx-noise/src/commonMain/kotlin/hammersley/Hammersley.kt

@@ -0,0 +1,75 @@
+package org.openrndr.extra.noise.hammersley
+
+import org.openrndr.math.Vector2
+import org.openrndr.math.Vector3
+import org.openrndr.math.Vector4
+
+/**
+ * Computes a 2D Hammersley point based on the given index and total number of samples.
+ *
+ * @param i The index of the sample, typically in the range [0, n).
+ * @param n The total number of samples.
+ * @return A 2D point as a `Vector2` within the unit square [0, 1] x [0, 1].
+ */
+fun hammersley2D(i: Int, n: Int): Vector2 {
+    return Vector2(i.toDouble() / n, radicalInverseBase2(i.toUInt()))
+}
+
+/**
+ * Computes a 3D point in the Hammersley sequence based on the given index and total number of samples.
+ *
+ * @param i The index of the sample, typically in the range [0, n).
+ * @param n The total number of samples.
+ * @return A 3D point as a `Vector3` within the unit cube [0, 1] x [0, 1] x [0, 1].
+ */
+fun hammersley3D(i: Int, n: Int): Vector3 {
+    return Vector3(i.toDouble() / n, radicalInverseBase2(i.toUInt()), radicalInverse(3, i))
+}
+
+/**
+ * Computes a 4D Hammersley point based on the given index and total number of samples.
+ *
+ * @param i The index of the sample, typically in the range [0, n).
+ * @param n The total number of samples.
+ * @return A 4D point as a `Vector4` where each component lies within the range [0, 1].
+ */
+fun hammersley4D(i: Int, n: Int): Vector4 {
+    return Vector4(i.toDouble() / n, radicalInverseBase2(i.toUInt()), radicalInverse(3, i), radicalInverse(5, i))
+}
+
+/**
+ * Computes the radical inverse of a given unsigned integer `i` in base 2.
+ *
+ * @param i The input unsigned integer for which the radical inverse in base 2 is computed.
+ * @return The radical inverse value of the input as a `Double`, mapped to the range [0, 1).
+ */
+fun radicalInverseBase2(i: UInt): Double {
+    var bits = i
+    bits = ((bits shl 16) or (bits shr 16))
+    bits = ((bits and 0x55555555u) shl 1) or ((bits and 0xAAAAAAAAu) shr 1)
+    bits = ((bits and 0x33333333u) shl 2) or ((bits and 0xCCCCCCCCu) shr 2)
+    bits = ((bits and 0x0F0F0F0Fu) shl 4) or ((bits and 0xF0F0F0F0u) shr 4)
+    bits = ((bits and 0x00FF00FFu) shl 8) or ((bits and 0xFF00FF00u) shr 8)
+    return bits.toDouble() * 2.3283064365386963e-10
+}
+
+/**
+ * Computes the radical inverse of an integer `i` in a given base.
+ * This method is often used in quasi-random sequence generation for sampling.
+ *
+ * @param base The base in which to compute the radical inverse. Must be greater than 1.
+ * @param i The integer for which the radical inverse is calculated. Must be non-negative.
+ * @return The radical inverse value as a `Double`, within the range [0, 1).
+ */
+fun radicalInverse(base: Int, i: Int): Double {
+    var v = 0.0
+    var denom = 1.0
+    var n = i
+    while (n > 0) {
+        denom *= base
+        val remainder = n.mod(base)
+        n /= base
+        v += remainder / denom
+    }
+    return v
+}

orx-noise/src/commonMain/kotlin/rseq/Rseq.kt

@@ -0,0 +1,67 @@
+package org.openrndr.extra.noise.rsequence
+
+import org.openrndr.math.Vector2
+import org.openrndr.math.Vector3
+import org.openrndr.math.Vector4
+
+private const val g1 = 1.618033988749895
+private const val a11 = 1.0 / g1
+
+private const val g2 = 1.324717957244746
+private const val a21 = 1.0 / g2
+private const val a22 = 1.0 / (g2 * g2)
+
+private const val g3 = 1.2207440846057596
+private const val a31 = 1.0 / g3
+private const val a32 = 1.0 / (g3 * g3)
+private const val a33 = 1.0 / (g3 * g3 * g3)
+
+private const val g4 = 1.1673039782614187
+private const val a41 = 1.0 / g4
+private const val a42 = 1.0 / (g4 * g4)
+private const val a43 = 1.0 / (g4 * g4 * g4)
+private const val a44 = 1.0 / (g4 * g4 * g4 * g4)
+
+/**
+ * Computes the R1 low-discrepancy quasirandom sequence value for a given index as described by Martin Roberts.
+ *
+ * @param n The index for which the R1 sequence value is to be calculated.
+ * @return The R1 sequence value as a Double, providing a low-discrepancy quasirandom number.
+ */
+fun rSeq1D(n: Int): Double = (0.5 + a11 * n).mod(1.0)
+
+/**
+ * Computes the R2 low-discrepancy quasirandom sequence value for a given index as described by Martin Roberts.
+ *
+ * @param n The index for which the R2 sequence value is to be calculated.
+ * @return The R2 sequence value as a [Vector2], providing a low-discrepancy quasirandom number.
+ */
+fun rSeq2D(n: Int): Vector2 = Vector2(
+    (0.5 + a21 * n).mod(1.0),
+    (0.5 + a22 * n).mod(1.0)
+)
+
+/**
+ * Computes the R3 low-discrepancy quasirandom sequence value for a given index as described by Martin Roberts.
+ *
+ * @param n The index for which the R3 sequence value is to be calculated.
+ * @return The R3 sequence value as a [Vector3], providing a low-discrepancy quasirandom number.
+ */
+fun rSeq3D(n: Int): Vector3 = Vector3(
+    (0.5 + a31 * n).mod(1.0),
+    (0.5 + a32 * n).mod(1.0),
+    (0.5 + a33 * n).mod(1.0)
+)
+
+/**
+ * Computes the R4 low-discrepancy quasirandom sequence value for a given index as described by Martin Roberts.
+ *
+ * @param n The index for which the R4 sequence value is to be calculated.
+ * @return The R4 sequence value as a [Vector4], providing a low-discrepancy quasirandom number.
+ */
+fun rSeq4D(n: Int): Vector4 = Vector4(
+    (0.5 + a41 * n).mod(1.0),
+    (0.5 + a42 * n).mod(1.0),
+    (0.5 + a43 * n).mod(1.0),
+    (0.5 + a44 * n).mod(1.0)
+)

orx-noise/src/jvmDemo/kotlin/hammersley/DemoHammersley2D01.kt

@@ -0,0 +1,29 @@
+package hammersley
+
+import org.openrndr.application
+import org.openrndr.extra.noise.hammersley.hammersley2D
+
+/**
+ * Demo that visualizes a 2D Hammersley point set.
+ *
+ * The application is configured to run at 720x720 resolution. The program computes
+ * 400 2D Hammersley points mapped within the bounds of the application's resolution.
+ * These points are visualized by rendering circles at their respective positions.
+ */
+fun main() {
+    application {
+        configure {
+            width = 720
+            height = 720
+        }
+
+        program {
+            extend {
+                val points = (0 until 400).map {
+                    hammersley2D(it, 400) * 720.0
+                }
+                drawer.circles(points, 5.0)
+            }
+        }
+    }
+}

orx-noise/src/jvmDemo/kotlin/hammersley/DemoHammersley3D01.kt

@@ -0,0 +1,46 @@
+package hammersley
+
+import org.openrndr.application
+import org.openrndr.draw.DrawPrimitive
+import org.openrndr.draw.isolated
+import org.openrndr.extra.camera.Orbital
+import org.openrndr.extra.meshgenerators.sphereMesh
+import org.openrndr.extra.noise.hammersley.hammersley3D
+import org.openrndr.math.Vector3
+
+/**
+ * Demo program rendering a 3D visualization of points distributed using the Hammersley sequence in 3D space.
+ *
+ * The application is set up at a resolution of 720x720 pixels. Within the visual
+ * program, a sphere mesh is created and a set of 1400 points is generated using
+ * the Hammersley sequence. Each point is translated and rendered as a small sphere
+ * in 3D space. This is achieved by mapping the generated points into a scaled domain.
+ *
+ * The rendering utilizes the Orbital extension, enabling an interactive 3D camera
+ * to navigate the scene. The visualization relies on the draw loop for continuous
+ * rendering of the points.
+ */
+fun main() {
+    application {
+        configure {
+            width = 720
+            height = 720
+        }
+
+        program {
+            val sphere = sphereMesh(radius = 0.1)
+            extend(Orbital())
+            extend {
+                val points = (0 until 1400).map {
+                    (hammersley3D(it, 1400) - Vector3(0.5)) * 10.0
+                }
+                for (point in points) {
+                    drawer.isolated {
+                        drawer.translate(point)
+                        drawer.vertexBuffer(sphere, DrawPrimitive.TRIANGLES)
+                    }
+                }
+            }
+        }
+    }
+}

orx-noise/src/jvmDemo/kotlin/hammersley/DemoHammersley4D01.kt

@@ -0,0 +1,52 @@
+package hammersley
+
+import org.openrndr.application
+import org.openrndr.color.ColorRGBa
+import org.openrndr.draw.DrawPrimitive
+import org.openrndr.draw.isolated
+import org.openrndr.extra.camera.Orbital
+import org.openrndr.extra.meshgenerators.sphereMesh
+import org.openrndr.extra.noise.hammersley.hammersley4D
+import org.openrndr.extra.noise.rsequence.rSeq4D
+import org.openrndr.math.Vector4
+import kotlin.math.abs
+import kotlin.math.min
+
+/**
+ * Demo that visualizes a 4D Hammersley point set in a 3D space, with colors determined by the 4th dimension.
+ *
+ * The application is configured at a resolution of 720x720 pixels. A sphere mesh is created
+ * using the `sphereMesh` utility, and a total of 10,000 4D points are generated with the
+ * `hammersley4D` sequence. These points are scaled, translated, and rendered as small spheres.
+ * The color of each sphere is modified based on the 4th dimension of its corresponding point by
+ * shifting the hue in HSV color space.
+ *
+ * This program employs the `Orbital` extension, enabling camera interaction for 3D navigation
+ * of the scene. Rendering occurs within the draw loop, providing continuous visualization
+ * of the point distribution.
+ */
+fun main() {
+    application {
+        configure {
+            width = 720
+            height = 720
+        }
+
+        program {
+            val sphere = sphereMesh(radius = 0.1)
+            extend(Orbital())
+            extend {
+                val points = (0 until 10000).map {
+                    (hammersley4D(it, 10000) - Vector4(0.5, 0.5, 0.5, 0.0)) * Vector4(10.0, 10.0, 10.0, 1.0)
+                }
+                for (point in points) {
+                    drawer.isolated {
+                        drawer.translate(point.xyz)
+                        drawer.fill = ColorRGBa.RED.toHSVa().shiftHue(point.w * 360.0).toRGBa()
+                        drawer.vertexBuffer(sphere, DrawPrimitive.TRIANGLES)
+                    }
+                }
+            }
+        }
+    }
+}

orx-noise/src/jvmDemo/kotlin/rseq/DemoRseq2D01.kt

@@ -0,0 +1,27 @@
+package rseq
+
+import org.openrndr.application
+import org.openrndr.extra.noise.rsequence.rSeq2D
+
+/**
+ * This demo sets up a window with dimensions 720x720 and renders frames
+ * demonstrating 2D quasirandomly distributed points. The points are generated
+ * using the R2 sequence and drawn as circles with a radius of 5.0.
+ */
+fun main() {
+    application {
+        configure {
+            width = 720
+            height = 720
+        }
+
+        program {
+            extend {
+                val points = (0 until 4000).map {
+                    rSeq2D(it) * 720.0
+                }
+                drawer.circles(points, 5.0)
+            }
+        }
+    }
+}

orx-noise/src/jvmDemo/kotlin/rseq/DemoRseq3D01.kt

@@ -0,0 +1,45 @@
+package rseq
+
+import org.openrndr.application
+import org.openrndr.draw.DrawPrimitive
+import org.openrndr.draw.isolated
+import org.openrndr.extra.camera.Orbital
+import org.openrndr.extra.meshgenerators.sphereMesh
+import org.openrndr.extra.noise.rsequence.rSeq3D
+import org.openrndr.math.Vector3
+
+/**
+ * This demo renders a 3D visualizationof points distributed using the R3 quasirandom sequence. Each point is
+ * represented as a sphere and positioned in 3D space based on the quasirandom sequence values.
+ *
+ * The visualization setup includes:
+ * - Configuration of application window size to 720x720.
+ * - Usage of an orbital camera for interactive 3D navigation.
+ * - Creation of a reusable sphere mesh with a specified radius.
+ * - Generation of quasirandom points in 3D space using the `rSeq3D` function.
+ * - Transformation and rendering of each point as a sphere using vertex buffers.
+ */
+fun main() {
+    application {
+        configure {
+            width = 720
+            height = 720
+        }
+
+        program {
+            val sphere = sphereMesh(radius = 0.1)
+            extend(Orbital())
+            extend {
+                val points = (0 until 1400).map {
+                    (rSeq3D(it) - Vector3(0.5)) * 10.0
+                }
+                for (point in points) {
+                    drawer.isolated {
+                        drawer.translate(point)
+                        drawer.vertexBuffer(sphere, DrawPrimitive.TRIANGLES)
+                    }
+                }
+            }
+        }
+    }
+}

orx-noise/src/jvmDemo/kotlin/rseq/DemoRseq4D01.kt

@@ -0,0 +1,54 @@
+package rseq
+
+import org.openrndr.application
+import org.openrndr.color.ColorRGBa
+import org.openrndr.draw.DrawPrimitive
+import org.openrndr.draw.isolated
+import org.openrndr.extra.camera.Orbital
+import org.openrndr.extra.meshgenerators.sphereMesh
+import org.openrndr.extra.noise.rsequence.rSeq3D
+import org.openrndr.extra.noise.rsequence.rSeq4D
+import org.openrndr.math.Vector3
+import org.openrndr.math.Vector4
+import kotlin.math.abs
+import kotlin.math.min
+
+/**
+ * Demo that presents a 3D visualization of points distributed using a 4D quasirandom sequence (R4).
+ * Each point is represented as a sphere with it position and color derived from the sequence values.
+ *
+ * This function performs the following tasks:
+ * - Configures the application window dimensions to 720x720 pixels.
+ * - Initializes a 3D camera for orbital navigation of the scene.
+ * - Generates 10,000 points in 4D space using the `rSeq4D` function. The points are scaled
+ *   and transformed into 3D positions with an additional w-coordinate for color variation.
+ * - Creates a reusable sphere mesh for rendering.
+ * - Renders each point as a sphere with its position determined by the 3D coordinates
+ *   of the point and its color calculated by shifting the hue of a base color using
+ *   the w-coordinate value.
+ */
+fun main() {
+    application {
+        configure {
+            width = 720
+            height = 720
+        }
+
+        program {
+            val sphere = sphereMesh(radius = 0.1)
+            val points = (0 until 10000).map {
+                (rSeq4D(it) - Vector4(0.5, 0.5, 0.5, 0.0)) * Vector4(10.0, 10.0, 10.0, 1.0)
+            }
+            extend(Orbital())
+            extend {
+                for (point in points) {
+                    drawer.isolated {
+                        drawer.translate(point.xyz)
+                        drawer.fill = ColorRGBa.RED.toHSVa().shiftHue(point.w * 360.0).toRGBa()
+                        drawer.vertexBuffer(sphere, DrawPrimitive.TRIANGLES)
+                    }
+                }
+            }
+        }
+    }
+}