Add HierarchicalSampleWarping utility

src/org/lwjgl/demo/util/HierarchicalSampleWarping.java

@@ -0,0 +1,60 @@
+package org.lwjgl.demo.util;
+
+import org.joml.Vector2f;
+import org.joml.Vector2i;
+
+/**
+ * Implements hierarchical sample warping as first proposed in the paper
+ * "Wavelet Importance: Efficiently Evaluating Products of Complex Functions" by Clarberg et al.
+ * <p>
+ * This can be used for importance sampling of discrete distributions represented by a texture mip chain, such as for
+ * image based lighting or for textures used as an irradiance cache as used by EA's SEED project shown in the
+ * SIGGRAPH 2021 presentation "Global Illumination Based on Surfels".
+ * <p>
+ * See:
+ * <ul>
+ * <li><a href="https://link.springer.com/content/pdf/10.1007/978-1-4842-4427-2_16.pdf">section 16.4.2.3 HIERARCHICAL TRANSFORMATION in chapter "Transformations Zoo" of "Ray Tracing Gems".</a></li>
+ * <li><a href="http://graphics.ucsd.edu/~henrik/papers/wavelet_importance_sampling.pdf">"Wavelet Importance: Efficiently Evaluating Products of Complex Functions" by Clarberg et al.</a></li>
+ * <li><a href="https://www.ea.com/seed/news/siggraph21-global-illumination-surfels">SIGGRAPH 21: Global Illumination Based on Surfels</a></li>
+ * </ul>
+ *
+ * @author Kai Burjack
+ */
+public class HierarchicalSampleWarping {
+  private static int idx(int x, int y, int lod) {
+    return x + y * (2 << lod);
+  }
+  private static float mix(float a, float b, float v) {
+    return a*(1-v) + b*v;
+  }
+  private static float step(float edge, float x) {
+    return x < edge ? 0 : 1;
+  }
+
+  public static Vector2i sample(float[][] levels, Vector2f u, float[] pdf) {
+    int x = 0, y = 0;
+    pdf[0] = 1.0f;
+    for (int lod = 0; lod < levels.length; lod++) {
+      // here, lod=0 is the _highest_ lod level (with the smallest image dimension)
+      x <<= 1; y <<= 1;
+      float s0 = levels[lod][idx(x  ,y  ,lod)];
+      float s1 = levels[lod][idx(x+1,y  ,lod)];
+      float s2 = levels[lod][idx(x  ,y+1,lod)];
+      float s3 = levels[lod][idx(x+1,y+1,lod)];
+      float left = s0 + s2;
+      float right = s1 + s3;
+      float pLeft = left / (left + right);
+      float uxFactor = step(pLeft, u.x);
+      float pLower = mix(s0 / left, s1 / right, uxFactor);
+      float uyFactor = step(pLower, u.y);
+      float uxDen = mix(pLeft, 1.0f - pLeft, uxFactor);
+      float uyDen = mix(pLower, 1.0f - pLower, uyFactor);
+      if (u.x >= pLeft) x++;
+      if (u.y >= pLower) y++;
+      u.x = mix(u.x, u.x - pLeft, uxFactor) / uxDen;
+      u.y = mix(u.y, u.y - pLower, uyFactor) / uyDen;
+      pdf[0] *= uxDen * uyDen;
+    }
+    return new Vector2i(x, y);
+  }
+}