fix preview of final scene

The previous image was generated with a version of this code that did not apply gamma to textures which resulted in incorrect colors of the globe.

README.md

@@ -47,3 +47,11 @@ java -jar raytracing.jar --samples 50000 --height 600 CORNELL_SMOKE
 ```
 java -jar raytracing.jar --samples 1000 --height 1080 DIAGRAMM
 ```
+
+### a little bit of everything
+
+![](./docs/final.png)
+
+```
+java -jar raytracing.jar --samples 10000 --height 1200 FINAL
+```

src/main/java/eu/jonahbauer/raytracing/Examples.java

@@ -1,16 +1,21 @@
 package eu.jonahbauer.raytracing;
 
+import eu.jonahbauer.raytracing.math.AABB;
 import eu.jonahbauer.raytracing.math.Vec3;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.CheckerTexture;
+import eu.jonahbauer.raytracing.render.texture.Color;
 import eu.jonahbauer.raytracing.render.camera.SimpleCamera;
 import eu.jonahbauer.raytracing.render.material.*;
+import eu.jonahbauer.raytracing.render.texture.ImageTexture;
+import eu.jonahbauer.raytracing.render.texture.PerlinTexture;
 import eu.jonahbauer.raytracing.scene.Hittable;
 import eu.jonahbauer.raytracing.scene.Scene;
 import eu.jonahbauer.raytracing.scene.SkyBox;
 import eu.jonahbauer.raytracing.scene.hittable2d.Parallelogram;
+import eu.jonahbauer.raytracing.scene.hittable3d.Box;
 import eu.jonahbauer.raytracing.scene.hittable3d.ConstantMedium;
 import eu.jonahbauer.raytracing.scene.hittable3d.Sphere;
-import eu.jonahbauer.raytracing.scene.util.Hittables;
+import eu.jonahbauer.raytracing.scene.util.HittableBinaryTree;
 import org.jetbrains.annotations.NotNull;
 
 import java.util.*;
@@ -30,7 +35,11 @@ public class Examples {
         register("LIGHT", Examples::getLight);
         register("CORNELL", Examples::getCornellBox);
         register("CORNELL_SMOKE", Examples::getCornellBoxSmoke);
+        register("CORNELL_SPHERE", Examples::getCornellBoxSphere);
         register("DIAGRAMM", Examples::getDiagramm);
+        register("EARTH", Examples::getEarth);
+        register("PERLIN", Examples::getPerlin);
+        register("FINAL", Examples::getFinal);
     }
 
     public static @NotNull IntFunction<Example> getByName(@NotNull String name) {
@@ -42,14 +51,13 @@ public class Examples {
     public static @NotNull Example getSimpleScene(int height) {
         if (height <= 0) height = 675;
         return new Example(
-                new Scene(
+                new Scene(getSkyBox(), List.of(
-                        getSkyBox(),
                         new Sphere(new Vec3(0, -100.5, -1.0), 100.0, new LambertianMaterial(new Color(0.8, 0.8, 0.0))),
                         new Sphere(new Vec3(0, 0, -1.2), 0.5, new LambertianMaterial(new Color(0.1, 0.2, 0.5))),
                         new Sphere(new Vec3(-1.0, 0, -1.2), 0.5, new DielectricMaterial(1.5)),
                         new Sphere(new Vec3(-1.0, 0, -1.2), 0.4, new DielectricMaterial(1 / 1.5)),
                         new Sphere(new Vec3(1.0, 0, -1.2), 0.5, new MetallicMaterial(new Color(0.8, 0.6, 0.2), 0.0))
-                ),
+                )),
                 SimpleCamera.builder()
                         .withImage(height * 16 / 9, height)
                         .build()
@@ -61,7 +69,10 @@ public class Examples {
 
         var rng = new Random(1);
         var objects = new ArrayList<Hittable>();
-        objects.add(new Sphere(new Vec3(0, -1000, 0), 1000, new LambertianMaterial(new Color(0.5, 0.5, 0.5))));
+        objects.add(new Sphere(
+                new Vec3(0, -1000, 0), 1000,
+                new LambertianMaterial(new CheckerTexture(0.32, new Color(.2, .3, .1), new Color(.9, .9, .9)))
+        ));
 
         for (int a = -11; a < 11; a++) {
             for (int b = -11; b < 11; b++) {
@@ -107,14 +118,13 @@ public class Examples {
     public static @NotNull Example getSquares(int height) {
         if (height <= 0) height = 600;
         return new Example(
-                new Scene(
+                new Scene(getSkyBox(), List.of(
-                        getSkyBox(),
                         new Parallelogram(new Vec3(-3, -2, 5), new Vec3(0, 0, -4), new Vec3(0, 4, 0), new LambertianMaterial(new Color(1.0, 0.2, 0.2))),
                         new Parallelogram(new Vec3(-2, -2, 0), new Vec3(4, 0, 0), new Vec3(0, 4, 0), new LambertianMaterial(new Color(0.2, 1.0, 0.2))),
                         new Parallelogram(new Vec3(3, -2, 1), new Vec3(0, 0, 4), new Vec3(0, 4, 0), new LambertianMaterial(new Color(0.2, 0.2, 1.0))),
                         new Parallelogram(new Vec3(-2, 3, 1), new Vec3(4, 0, 0), new Vec3(0, 0, 4), new LambertianMaterial(new Color(1.0, 0.5, 0.0))),
                         new Parallelogram(new Vec3(-2, -3, 5), new Vec3(4, 0, 0), new Vec3(0, 0, -4), new LambertianMaterial(new Color(0.2, 0.8, 0.8)))
-                ),
+                )),
                 SimpleCamera.builder()
                         .withImage(height, height)
                         .withFieldOfView(Math.toRadians(80))
@@ -127,12 +137,12 @@ public class Examples {
     public static @NotNull Example getLight(int height) {
         if (height <= 0) height = 225;
         return new Example(
-                new Scene(
+                new Scene(List.of(
                         new Sphere(new Vec3(0, -1000, 0), 1000, new LambertianMaterial(new Color(0.2, 0.2, 0.2))),
                         new Sphere(new Vec3(0, 2, 0), 2, new LambertianMaterial(new Color(0.2, 0.2, 0.2))),
                         new Parallelogram(new Vec3(3, 1, -2), new Vec3(2, 0, 0), new Vec3(0, 2, 0), new DiffuseLight(new Color(4.0, 4.0, 4.0))),
                         new Sphere(new Vec3(0, 7, 0), 2, new DiffuseLight(new Color(4.0, 4.0, 4.0)))
-                ),
+                )),
                 SimpleCamera.builder()
                         .withImage(height * 16 / 9, height)
                         .withFieldOfView(Math.toRadians(20))
@@ -151,16 +161,16 @@ public class Examples {
         var light = new DiffuseLight(new Color(15.0, 15.0, 15.0));
 
         return new Example(
-                new Scene(
+                new Scene(List.of(
-                        new Parallelogram(new Vec3(555, 0, 0), new Vec3(0, 555, 0), new Vec3(0, 0, 555), green),
+                        new Box(new Vec3(0, 0, 0), new Vec3(555, 555, 555), white, white, red, green, white, null),
-                        new Parallelogram(new Vec3(0, 0, 0), new Vec3(0, 555, 0), new Vec3(0, 0, 555), red),
                         new Parallelogram(new Vec3(343, 554, 332), new Vec3(-130, 0, 0), new Vec3(0, 0, -105), light),
-                        new Parallelogram(new Vec3(0, 0, 0), new Vec3(555, 0, 0), new Vec3(0, 0, 555), white),
+                        new Box(new Vec3(0, 0, 0), new Vec3(165, 330, 165), white)
-                        new Parallelogram(new Vec3(555, 555, 555), new Vec3(-555, 0, 0), new Vec3(0, 0, -555), white),
+                                .rotateY(Math.toRadians(15))
-                        new Parallelogram(new Vec3(0, 0, 555), new Vec3(555, 0, 0), new Vec3(0, 555, 0), white),
+                                .translate(new Vec3(265, 0, 295)),
-                        Hittables.box(new Vec3(0, 0, 0), new Vec3(165, 330, 165), white).rotateY(Math.toRadians(15)).translate(new Vec3(265, 0, 295)),
+                        new Box(new Vec3(0, 0, 0), new Vec3(165, 165, 165), white)
-                        Hittables.box(new Vec3(0, 0, 0), new Vec3(165, 165, 165), white).rotateY(Math.toRadians(-18)).translate(new Vec3(130, 0, 65))
+                                .rotateY(Math.toRadians(-18))
-                ),
+                                .translate(new Vec3(130, 0, 65))
+                )),
                 SimpleCamera.builder()
                         .withImage(height, height)
                         .withFieldOfView(Math.toRadians(40))
@@ -178,22 +188,49 @@ public class Examples {
         var light = new DiffuseLight(new Color(7.0, 7.0, 7.0));
 
         return new Example(
-                new Scene(
+                new Scene(List.of(
-                        new Parallelogram(new Vec3(555, 0, 0), new Vec3(0, 555, 0), new Vec3(0, 0, 555), green),
+                        new Box(new Vec3(0, 0, 0), new Vec3(555, 555, 555), white, white, red, green, white, null),
-                        new Parallelogram(new Vec3(0, 0, 0), new Vec3(0, 555, 0), new Vec3(0, 0, 555), red),
                         new Parallelogram(new Vec3(113, 554, 127), new Vec3(330, 0, 0), new Vec3(0, 0, 305), light),
-                        new Parallelogram(new Vec3(0, 0, 0), new Vec3(555, 0, 0), new Vec3(0, 0, 555), white),
-                        new Parallelogram(new Vec3(555, 555, 555), new Vec3(-555, 0, 0), new Vec3(0, 0, -555), white),
-                        new Parallelogram(new Vec3(0, 0, 555), new Vec3(555, 0, 0), new Vec3(0, 555, 0), white),
                         new ConstantMedium(
-                                Hittables.box(new Vec3(0, 0, 0), new Vec3(165, 330, 165), white).rotateY(Math.toRadians(15)).translate(new Vec3(265, 0, 295)),
+                                new Box(new Vec3(0, 0, 0), new Vec3(165, 330, 165), white)
+                                        .rotateY(Math.toRadians(15))
+                                        .translate(new Vec3(265, 0, 295)),
                                 0.01, new IsotropicMaterial(Color.BLACK)
                         ),
                         new ConstantMedium(
-                                Hittables.box(new Vec3(0, 0, 0), new Vec3(165, 165, 165), white).rotateY(Math.toRadians(-18)).translate(new Vec3(130, 0, 65)),
+                                new Box(new Vec3(0, 0, 0), new Vec3(165, 165, 165), white)
+                                        .rotateY(Math.toRadians(-18))
+                                        .translate(new Vec3(130, 0, 65)),
                                 0.01, new IsotropicMaterial(Color.WHITE)
                         )
-                ),
+                )),
+                SimpleCamera.builder()
+                        .withImage(height, height)
+                        .withFieldOfView(Math.toRadians(40))
+                        .withPosition(new Vec3(278, 278, -800))
+                        .withTarget(new Vec3(278, 278, 0))
+                        .build()
+        );
+    }
+
+    public static @NotNull Example getCornellBoxSphere(int height) {
+        if (height <= 0) height = 600;
+
+        var red = new LambertianMaterial(new Color(.65, .05, .05));
+        var white = new LambertianMaterial(new Color(.73, .73, .73));
+        var green = new LambertianMaterial(new Color(.12, .45, .15));
+        var light = new DiffuseLight(new Color(7.0, 7.0, 7.0));
+        var glass = new DielectricMaterial(1.5);
+
+        var room = new Box(new Vec3(0, 0, 0), new Vec3(555, 555, 555), white, white, red, green, white, null);
+        var lamp = new Parallelogram(new Vec3(343, 554, 332), new Vec3(-130, 0, 0), new Vec3(0, 0, -105), light);
+        var box = new Box(new Vec3(0, 0, 0), new Vec3(165, 330, 165), white)
+                .rotateY(Math.toRadians(15))
+                .translate(new Vec3(265, 0, 295));
+        var sphere = new Sphere(new Vec3(190, 90, 190), 90, glass);
+
+        return new Example(
+                new Scene(List.of(room, box), List.of(lamp, sphere)),
                 SimpleCamera.builder()
                         .withImage(height, height)
                         .withFieldOfView(Math.toRadians(40))
@@ -233,7 +270,7 @@ public class Examples {
 
         for (int i = 0; i < data.size(); i++) {
             var partei = data.get(i);
-            objects.add(Hittables.box(
+            objects.add(new Box(
                     new Vec3((i + 1) * spacing +       i * size, 0, spacing),
                     new Vec3((i + 1) * spacing + (i + 1) * size, partei.stimmen() * 15, spacing + size),
                     new DielectricMaterial(1.5, partei.color())
@@ -251,6 +288,109 @@ public class Examples {
         );
     }
 
+    public static @NotNull Example getEarth(int height) {
+        if (height <= 0) height = 450;
+
+        return new Example(
+                new Scene(getSkyBox(), List.of(
+                        new Sphere(Vec3.ZERO, 2, new LambertianMaterial(new ImageTexture("/earthmap.jpg")))
+                )),
+                SimpleCamera.builder()
+                        .withImage(height * 16 / 9, height)
+                        .withFieldOfView(Math.toRadians(20))
+                        .withPosition(new Vec3(12, 0, 0))
+                        .withTarget(Vec3.ZERO)
+                        .build()
+        );
+    }
+
+    public static @NotNull Example getPerlin(int height) {
+        if (height <= 0) height = 450;
+
+        var material = new LambertianMaterial(new PerlinTexture(4));
+
+        return new Example(
+                new Scene(getSkyBox(), List.of(
+                        new Sphere(new Vec3(0, -1000, 0), 1000, material),
+                        new Sphere(new Vec3(0, 2, 0), 2, material)
+                )),
+                SimpleCamera.builder()
+                        .withImage(height * 16 / 9, height)
+                        .withFieldOfView(Math.toRadians(20))
+                        .withPosition(new Vec3(13, 2, 3))
+                        .withTarget(Vec3.ZERO)
+                        .build()
+        );
+    }
+
+    public static @NotNull Example getFinal(int height) {
+        if (height <= 0) height = 400;
+
+        var objects = new ArrayList<Hittable>();
+        var random = new Random(1);
+
+        // boxes
+        var boxes = new ArrayList<Hittable>();
+        var ground = new LambertianMaterial(new Color(0.48, 0.83, 0.53));
+        for (int i = 0; i < 20; i++) {
+            for (int j = 0; j < 20; j++) {
+                var w = 100.0;
+                var x0 = -1000.0 + i * w;
+                var z0 = -1000.0 + j * w;
+                var y0 = 0.0;
+                var x1 = x0 + w;
+                var y1 = random.nextInt(1, 101);
+                var z1 = z0 + w;
+                boxes.add(new Box(new Vec3(x0, y0, z0), new Vec3(x1, y1, z1), ground));
+            }
+        }
+        objects.add(new HittableBinaryTree(boxes));
+
+        // light
+        objects.add(new Parallelogram(
+                new Vec3(123, 554, 147), new Vec3(300, 0, 0), new Vec3(0, 0, 265),
+                new DiffuseLight(new Color(7., 7., 7.))
+        ));
+
+        // spheres with different materials
+        objects.add(new Sphere(new Vec3(400, 400, 200), 50, new LambertianMaterial(new Color(0.7, 0.3, 0.1))));
+        objects.add(new Sphere(new Vec3(260, 150, 45), 50, new DielectricMaterial(1.5)));
+        objects.add(new Sphere(new Vec3(0, 150, 145), 50, new MetallicMaterial(new Color(0.8, 0.8, 0.9), 1.0)));
+
+        // glass sphere filled with gas
+        var boundary = new Sphere(new Vec3(360, 150, 145), 70, new DielectricMaterial(1.5));
+        objects.add(boundary);
+        objects.add(new ConstantMedium(boundary, 0.2, new IsotropicMaterial(new Color(0.2, 0.4, 0.9))));
+
+        // put the world in a glass sphere
+        objects.add(new ConstantMedium(
+                new Sphere(new Vec3(0, 0, 0), 5000, new DielectricMaterial(1.5)),
+                0.0001, new IsotropicMaterial(new Color(1., 1., 1.))
+        ));
+
+        // textures spheres
+        objects.add(new Sphere(new Vec3(400, 200, 400), 100, new LambertianMaterial(new ImageTexture("/earthmap.jpg"))));
+        objects.add(new Sphere(new Vec3(220, 280, 300), 80, new LambertianMaterial(new PerlinTexture(0.2))));
+
+        // box from spheres
+        var white = new LambertianMaterial(new Color(.73, .73, .73));
+        var spheres = new ArrayList<Hittable>();
+        for (int j = 0; j < 1000; j++) {
+            spheres.add(new Sphere(new Vec3(random.nextDouble(165), random.nextDouble(165), random.nextDouble(165)), 10, white));
+        }
+        objects.add(new HittableBinaryTree(spheres).rotateY(Math.toRadians(15)).translate(new Vec3(-100, 270, 395)));
+
+        return new Example(
+                new Scene(objects),
+                SimpleCamera.builder()
+                        .withImage(height, height)
+                        .withFieldOfView(Math.toRadians(40))
+                        .withPosition(new Vec3(478, 278, -600))
+                        .withTarget(new Vec3(278, 278, 0))
+                        .build()
+        );
+    }
+
     private static @NotNull SkyBox getSkyBox() {
         return SkyBox.gradient(new Color(0.5, 0.7, 1.0), Color.WHITE);
     }

src/main/java/eu/jonahbauer/raytracing/Main.java

@@ -13,6 +13,8 @@ import java.nio.file.Path;
 import java.util.function.IntFunction;
 
 public class Main {
+    public static final boolean DEBUG = false;
+
     public static void main(String[] args) throws IOException {
         var config = Config.parse(args);
         var example = config.example;

src/main/java/eu/jonahbauer/raytracing/math/AABB.java

@@ -11,7 +11,6 @@ import java.util.Optional;
  * An axis-aligned bounding box.
  */
 public record AABB(@NotNull Vec3 min, @NotNull Vec3 max) {
-    public static final AABB UNIVERSE = new AABB(Vec3.MIN, Vec3.MAX);
     public static final AABB EMPTY = new AABB(Vec3.ZERO, Vec3.ZERO);
     public static final Comparator<AABB> X_AXIS = Comparator.comparing(AABB::min, Comparator.comparingDouble(Vec3::x));
     public static final Comparator<AABB> Y_AXIS = Comparator.comparing(AABB::min, Comparator.comparingDouble(Vec3::y));
@@ -36,38 +35,53 @@ public record AABB(@NotNull Vec3 min, @NotNull Vec3 max) {
         return Optional.ofNullable(bbox);
     }
 
+    /**
+     * {@return the range of x values}
+     */
     public @NotNull Range x() {
         return new Range(min.x(), max.x());
     }
 
+    /**
+     * {@return the range of y values}
+     */
     public @NotNull Range y() {
         return new Range(min.y(), max.y());
     }
 
+    /**
+     * {@return the range of z values}
+     */
     public @NotNull Range z() {
         return new Range(min.z(), max.z());
     }
 
+    /**
+     * {@return the center of this bounding box}
+     */
     public @NotNull Vec3 center() {
         return Vec3.average(min, max, 2);
     }
 
+    /**
+     * Expands this bounding box to include the other bounding box.
+     * @param box a bounding box
+     * @return the expanded bounding box
+     */
     public @NotNull AABB expand(@NotNull AABB box) {
         return new AABB(Vec3.min(this.min, box.min), Vec3.max(this.max, box.max));
     }
 
-    public boolean hit(@NotNull Ray ray) {
+    /**
-        return intersect(ray).isPresent();
+     * Tests whether the {@code ray} intersects this bounding box withing the {@code range}
-    }
+     * @param ray a ray
-
+     * @param range a range of valid {@code t}s
-    public @NotNull Optional<Range> intersect(@NotNull Ray ray) {
+     * @return {@code true} iff the ray intersects this bounding box, {@code false} otherwise
-        if (this == UNIVERSE) return Optional.of(Range.UNIVERSE);
+     */
-        if (this == EMPTY) return Optional.empty();
+    public boolean hit(@NotNull Ray ray, @NotNull Range range) {
-
-        int vmask = ray.vmask();
-
         var origin = ray.origin();
-        var invDirection = ray.direction().inv();
+        var direction = ray.direction();
+        var invDirection = direction.inv();
 
         // calculate t values for intersection points of ray with planes through min
         var tmin = intersect(min(), origin, invDirection);
@@ -77,27 +91,31 @@ public record AABB(@NotNull Vec3 min, @NotNull Vec3 max) {
         // determine range of t for which the ray is inside this voxel
         double tlmax = Double.NEGATIVE_INFINITY; // lower limit maximum
         double tumin = Double.POSITIVE_INFINITY; // upper limit minimum
+
         for (int i = 0; i < 3; i++) {
-            // classify t values as lower or upper limit based on vmask
+            // classify t values as lower or upper limit based on ray direction
-            if ((vmask & (1 << i)) == 0) {
+            if (direction.get(i) >= 0) {
                 // min is lower limit and max is upper limit
-                tlmax = Math.max(tlmax, tmin[i]);
+                if (tmin[i] > tlmax) tlmax = tmin[i];
-                tumin = Math.min(tumin, tmax[i]);
+                if (tmax[i] < tumin) tumin = tmax[i];
             } else {
                 // max is lower limit and min is upper limit
-                tlmax = Math.max(tlmax, tmax[i]);
+                if (tmax[i] > tlmax) tlmax = tmax[i];
-                tumin = Math.min(tumin, tmin[i]);
+                if (tmin[i] < tumin) tumin = tmin[i];
             }
         }
 
-        return tlmax < tumin ? Optional.of(new Range(tlmax, tumin)) : Optional.empty();
+        return tlmax < tumin && tumin >= range.min() && tlmax <= range.max();
     }
 
-    public static double @NotNull[] intersect(@NotNull Vec3 corner, @NotNull Ray ray) {
+    /**
-        return intersect(corner, ray.origin(), ray.direction().inv());
+     * Computes the {@code t} values of the intersections of a ray with the axis-aligned planes through a point.
-    }
+     * @param corner the point
-
+     * @param origin the origin point of the ray
-    private static double @NotNull[] intersect(@NotNull Vec3 corner, @NotNull Vec3 origin, @NotNull Vec3 invDirection) {
+     * @param invDirection the {@linkplain Vec3#inv() inverted} direction of the ray
+     * @return a three-element array of the {@code t} values of the intersection with the yz-, xz- and xy-plane through {@code corner}
+     */
+    public static double @NotNull[] intersect(@NotNull Vec3 corner, @NotNull Vec3 origin, @NotNull Vec3 invDirection) {
         return new double[] {
                 (corner.x() - origin.x()) * invDirection.x(),
                 (corner.y() - origin.y()) * invDirection.y(),

src/main/java/eu/jonahbauer/raytracing/math/Ray.java

@@ -11,16 +11,6 @@ public record Ray(@NotNull Vec3 origin, @NotNull Vec3 direction) {
     }
 
     public @NotNull Vec3 at(double t) {
-        return new Vec3(
+        return Vec3.fma(t, direction, origin);
-                Math.fma(t, direction.x(), origin.x()),
-                Math.fma(t, direction.y(), origin.y()),
-                Math.fma(t, direction.z(), origin.z())
-        );
-    }
-
-    public int vmask() {
-        return (direction().x() < 0 ? 1 : 0)
-                | (direction().y() < 0 ? 2 : 0)
-                | (direction().z() < 0 ? 4 : 0);
     }
 }

src/main/java/eu/jonahbauer/raytracing/math/Vec3.java

@@ -5,6 +5,8 @@ import org.jetbrains.annotations.NotNull;
 import java.util.Optional;
 import java.util.random.RandomGenerator;
 
+import static eu.jonahbauer.raytracing.Main.DEBUG;
+
 public record Vec3(double x, double y, double z) {
     public static final Vec3 ZERO = new Vec3(0, 0, 0);
     public static final Vec3 MAX = new Vec3(Double.MAX_VALUE, Double.MAX_VALUE, Double.MAX_VALUE);
@@ -14,31 +16,63 @@ public record Vec3(double x, double y, double z) {
     public static final Vec3 UNIT_Z = new Vec3(0, 0, 1);
 
     public Vec3 {
-        assert Double.isFinite(x) && Double.isFinite(y) && Double.isFinite(z) : "x, y and z must be finite";
+        if (DEBUG) {
+            if (!Double.isFinite(x) || !Double.isFinite(y) || !Double.isFinite(z)) {
+                throw new IllegalArgumentException("x, y and z must be finite");
+            }
+        }
     }
 
+    /**
+     * {@return a uniformly random unit vector}
+     */
     public static @NotNull Vec3 random(@NotNull RandomGenerator random) {
-        return random(random, false);
+        double x, y, z;
+        double squared;
+        do {
+            x = Math.fma(2, random.nextDouble(), -1);
+            y = Math.fma(2, random.nextDouble(), -1);
+            z = Math.fma(2, random.nextDouble(), -1);
+            squared = x * x + y * y + z * z;
+        } while (squared > 1);
+        var factor = 1 / Math.sqrt(squared);
+        return new Vec3(x * factor, y * factor, z * factor);
     }
 
-    public static @NotNull Vec3 random(@NotNull RandomGenerator random, boolean unit) {
+    /**
-        var vec = new Vec3(
+     * {@return a uniformly random unit vector on the opposite hemisphere of the given <code>direction</code>}
-                Math.fma(2, random.nextDouble(), -1),
+     */
-                Math.fma(2, random.nextDouble(), -1),
+    public static @NotNull Vec3 randomOppositeHemisphere(@NotNull RandomGenerator random, @NotNull Vec3 direction) {
-                Math.fma(2, random.nextDouble(), -1)
+        double x, y, z;
-        );
+        double squared;
-        return unit ? vec.unit() : vec;
+        do {
+            x = Math.fma(2, random.nextDouble(), -1);
+            y = Math.fma(2, random.nextDouble(), -1);
+            z = Math.fma(2, random.nextDouble(), -1);
+            squared = x * x + y * y + z * z;
+        } while (squared > 1 || direction.x() * x + direction.y() * y + direction.z() * z >= 0);
+        var factor = 1 / Math.sqrt(squared);
+        return new Vec3(x * factor, y * factor, z * factor);
     }
 
+    /**
+     * Reflects a vector on the given {@code normal} vector.
+     * @param vec a vector
+     * @param normal the surface normal (must be a unit vector)
+     * @return the reflected vector
+     */
     public static @NotNull Vec3 reflect(@NotNull Vec3 vec, @NotNull Vec3 normal) {
         var factor = - 2 * normal.times(vec);
-        return new Vec3(
+        return Vec3.fma(factor, normal, vec);
-                Math.fma(factor, normal.x(), vec.x()),
-                Math.fma(factor, normal.y(), vec.y()),
-                Math.fma(factor, normal.z(), vec.z())
-        );
     }
 
+    /**
+     * Refracts a vector on the given {@code normal} vector.
+     * @param vec a vector
+     * @param normal the surface normal (must be a unit vector)
+     * @param ri the refractive index
+     * @return the refracted vector
+     */
     public static @NotNull Optional<Vec3> refract(@NotNull Vec3 vec, @NotNull Vec3 normal, double ri) {
         vec = vec.unit();
         var cosTheta = Math.min(- vec.times(normal), 1.0);
@@ -50,16 +84,35 @@ public record Vec3(double x, double y, double z) {
         return Optional.of(rOutPerp.plus(rOutParallel));
     }
 
+    /**
+     * Rotates a vector around an {@code axis}.
+     * @param vec a vector
+     * @param axis the rotation axis
+     * @param angle the angle in radians
+     * @return the rotated vector
+     */
     public static @NotNull Vec3 rotate(@NotNull Vec3 vec, @NotNull Vec3 axis, double angle) {
         Vec3 vxp = axis.cross(vec);
         Vec3 vxvxp = axis.cross(vxp);
         return vec.plus(vxp.times(Math.sin(angle))).plus(vxvxp.times(1 - Math.cos(angle)));
     }
 
+    /**
+     * {@return the euclidean distance between two vectors}
+     * @param a a vector
+     * @param b another vector
+     */
     public static double distance(@NotNull Vec3 a, @NotNull Vec3 b) {
         return a.minus(b).length();
     }
 
+    /**
+     * Computes a running average of vectors.
+     * @param current the current running average
+     * @param next the next vector
+     * @param index the one-based index of the next vector
+     * @return the new running average
+     */
     public static @NotNull Vec3 average(@NotNull Vec3 current, @NotNull Vec3 next, int index) {
         var factor = 1d / index;
         return new Vec3(
@@ -69,6 +122,11 @@ public record Vec3(double x, double y, double z) {
         );
     }
 
+    /**
+     * {@return a component-wise maximum vector}
+     * @param a a vector
+     * @param b another vector
+     */
     public static @NotNull Vec3 max(@NotNull Vec3 a, @NotNull Vec3 b) {
         return new Vec3(
                 Math.max(a.x(), b.x()),
@@ -77,6 +135,11 @@ public record Vec3(double x, double y, double z) {
         );
     }
 
+    /**
+     * {@return a component-wise minimum vector}
+     * @param a a vector
+     * @param b another vector
+     */
     public static @NotNull Vec3 min(@NotNull Vec3 a, @NotNull Vec3 b) {
         return new Vec3(
                 Math.min(a.x(), b.x()),
@@ -85,6 +148,24 @@ public record Vec3(double x, double y, double z) {
         );
     }
 
+    /**
+     * {@return <code>a * b + c</code>}
+     * @param a scalar
+     * @param b a vector
+     * @param c another vector
+     */
+    public static @NotNull Vec3 fma(double a, @NotNull Vec3 b, @NotNull Vec3 c) {
+        return new Vec3(
+                Math.fma(a, b.x(), c.x()),
+                Math.fma(a, b.y(), c.y()),
+                Math.fma(a, b.z(), c.z())
+        );
+    }
+
+    public static double tripleProduct(@NotNull Vec3 a, @NotNull Vec3 b, @NotNull Vec3 c) {
+        return a.x * b.y * c.z + a.y * b.z * c.x + a.z * b.x * c.y - c.x * b.y * a.z - c.y * b.z * a.x - c.z * b.x * a.y;
+    }
+
     public @NotNull Vec3 plus(double x, double y, double z) {
         return new Vec3(this.x + x, this.y + y, this.z + z);
     }
@@ -93,57 +174,122 @@ public record Vec3(double x, double y, double z) {
         return new Vec3(this.x - x, this.y - y, this.z - z);
     }
 
-    public @NotNull Vec3 plus(@NotNull Vec3 b) {
+    /**
-        return new Vec3(this.x + b.x, this.y + b.y, this.z + b.z);
+     * Adds a vector to this vector
+     * @param other a vector
+     * @return the sum of this and the other vector
+     */
+    public @NotNull Vec3 plus(@NotNull Vec3 other) {
+        return new Vec3(this.x + other.x, this.y + other.y, this.z + other.z);
     }
 
-    public @NotNull Vec3 minus(@NotNull Vec3 b) {
+    /**
-        return new Vec3(this.x - b.x, this.y - b.y, this.z - b.z);
+     * Subtracts a vector from this vector
+     * @param other a vector
+     * @return the difference of this and the other vector
+     */
+    public @NotNull Vec3 minus(@NotNull Vec3 other) {
+        return new Vec3(this.x - other.x, this.y - other.y, this.z - other.z);
     }
 
-    public double times(@NotNull Vec3 b) {
+    /**
-        return this.x * b.x + this.y * b.y + this.z * b.z;
+     * Computes the scalar product of this and another vector
+     * @param other a vector
+     * @return the scalar product
+     */
+    public double times(@NotNull Vec3 other) {
+        return this.x * other.x + this.y * other.y + this.z * other.z;
     }
 
-    public @NotNull Vec3 times(double b) {
+    /**
-        return new Vec3(this.x * b, this.y * b, this.z * b);
+     * Multiplies this vector with a scalar
+     * @param t a scalar
+     * @return the product of this vector and the scalar
+     */
+    public @NotNull Vec3 times(double t) {
+        return new Vec3(this.x * t, this.y * t, this.z * t);
     }
 
+    /**
+     * Negates this vector.
+     * {@return the negated vector}
+     */
     public @NotNull Vec3 neg() {
         return new Vec3(-x, -y, -z);
     }
 
+    /**
+     * Inverts each component of this vector.
+     * @return the inverted vector.
+     */
     public @NotNull Vec3 inv() {
         return new Vec3(1 / x, 1 / y, 1 / z);
     }
 
-    public @NotNull Vec3 cross(@NotNull Vec3 b) {
+    /**
+     * Computes the cross-product of this and another vector
+     * @param other a vector
+     * @return the cross-product
+     */
+    public @NotNull Vec3 cross(@NotNull Vec3 other) {
         return new Vec3(
-                this.y() * b.z() - b.y() * this.z(),
+                Math.fma(this.y, other.z, - other.y * this.z),
-                this.z() * b.x() - b.z() * this.x(),
+                Math.fma(this.z, other.x, - other.z * this.x),
-                this.x() * b.y() - b.x() * this.y()
+                Math.fma(this.x, other.y, - other.x * this.y)
         );
     }
 
-    public @NotNull Vec3 div(double b) {
+    /**
-        return new Vec3(this.x / b, this.y / b, this.z / b);
+     * Divides this vector by a scalar
+     * @param t a scalar
+     * @return this vector divided by the scalar
+     */
+    public @NotNull Vec3 div(double t) {
+        return new Vec3(this.x / t, this.y / t, this.z / t);
     }
 
+    /**
+     * {@return the squared length of this vector}
+     */
     public double squared() {
         return this.x * this.x + this.y * this.y + this.z * this.z;
     }
 
+    /**
+     * {@return the length of this vector}
+     */
     public double length() {
         return Math.sqrt(squared());
     }
 
+    /**
+     * {@return whether this vector is near zero}
+     */
     public boolean isNearZero() {
         var s = 1e-8;
         return Math.abs(x) < s && Math.abs(y) < s && Math.abs(z) < s;
     }
 
+    /**
+     * {@return a unit vector with the same direction as this vector}
+     */
     public @NotNull Vec3 unit() {
-        return div(length());
+        var squared = squared();
+        if (squared == 1) return this;
+        return div(Math.sqrt(squared));
+    }
+
+    /**
+     * {@return the n-th component of this vector}
+     * @param axis the component index
+     */
+    public double get(int axis) {
+        return switch (axis) {
+            case 0 -> x;
+            case 1 -> y;
+            case 2 -> z;
+            default -> throw new IndexOutOfBoundsException(axis);
+        };
     }
 
     public @NotNull Vec3 withX(double x) {
@@ -157,4 +303,9 @@ public record Vec3(double x, double y, double z) {
     public @NotNull Vec3 withZ(double z) {
         return new Vec3(x, y, z);
     }
+
+    @Override
+    public @NotNull String toString() {
+        return "(" + x + "," + y + "," + z + ")";
+    }
 }

src/main/java/eu/jonahbauer/raytracing/render/camera/Camera.java

@@ -18,7 +18,13 @@ public interface Camera {
 
     /**
      * Casts a ray through the given pixel.
+     * @param x the pixel x coordinate
+     * @param y the pixel y coordinate
+     * @param i the subpixel x coordinate
+     * @param j the subpixel y coordinate
+     * @param n the subpixel count (per side)
+     * @param random a random number generator
      * @return a new ray
      */
-    @NotNull Ray cast(int x, int y, @NotNull RandomGenerator random);
+    @NotNull Ray cast(int x, int y, int i, int j, int n, @NotNull RandomGenerator random);
 }

src/main/java/eu/jonahbauer/raytracing/render/camera/SimpleCamera.java

@@ -60,7 +60,7 @@ public final class SimpleCamera implements Camera {
 
         this.pixel00 = origin.plus(direction.times(builder.focusDistance))
                 .minus(u.times(0.5 * viewportWidth)).minus(v.times(0.5 * viewportHeight))
-                .plus(pixelU.div(2)).plus(pixelV.div(2));
+                .plus(pixelU.times(.5)).plus(pixelV.times(.5));
     }
 
     /**
@@ -79,13 +79,20 @@ public final class SimpleCamera implements Camera {
 
     /**
      * {@inheritDoc}
+     * @param x {@inheritDoc}
+     * @param y {@inheritDoc}
+     * @param i {@inheritDoc}
+     * @param j {@inheritDoc}
+     * @param n {@inheritDoc}
+     * @param random {@inheritDoc}
      */
-    public @NotNull Ray cast(int x, int y, @NotNull RandomGenerator random) {
+    @Override
+    public @NotNull Ray cast(int x, int y, int i, int j, int n, @NotNull RandomGenerator random) {
         Objects.checkIndex(x, width);
         Objects.checkIndex(y, height);
 
         var origin = getRayOrigin(random);
-        var target = getRayTarget(x, y, random);
+        var target = getRayTarget(x, y, i, j, n, random);
         return new Ray(origin, target.minus(origin));
     }
 
@@ -98,8 +105,8 @@ public final class SimpleCamera implements Camera {
         if (blurRadius <= 0) return origin;
 
         while (true) {
-            var du = 2 * random.nextDouble() - 1;
+            var du = Math.fma(2, random.nextDouble(), -1);
-            var dv = 2 * random.nextDouble() - 1;
+            var dv = Math.fma(2, random.nextDouble(), -1);
             if (du * du + dv * dv >= 1) continue;
 
             var ru = blurRadius * du;
@@ -116,9 +123,10 @@ public final class SimpleCamera implements Camera {
     /**
      * {@return the target vector for a ray through the given pixel} The position is randomized within the pixel.
      */
-    private @NotNull Vec3 getRayTarget(int x, int y, @NotNull RandomGenerator random) {
+    private @NotNull Vec3 getRayTarget(int x, int y, int i, int j, int n, @NotNull RandomGenerator random) {
-        double dx = x + random.nextDouble() - 0.5;
+        var factor = 1d / n;
-        double dy = y + random.nextDouble() - 0.5;
+        var dx = x + Math.fma(factor, i + random.nextDouble(), -0.5);
+        var dy = y + Math.fma(factor, j + random.nextDouble(), -0.5);
         return pixel00.plus(pixelU.times(dx)).plus(pixelV.times(dy));
     }
 

src/main/java/eu/jonahbauer/raytracing/render/canvas/Canvas.java

@@ -1,6 +1,6 @@
 package eu.jonahbauer.raytracing.render.canvas;
 
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Color;
 import org.jetbrains.annotations.NotNull;
 
 import java.util.function.Function;

src/main/java/eu/jonahbauer/raytracing/render/canvas/Image.java

@@ -1,8 +1,9 @@
 package eu.jonahbauer.raytracing.render.canvas;
 
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Color;
 import org.jetbrains.annotations.NotNull;
 
+import java.awt.image.BufferedImage;
 import java.util.Objects;
 
 public final class Image implements Canvas {
@@ -21,6 +22,16 @@ public final class Image implements Canvas {
         this.data = new Color[height][width];
     }
 
+    public Image(@NotNull BufferedImage image) {
+        this(image.getWidth(), image.getHeight());
+
+        for (int y = 0; y < height; y++) {
+            for (int x = 0; x < width; x++) {
+                this.data[y][x] = new Color(image.getRGB(x, y));
+            }
+        }
+    }
+
     @Override
     public int getWidth() {
         return width;

src/main/java/eu/jonahbauer/raytracing/render/canvas/LiveCanvas.java

@@ -1,6 +1,6 @@
 package eu.jonahbauer.raytracing.render.canvas;
 
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Color;
 import org.jetbrains.annotations.NotNull;
 
 import javax.swing.*;

src/main/java/eu/jonahbauer/raytracing/render/material/DielectricMaterial.java

@@ -2,7 +2,8 @@ package eu.jonahbauer.raytracing.render.material;
 
 import eu.jonahbauer.raytracing.math.Ray;
 import eu.jonahbauer.raytracing.math.Vec3;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import eu.jonahbauer.raytracing.render.texture.Texture;
 import eu.jonahbauer.raytracing.scene.HitResult;
 import org.jetbrains.annotations.NotNull;
 
@@ -10,18 +11,18 @@ import java.util.Objects;
 import java.util.Optional;
 import java.util.random.RandomGenerator;
 
-public record DielectricMaterial(double refractionIndex, @NotNull Color albedo) implements Material {
+public record DielectricMaterial(double refractionIndex, @NotNull Texture texture) implements Material {
     public DielectricMaterial(double refractionIndex) {
         this(refractionIndex, Color.WHITE);
     }
 
     public DielectricMaterial {
-        Objects.requireNonNull(albedo, "albedo");
+        Objects.requireNonNull(texture, "texture");
     }
 
     @Override
     public @NotNull Optional<ScatterResult> scatter(@NotNull Ray ray, @NotNull HitResult hit, @NotNull RandomGenerator random) {
-        var ri = hit.frontFace() ? (1 / refractionIndex) : refractionIndex;
+        var ri = hit.isFrontFace() ? (1 / refractionIndex) : refractionIndex;
 
         var cosTheta = Math.min(- ray.direction().unit().times(hit.normal()), 1.0);
         var reflectance = reflectance(cosTheta);
@@ -30,7 +31,8 @@ public record DielectricMaterial(double refractionIndex, @NotNull Color albedo)
         var newDirection = (reflect ? Optional.<Vec3>empty() : Vec3.refract(ray.direction(), hit.normal(), ri))
                 .orElseGet(() -> Vec3.reflect(ray.direction(), hit.normal()));
 
-        return Optional.of(new ScatterResult(new Ray(hit.position(), newDirection), albedo));
+        var attenuation = texture.get(hit);
+        return Optional.of(new SpecularScatterResult(attenuation, new Ray(hit.position(), newDirection)));
     }
 
     private double reflectance(double cos) {

src/main/java/eu/jonahbauer/raytracing/render/material/DiffuseLight.java

@@ -1,14 +1,15 @@
 package eu.jonahbauer.raytracing.render.material;
 
 import eu.jonahbauer.raytracing.math.Ray;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import eu.jonahbauer.raytracing.render.texture.Texture;
 import eu.jonahbauer.raytracing.scene.HitResult;
 import org.jetbrains.annotations.NotNull;
 
 import java.util.Optional;
 import java.util.random.RandomGenerator;
 
-public record DiffuseLight(@NotNull Color emit) implements Material {
+public record DiffuseLight(@NotNull Texture texture) implements Material {
     @Override
     public @NotNull Optional<ScatterResult> scatter(@NotNull Ray ray, @NotNull HitResult hit, @NotNull RandomGenerator random) {
         return Optional.empty();
@@ -16,6 +17,6 @@ public record DiffuseLight(@NotNull Color emit) implements Material {
 
     @Override
     public @NotNull Color emitted(@NotNull HitResult hit) {
-        return emit;
+        return texture.get(hit);
     }
 }

src/main/java/eu/jonahbauer/raytracing/render/material/DirectionalMaterial.java

@@ -0,0 +1,68 @@
+package eu.jonahbauer.raytracing.render.material;
+
+import eu.jonahbauer.raytracing.math.Ray;
+import eu.jonahbauer.raytracing.math.Vec3;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import eu.jonahbauer.raytracing.render.texture.Texture;
+import eu.jonahbauer.raytracing.scene.HitResult;
+import org.jetbrains.annotations.NotNull;
+import org.jetbrains.annotations.Nullable;
+
+import java.util.Optional;
+import java.util.random.RandomGenerator;
+
+public final class DirectionalMaterial implements Material {
+    private final @Nullable Material front;
+    private final @Nullable Material back;
+
+    private final @NotNull Texture texture;
+
+    public DirectionalMaterial(@Nullable Material front, @Nullable Material back) {
+        if (front == null && back == null) throw new IllegalArgumentException("front and back must not both be null");
+        this.front = front;
+        this.back = back;
+        this.texture = new DirectionalTexture(
+                front != null ? front.texture() : null,
+                back != null ? back.texture() : null
+        );
+    }
+
+    @Override
+    public @NotNull Texture texture() {
+        return texture;
+    }
+
+    @Override
+    public @NotNull Optional<ScatterResult> scatter(@NotNull Ray ray, @NotNull HitResult hit, @NotNull RandomGenerator random) {
+        if (hit.isFrontFace()) {
+            if (front != null) return front.scatter(ray, hit, random);
+        } else {
+            if (back != null) return back.scatter(ray, hit, random);
+        }
+        // let the ray pass through without obstruction
+        return Optional.of(new SpecularScatterResult(Color.WHITE, new Ray(ray.at(hit.t()), ray.direction())));
+    }
+
+    @Override
+    public @NotNull Color emitted(@NotNull HitResult hit) {
+        if (hit.isFrontFace()) {
+            if (front != null) return front.emitted(hit);
+        } else {
+            if (back != null) return back.emitted(hit);
+        }
+        return Material.super.emitted(hit);
+    }
+
+    private record DirectionalTexture(@Nullable Texture front, @Nullable Texture back) implements Texture {
+
+        @Override
+        public @NotNull Color get(double u, double v, @NotNull Vec3 p) {
+            throw new UnsupportedOperationException();
+        }
+
+        @Override
+        public boolean isUVRequired() {
+            return front() != null && front().isUVRequired() || back() != null && back().isUVRequired();
+        }
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/material/IsotropicMaterial.java

@@ -1,8 +1,9 @@
 package eu.jonahbauer.raytracing.render.material;
 
 import eu.jonahbauer.raytracing.math.Ray;
-import eu.jonahbauer.raytracing.math.Vec3;
+import eu.jonahbauer.raytracing.render.renderer.pdf.SphereProbabilityDensityFunction;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import eu.jonahbauer.raytracing.render.texture.Texture;
 import eu.jonahbauer.raytracing.scene.HitResult;
 import org.jetbrains.annotations.NotNull;
 
@@ -12,6 +13,11 @@ import java.util.random.RandomGenerator;
 public record IsotropicMaterial(@NotNull Color albedo) implements Material {
     @Override
     public @NotNull Optional<ScatterResult> scatter(@NotNull Ray ray, @NotNull HitResult hit, @NotNull RandomGenerator random) {
-        return Optional.of(new ScatterResult(new Ray(hit.position(), Vec3.random(random, true)), albedo()));
+        return Optional.of(new PdfScatterResult(albedo(), new SphereProbabilityDensityFunction()));
+    }
+
+    @Override
+    public @NotNull Texture texture() {
+        return albedo();
     }
 }

src/main/java/eu/jonahbauer/raytracing/render/material/LambertianMaterial.java

@@ -1,8 +1,8 @@
 package eu.jonahbauer.raytracing.render.material;
 
 import eu.jonahbauer.raytracing.math.Ray;
-import eu.jonahbauer.raytracing.math.Vec3;
+import eu.jonahbauer.raytracing.render.renderer.pdf.CosineProbabilityDensityFunction;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Texture;
 import eu.jonahbauer.raytracing.scene.HitResult;
 import org.jetbrains.annotations.NotNull;
 
@@ -10,17 +10,14 @@ import java.util.Objects;
 import java.util.Optional;
 import java.util.random.RandomGenerator;
 
-public record LambertianMaterial(@NotNull Color albedo) implements Material {
+public record LambertianMaterial(@NotNull Texture texture) implements Material {
     public LambertianMaterial {
-        Objects.requireNonNull(albedo, "albedo");
+        Objects.requireNonNull(texture, "texture");
     }
 
     @Override
     public @NotNull Optional<ScatterResult> scatter(@NotNull Ray ray, @NotNull HitResult hit, @NotNull RandomGenerator random) {
-        var newDirection = hit.normal().plus(Vec3.random(random, true));
+        var attenuation = texture.get(hit);
-        if (newDirection.isNearZero()) newDirection = hit.normal();
+        return Optional.of(new PdfScatterResult(attenuation, new CosineProbabilityDensityFunction(hit.normal())));
-
-        var scattered = new Ray(hit.position(), newDirection);
-        return Optional.of(new ScatterResult(scattered, albedo));
     }
 }

src/main/java/eu/jonahbauer/raytracing/render/material/Material.java

@@ -1,7 +1,9 @@
 package eu.jonahbauer.raytracing.render.material;
 
 import eu.jonahbauer.raytracing.math.Ray;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.renderer.pdf.ProbabilityDensityFunction;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import eu.jonahbauer.raytracing.render.texture.Texture;
 import eu.jonahbauer.raytracing.scene.HitResult;
 import org.jetbrains.annotations.NotNull;
 
@@ -11,16 +13,59 @@ import java.util.random.RandomGenerator;
 
 public interface Material {
 
+    /**
+     * {@return the texture associated with this material}
+     */
+    @NotNull Texture texture();
+
+    /**
+     * Scatters a light ray after it hit a surface.
+     * @param ray the incoming light ray
+     * @param hit information about the light ray hitting some object
+     * @param random a random number generator
+     * @return a {@code ScatterResult} if the ray is scattered or an {@linkplain Optional#empty() empty optional} if the
+     * ray is absorbed.
+     */
     @NotNull Optional<ScatterResult> scatter(@NotNull Ray ray, @NotNull HitResult hit, @NotNull RandomGenerator random);
 
+    /**
+     * {@return the color emitted for a given hit}
+     * @implSpec the default implementation returns {@linkplain Color#BLACK black}, i.e. no emission
+     */
     default @NotNull Color emitted(@NotNull HitResult hit) {
         return Color.BLACK;
     }
 
-    record ScatterResult(@NotNull Ray ray, @NotNull Color attenuation) {
+    /**
-        public ScatterResult {
+     * The result of a {@linkplain Material#scatter(Ray, HitResult, RandomGenerator) scattering operation}.
-            Objects.requireNonNull(ray, "ray");
+     */
+    sealed interface ScatterResult {}
+
+    /**
+     * The result of a specular {@linkplain #scatter(Ray, HitResult, RandomGenerator) scattering operation}. A
+     * specular is a scattering operation with a very small number of possible scattered rays (like a
+     * perfect reflection which only has one possible scattered ray).
+     * @param attenuation the attenuation of the scattered light ray
+     * @param ray the scattered light ray
+     */
+    record SpecularScatterResult(@NotNull Color attenuation, @NotNull Ray ray) implements ScatterResult {
+        public SpecularScatterResult {
             Objects.requireNonNull(attenuation, "attenuation");
+            Objects.requireNonNull(ray, "ray");
+        }
+    }
+
+    /**
+     * The result of a probability density function based
+     * {@linkplain #scatter(Ray, HitResult, RandomGenerator) scattering operation}. A probability density function
+     * based scattering operation uses a probability density function to determine the scatter direction.
+     * @param attenuation the attenuation of the scattered light ray
+     * @param pdf the probability density function
+     */
+    record PdfScatterResult(@NotNull Color attenuation, @NotNull ProbabilityDensityFunction pdf) implements ScatterResult {
+        public PdfScatterResult {
+            Objects.requireNonNull(attenuation, "attenuation");
+            Objects.requireNonNull(pdf, "pdf");
         }
     }
 }

src/main/java/eu/jonahbauer/raytracing/render/material/MetallicMaterial.java

@@ -2,7 +2,7 @@ package eu.jonahbauer.raytracing.render.material;
 
 import eu.jonahbauer.raytracing.math.Ray;
 import eu.jonahbauer.raytracing.math.Vec3;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Texture;
 import eu.jonahbauer.raytracing.scene.HitResult;
 import org.jetbrains.annotations.NotNull;
 
@@ -10,14 +10,14 @@ import java.util.Objects;
 import java.util.Optional;
 import java.util.random.RandomGenerator;
 
-public record MetallicMaterial(@NotNull Color albedo, double fuzz) implements Material {
+public record MetallicMaterial(@NotNull Texture texture, double fuzz) implements Material {
 
-    public MetallicMaterial(@NotNull Color albedo) {
+    public MetallicMaterial(@NotNull Texture texture) {
-        this(albedo, 0);
+        this(texture, 0);
     }
 
     public MetallicMaterial {
-        Objects.requireNonNull(albedo, "albedo");
+        Objects.requireNonNull(texture, "texture");
         if (fuzz < 0 || !Double.isFinite(fuzz)) throw new IllegalArgumentException("fuzz must be non-negative");
     }
 
@@ -25,8 +25,9 @@ public record MetallicMaterial(@NotNull Color albedo, double fuzz) implements Ma
     public @NotNull Optional<ScatterResult> scatter(@NotNull Ray ray, @NotNull HitResult hit, @NotNull RandomGenerator random) {
         var newDirection = Vec3.reflect(ray.direction(), hit.normal());
         if (fuzz > 0) {
-            newDirection = newDirection.unit().plus(Vec3.random(random, true).times(fuzz));
+            newDirection = Vec3.fma(fuzz, Vec3.random(random), newDirection.unit());
         }
-        return Optional.of(new ScatterResult(new Ray(hit.position(), newDirection), albedo));
+        var attenuation = texture.get(hit);
+        return Optional.of(new SpecularScatterResult(attenuation, new Ray(hit.position(), newDirection)));
     }
 }

src/main/java/eu/jonahbauer/raytracing/render/renderer/SimpleRenderer.java

@@ -2,7 +2,10 @@ package eu.jonahbauer.raytracing.render.renderer;
 
 import eu.jonahbauer.raytracing.math.Range;
 import eu.jonahbauer.raytracing.math.Ray;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.material.Material;
+import eu.jonahbauer.raytracing.render.renderer.pdf.TargetingProbabilityDensityFunction;
+import eu.jonahbauer.raytracing.render.renderer.pdf.MixtureProbabilityDensityFunction;
+import eu.jonahbauer.raytracing.render.texture.Color;
 import eu.jonahbauer.raytracing.render.camera.Camera;
 import eu.jonahbauer.raytracing.render.canvas.Canvas;
 import eu.jonahbauer.raytracing.scene.Scene;
@@ -13,8 +16,10 @@ import java.util.SplittableRandom;
 import java.util.random.RandomGenerator;
 import java.util.stream.IntStream;
 
+import static eu.jonahbauer.raytracing.Main.DEBUG;
+
 public final class SimpleRenderer implements Renderer {
-    private final int samplesPerPixel;
+    private final int sqrtSamplesPerPixel;
     private final int maxDepth;
     private final double gamma;
 
@@ -30,7 +35,7 @@ public final class SimpleRenderer implements Renderer {
     }
 
     private SimpleRenderer(@NotNull Builder builder) {
-        this.samplesPerPixel = builder.samplesPerPixel;
+        this.sqrtSamplesPerPixel = (int) Math.sqrt(builder.samplesPerPixel);
         this.maxDepth = builder.maxDepth;
         this.gamma = builder.gamma;
 
@@ -38,6 +43,9 @@ public final class SimpleRenderer implements Renderer {
         this.iterative = builder.iterative;
     }
 
+    /**
+     * {@inheritDoc}
+     */
     @Override
     public void render(@NotNull Camera camera, @NotNull Scene scene, @NotNull Canvas canvas) {
         if (canvas.getWidth() != camera.getWidth() || canvas.getHeight() != camera.getHeight()) {
@@ -45,19 +53,35 @@ public final class SimpleRenderer implements Renderer {
         }
 
         if (iterative) {
-            var random = new Random();
+            renderIterative(camera, scene, canvas);
+        } else {
+            renderNonIterative(camera, scene, canvas);
+        }
+    }
+
+    /**
+     * Renders the {@code scene} as seen by the {@code camera} to the {@code canvas}, taking one sample per pixel at
+     * a time and updating the canvas after each sample.
+     */
+    private void renderIterative(@NotNull Camera camera, @NotNull Scene scene, @NotNull Canvas canvas) {
+        var random = new Random(0);
 
         // render one sample after the other
-            for (int i = 1 ; i <= samplesPerPixel; i++) {
+        int i = 0;
-                var sample = i;
+        for (int sj = 0; sj < sqrtSamplesPerPixel; sj++) {
+            for (int si = 0; si < sqrtSamplesPerPixel; si++) {
+                var sample = ++i;
+                var sif = si;
+                var sjf = sj;
                 getScanlineStream(camera.getHeight(), parallel).forEach(y -> {
                     for (int x = 0; x < camera.getWidth(); x++) {
-                        var ray = camera.cast(x, y, random);
+                        var ray = camera.cast(x, y, sif, sjf, sqrtSamplesPerPixel, random);
                         var c = getColor(scene, ray, random);
                         canvas.set(x, y, Color.average(canvas.get(x, y), c, sample));
                     }
                 });
             }
+        }
 
         // apply gamma correction
         getScanlineStream(camera.getHeight(), parallel).forEach(y -> {
@@ -65,23 +89,34 @@ public final class SimpleRenderer implements Renderer {
                 canvas.set(x, y, Color.gamma(canvas.get(x, y), gamma));
             }
         });
-        } else {
+    }
-            var splittable = new SplittableRandom();
+
+    /**
+     * Renders the {@code scene} as seen by the {@code camera} to the {@code canvas}, taking some amount of samples
+     * per pixel and updating the canvas after each pixel.
+     */
+    private void renderNonIterative(@NotNull Camera camera, @NotNull Scene scene, @NotNull Canvas canvas) {
+        var splittable = new SplittableRandom(0);
         // render one pixel after the other
         getScanlineStream(camera.getHeight(), parallel).forEach(y -> {
             var random = splittable.split();
             for (int x = 0; x < camera.getWidth(); x++) {
                 var color = Color.BLACK;
-                    for (int i = 1; i <= samplesPerPixel; i++) {
+                int i = 0;
-                        var ray = camera.cast(x, y, random);
+                for (int sj = 0; sj < sqrtSamplesPerPixel; sj++) {
+                    for (int si = 0; si < sqrtSamplesPerPixel; si++) {
+                        var ray = camera.cast(x, y, si, sj, sqrtSamplesPerPixel, random);
+                        if (DEBUG) {
+                            System.out.println("Casting ray " + ray + " through pixel (" + x + "," + y + ") at subpixel (" + si + "," + sj + ")...");
+                        }
                         var c = getColor(scene, ray, random);
-                        color = Color.average(color, c, i);
+                        color = Color.average(color, c, ++i);
+                    }
                 }
                 canvas.set(x, y, Color.gamma(color, gamma));
             }
         });
     }
-    }
 
     /**
      * {@return the color of the given ray in the given scene}
@@ -95,21 +130,82 @@ public final class SimpleRenderer implements Renderer {
         var attenuation = Color.WHITE;
 
         while (depth-- > 0) {
-            var optional = scene.hit(ray, new Range(0.001, Double.POSITIVE_INFINITY));
+            var optional = scene.hit(ray);
             if (optional.isEmpty()) {
-                color = Color.add(color, Color.multiply(attenuation, scene.getBackgroundColor(ray)));
+                var background = scene.getBackgroundColor(ray);
+                color = Color.add(color, Color.multiply(attenuation, background));
+                if (DEBUG) {
+                    System.out.println("  Hit background: " + background);
+                }
                 break;
             }
 
             var hit = optional.get();
+            if (DEBUG) {
+                System.out.println("  Hit " + hit.target() + " at t=" + hit.t() + " (" + hit.position() + ")");
+            }
             var material = hit.material();
             var emitted = material.emitted(hit);
-            var scatter = material.scatter(ray, hit, random);
+            if (DEBUG && !Color.BLACK.equals(emitted)) {
+                System.out.println("  Emitted: " + emitted);
+            }
+
+            var result = material.scatter(ray, hit, random);
             color = Color.add(color, Color.multiply(attenuation, emitted));
 
-            if (scatter.isEmpty()) break;
+            if (result.isEmpty()) {
-            attenuation = Color.multiply(attenuation, scatter.get().attenuation());
+                if (DEBUG) {
-            ray = scatter.get().ray();
+                    System.out.println("  Absorbed");
+                }
+                break;
+            }
+
+            switch (result.get()) {
+                case Material.SpecularScatterResult(var a, var scattered) -> {
+                    attenuation = Color.multiply(attenuation, a);
+                    ray = scattered;
+
+                    if (DEBUG) {
+                        System.out.println("  Specular scattering with albedo " + a);
+                    }
+                }
+                case Material.PdfScatterResult(var a, var pdf) -> {
+                    if (scene.getTargets() == null) {
+                        attenuation = Color.multiply(attenuation, a);
+                        ray = new Ray(hit.position(), pdf.generate(random));
+
+                        if (DEBUG) {
+                            System.out.println("  Pdf scattering with albedo " + a);
+                        }
+                    } else {
+                        var mixed = new MixtureProbabilityDensityFunction(new TargetingProbabilityDensityFunction(hit.position(), scene.getTargets()), pdf, 0.5);
+                        var direction = mixed.generate(random).unit();
+
+                        var idealPdf = pdf.value(direction);
+                        var actualPdf = mixed.value(direction);
+                        if (actualPdf == 0) break; // when actualPdf is 0, the ray should have never been generated by mixed.generate
+
+                        var factor =  idealPdf / actualPdf;
+
+                        attenuation = Color.multiply(attenuation, Color.multiply(a, factor));
+                        ray = new Ray(hit.position(), direction);
+
+                        if (DEBUG) {
+                            System.out.println("  Pdf scattering with albedo " + a + " and factor " + factor);
+                        }
+                    }
+                }
+            }
+
+            if (DEBUG) {
+                System.out.println("  Combined color is " + color);
+                System.out.println("  Combined attenuation is " + attenuation);
+                System.out.println("  New ray is " + ray);
+            }
+        }
+
+        if (DEBUG) {
+            System.out.println("  Final color is " + color);
         }
 
         return color;

src/main/java/eu/jonahbauer/raytracing/render/renderer/pdf/CosineProbabilityDensityFunction.java

@@ -0,0 +1,27 @@
+package eu.jonahbauer.raytracing.render.renderer.pdf;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.Objects;
+import java.util.random.RandomGenerator;
+
+public record CosineProbabilityDensityFunction(@NotNull Vec3 normal) implements ProbabilityDensityFunction {
+
+    public CosineProbabilityDensityFunction {
+        Objects.requireNonNull(normal, "normal");
+        normal = normal.unit();
+    }
+
+    @Override
+    public double value(@NotNull Vec3 direction) {
+        var cos = normal.times(direction);
+        return Math.max(0, cos / Math.PI);
+    }
+
+    @Override
+    public @NotNull Vec3 generate(@NotNull RandomGenerator random) {
+        var out = normal().plus(Vec3.random(random));
+        return out.isNearZero() ? normal() : out;
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/renderer/pdf/MixtureProbabilityDensityFunction.java

@@ -0,0 +1,46 @@
+package eu.jonahbauer.raytracing.render.renderer.pdf;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.Objects;
+import java.util.random.RandomGenerator;
+
+/**
+ * Mixes between two probability density functions (pdf) using a weight. When the weight is closer to zero, the
+ * influence of the second pdf is stronger. When the weight is closer to one, the influence of the first pdf is stronger.
+ * @param a the first probability density function
+ * @param b the second probability density function
+ * @param weight a weight in the range [0, 1]
+ */
+public record MixtureProbabilityDensityFunction(
+        @NotNull ProbabilityDensityFunction a,
+        @NotNull ProbabilityDensityFunction b,
+        double weight
+) implements ProbabilityDensityFunction {
+    public MixtureProbabilityDensityFunction(@NotNull ProbabilityDensityFunction a, @NotNull ProbabilityDensityFunction b) {
+        this(a, b, 0.5);
+    }
+
+    public MixtureProbabilityDensityFunction {
+        Objects.requireNonNull(a);
+        Objects.requireNonNull(b);
+        weight = Math.clamp(weight, 0, 1);
+    }
+
+    @Override
+    public double value(@NotNull Vec3 direction) {
+        var v = a.value(direction);
+        var w = b.value(direction);
+        return Math.fma(weight, v, Math.fma(-weight, w, w));
+    }
+
+    @Override
+    public @NotNull Vec3 generate(@NotNull RandomGenerator random) {
+        if (random.nextDouble() < weight) {
+            return a.generate(random);
+        } else {
+            return b.generate(random);
+        }
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/renderer/pdf/ProbabilityDensityFunction.java

@@ -0,0 +1,25 @@
+package eu.jonahbauer.raytracing.render.renderer.pdf;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.random.RandomGenerator;
+
+/**
+ * A probability density function used for sampling random directions when scattering a ray.
+ */
+public interface ProbabilityDensityFunction {
+
+    /**
+     * {@return the value of this probability density function at the given point}
+     * @param direction the direction
+     */
+    double value(@NotNull Vec3 direction);
+
+    /**
+     * Generates a random direction based on this probability density function.
+     * @param random a random number generator
+     * @return the random direction
+     */
+    @NotNull Vec3 generate(@NotNull RandomGenerator random);
+}

src/main/java/eu/jonahbauer/raytracing/render/renderer/pdf/SphereProbabilityDensityFunction.java

@@ -0,0 +1,22 @@
+package eu.jonahbauer.raytracing.render.renderer.pdf;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.random.RandomGenerator;
+
+/**
+ * A probability density function sampling the sphere uniformly.
+ */
+public record SphereProbabilityDensityFunction() implements ProbabilityDensityFunction {
+
+    @Override
+    public double value(@NotNull Vec3 direction) {
+        return 1 / (4 * Math.PI);
+    }
+
+    @Override
+    public @NotNull Vec3 generate(@NotNull RandomGenerator random) {
+        return Vec3.random(random);
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/renderer/pdf/TargetingProbabilityDensityFunction.java

@@ -0,0 +1,41 @@
+package eu.jonahbauer.raytracing.render.renderer.pdf;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import eu.jonahbauer.raytracing.scene.Target;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.ArrayList;
+import java.util.List;
+import java.util.Objects;
+import java.util.random.RandomGenerator;
+
+/**
+ * A probability density function targeting a target.
+ * @see Target
+ */
+public final class TargetingProbabilityDensityFunction implements ProbabilityDensityFunction {
+    private final @NotNull Vec3 origin;
+    private final @NotNull List<@NotNull Target> targets;
+
+    public TargetingProbabilityDensityFunction(@NotNull Vec3 origin, @NotNull List<@NotNull Target> targets) {
+        this.origin = Objects.requireNonNull(origin, "origin");
+        this.targets = new ArrayList<>(targets);
+    }
+
+    @Override
+    public double value(@NotNull Vec3 direction) {
+        var weight = 1d / targets.size();
+        var sum = 0.0;
+
+        for (var target : targets) {
+            sum = Math.fma(weight, target.getProbabilityDensity(origin, direction), sum);
+        }
+
+        return sum;
+    }
+
+    @Override
+    public @NotNull Vec3 generate(@NotNull RandomGenerator random) {
+        return targets.get(random.nextInt(targets.size())).getTargetingDirection(origin, random);
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/texture/CheckerTexture.java

@@ -0,0 +1,21 @@
+package eu.jonahbauer.raytracing.render.texture;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import org.jetbrains.annotations.NotNull;
+
+public record CheckerTexture(double scale, @NotNull Texture even, @NotNull Texture odd) implements Texture {
+
+    @Override
+    public @NotNull Color get(double u, double v, @NotNull Vec3 p) {
+        var x = (int) Math.floor(p.x() / scale);
+        var y = (int) Math.floor(p.y() / scale);
+        var z = (int) Math.floor(p.z() / scale);
+        var even = (x + y + z) % 2 == 0;
+        return even ? even().get(u, v, p) : odd().get(u, v, p);
+    }
+
+    @Override
+    public boolean isUVRequired() {
+        return even.isUVRequired() || odd.isUVRequired();
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/texture/Color.java

@@ -1,10 +1,15 @@
-package eu.jonahbauer.raytracing.render;
+package eu.jonahbauer.raytracing.render.texture;
 
+import eu.jonahbauer.raytracing.math.Ray;
+import eu.jonahbauer.raytracing.math.Vec3;
+import eu.jonahbauer.raytracing.scene.SkyBox;
 import org.jetbrains.annotations.NotNull;
 
 import java.util.Random;
 
-public record Color(double r, double g, double b) {
+import static eu.jonahbauer.raytracing.Main.DEBUG;
+
+public record Color(double r, double g, double b) implements Texture, SkyBox {
     public static final @NotNull Color BLACK = new Color(0.0, 0.0, 0.0);
     public static final @NotNull Color WHITE = new Color(1.0, 1.0, 1.0);
     public static final @NotNull Color RED = new Color(1.0, 0.0, 0.0);
@@ -25,6 +30,10 @@ public record Color(double r, double g, double b) {
         return new Color(a.r() * b.r(), a.g() * b.g(), a.b() * b.b());
     }
 
+    public static @NotNull Color multiply(@NotNull Color a, double b) {
+        return new Color(a.r() * b, a.g() * b, a.b() * b);
+    }
+
     public static @NotNull Color add(@NotNull Color a, @NotNull Color b) {
         return new Color(a.r() + b.r(), a.g() + b.g(), a.b() + b.b());
     }
@@ -43,10 +52,11 @@ public record Color(double r, double g, double b) {
     }
 
     public static @NotNull Color average(@NotNull Color current, @NotNull Color next, int index) {
+        var factor = 1d / index;
         return new Color(
-                current.r() + (next.r() - current.r()) / index,
+                Math.fma(factor, next.r() - current.r(), current.r()),
-                current.g() + (next.g() - current.g()) / index,
+                Math.fma(factor, next.g() - current.g(), current.g()),
-                current.b() + (next.b() - current.b()) / index
+                Math.fma(factor, next.b() - current.b(), current.b())
         );
     }
 
@@ -68,12 +78,25 @@ public record Color(double r, double g, double b) {
         }
     }
 
-    public Color {}
+    public Color(int rgb) {
+        this((rgb >> 16) & 0xFF, (rgb >> 8) & 0xFF, rgb & 0xFF);
+    }
     
     public Color(int red, int green, int blue) {
         this(red / 255f, green / 255f, blue / 255f);
     }
 
+    public Color {
+        if (DEBUG) {
+            if (!Double.isFinite(r) || !Double.isFinite(g) || !Double.isFinite(b)) {
+                throw new IllegalArgumentException("r, g and b must be finite");
+            }
+            if (r < 0 || g < 0 || b < 0) {
+                throw new IllegalArgumentException("r, g and b must be non-negative");
+            }
+        }
+    }
+
     public int red() {
         return toInt(r);
     }
@@ -86,7 +109,22 @@ public record Color(double r, double g, double b) {
         return toInt(b);
     }
 
+    @Override
+    public @NotNull Color get(double u, double v, @NotNull Vec3 p) {
+        return this;
+    }
+
+    @Override
+    public @NotNull Color getColor(@NotNull Ray ray) {
+        return this;
+    }
+
+    @Override
+    public boolean isUVRequired() {
+        return false;
+    }
+
     private static int toInt(double value) {
-        return Math.max(0, Math.min(255, (int) (255.99 * value)));
+        return Math.clamp((int) (255.99 * value), 0, 255);
     }
 }

src/main/java/eu/jonahbauer/raytracing/render/texture/ImageTexture.java

@@ -0,0 +1,43 @@
+package eu.jonahbauer.raytracing.render.texture;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import eu.jonahbauer.raytracing.render.canvas.Image;
+import org.jetbrains.annotations.NotNull;
+
+import javax.imageio.ImageIO;
+import java.awt.image.BufferedImage;
+import java.io.IOException;
+import java.io.UncheckedIOException;
+import java.util.Objects;
+
+public record ImageTexture(@NotNull Image image) implements Texture {
+
+    public ImageTexture {
+        Objects.requireNonNull(image, "image");
+    }
+
+    public ImageTexture(@NotNull BufferedImage image) {
+        this(new Image(image));
+    }
+
+    public ImageTexture(@NotNull String path) {
+        this(read(path));
+    }
+
+    private static @NotNull BufferedImage read(@NotNull String path) {
+        try (var in = Objects.requireNonNull(ImageTexture.class.getResourceAsStream(path))) {
+            return ImageIO.read(in);
+        } catch (IOException ex) {
+            throw new UncheckedIOException(ex);
+        }
+    }
+
+    @Override
+    public @NotNull Color get(double u, double v, @NotNull Vec3 p) {
+        u = Math.clamp(u, 0, 1);
+        v = 1 - Math.clamp(v, 0, 1);
+        int x = (int) (u * (image.getWidth() - 1));
+        int y = (int) (v * (image.getHeight() - 1));
+        return image.get(x, y);
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/texture/PerlinTexture.java

@@ -0,0 +1,152 @@
+package eu.jonahbauer.raytracing.render.texture;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.Objects;
+import java.util.Random;
+import java.util.function.DoubleFunction;
+import java.util.random.RandomGenerator;
+
+public final class PerlinTexture implements Texture {
+    private static final int POINT_COUNT = 256;
+    private static final @NotNull Random RANDOM = new Random();
+    private static final @NotNull DoubleFunction<Color> GREYSCALE = t -> new Color(t, t, t);
+
+    private final double scale;
+    private final int turbulence;
+    private final @NotNull DoubleFunction<Color> color;
+
+    private final int mask;
+    private final Vec3[] randvec;
+    private final int[] permX;
+    private final int[] permY;
+    private final int[] permZ;
+
+    public PerlinTexture() {
+        this(1.0);
+    }
+
+    public PerlinTexture(double scale) {
+        this(scale, 7);
+    }
+
+    public PerlinTexture(double scale, int turbulence) {
+        this(scale, turbulence, GREYSCALE);
+    }
+
+    public PerlinTexture(double scale, int turbulence, @NotNull DoubleFunction<Color> color) {
+        this(scale, turbulence, color, POINT_COUNT, RANDOM);
+    }
+
+    public PerlinTexture(
+            double scale, int turbulence, @NotNull DoubleFunction<Color> color,
+            int count, @NotNull RandomGenerator random
+    ) {
+        if ((count & (count - 1)) != 0) throw new IllegalArgumentException("count must be a power of two");
+        if (turbulence <= 0) throw new IllegalArgumentException("turbulence must be positive");
+
+        this.scale = scale;
+        this.turbulence = turbulence;
+        this.color = Objects.requireNonNull(color, "color");
+
+        this.mask = count - 1;
+        this.randvec = new Vec3[count];
+        for (int i = 0; i < count; i++) {
+            this.randvec[i] = Vec3.random(random);
+        }
+        this.permX = generatePerm(count, random);
+        this.permY = generatePerm(count, random);
+        this.permZ = generatePerm(count, random);
+    }
+
+    private static int @NotNull[] generatePerm(int count, @NotNull RandomGenerator random) {
+        int[] p = new int[count];
+        for (int i = 0; i < count; i++) {
+            p[i] = i;
+        }
+        permutate(p, random);
+        return p;
+    }
+
+    private static void permutate(int @NotNull[] p, @NotNull RandomGenerator random) {
+        for (int i = p.length - 1; i > 0; i--) {
+            int target = random.nextInt(i);
+            int tmp = p[i];
+            p[i] = p[target];
+            p[target] = tmp;
+        }
+    }
+
+    public double getNoise(@NotNull Vec3 p) {
+        var x = p.x() * scale;
+        var y = p.y() * scale;
+        var z = p.z() * scale;
+
+        var u = x - Math.floor(x);
+        var v = y - Math.floor(y);
+        var w = z - Math.floor(z);
+
+        int i = (int) Math.floor(x);
+        int j = (int) Math.floor(y);
+        int k = (int) Math.floor(z);
+
+        var c = new Vec3[8];
+        for (int di = 0; di < 2; di++) {
+            for (int dj = 0; dj < 2; dj++) {
+                for (int dk = 0; dk < 2; dk++) {
+                    c[di << 2 | dj << 1 | dk] = randvec[permX[(i + di) & mask] ^ permY[(j + dj) & mask] ^ permZ[(k + dk) & mask]];
+                }
+            }
+        }
+
+        return interpolate(c, u, v, w);
+    }
+
+    public double getNoise(@NotNull Vec3 p, int depth) {
+        var accum = 0.0;
+        var temp = p;
+        var weight = 1.0;
+
+        for (int i = 0; i < depth; i++) {
+            accum = Math.fma(weight, getNoise(temp), accum);
+            weight *= 0.5;
+            temp = temp.times(2);
+        }
+
+        return accum;
+    }
+
+    @Override
+    public @NotNull Color get(double u, double v, @NotNull Vec3 p) {
+        var noise = getNoise(p, turbulence);
+        var t = Math.fma(0.5, Math.sin(Math.PI * noise), 0.5);
+        return color.apply(t);
+    }
+
+    private static double interpolate(Vec3[] c, double u, double v, double w) {
+        var uu = u * u * Math.fma(-2, u, 3);
+        var vv = v * v * Math.fma(-2, v, 3);
+        var ww = w * w * Math.fma(-2, w, 3);
+
+        var accum = 0.0;
+        for (int i = 0; i < 2; i++) {
+            for (int j = 0; j < 2; j++) {
+                for (int k = 0; k < 2; k++) {
+                    var vec = c[i << 2 | j << 1 | k];
+                    var dot = (u - i) * vec.x() + (v - j) * vec.y() + (w - k) * vec.z();
+                    accum += Math.fma(i, uu, (1 - i) * (1 - uu))
+                             * Math.fma(j, vv, (1 - j) * (1 - vv))
+                             * Math.fma(k, ww, (1 - k) * (1 - ww))
+                             * dot;
+                }
+            }
+        }
+        return accum;
+    }
+
+    @Override
+    public boolean isUVRequired() {
+        return false;
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/texture/Texture.java

@@ -0,0 +1,32 @@
+package eu.jonahbauer.raytracing.render.texture;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import eu.jonahbauer.raytracing.scene.HitResult;
+import org.jetbrains.annotations.NotNull;
+
+public interface Texture {
+    /**
+     * {@return the color of <code>this</code> texture for a hit}
+     */
+    default @NotNull Color get(@NotNull HitResult hit) {
+        return get(hit.u(), hit.v(), hit.position());
+    }
+
+    /**
+     * {@return the color of <code>this</code> texture at the specified position}
+     * @param u the texture u coordinate
+     * @param v the texture v coordinate
+     * @param p the position
+     */
+    @NotNull Color get(double u, double v, @NotNull Vec3 p);
+
+    /**
+     * Returns whether {@link #get(double, double, Vec3)} uses the {@code u} and/or {@code v} parameters.
+     * When a texture indicates that the {@code u} and {@code v} coordinates are not required, the calculation may be
+     * skipped and {@link Double#NaN} will be passed.
+     * @return whether {@link #get(double, double, Vec3)} uses the {@code u} and/or {@code v} parameters
+     */
+    default boolean isUVRequired() {
+        return true;
+    }
+}

src/main/java/eu/jonahbauer/raytracing/scene/HitResult.java

@@ -1,23 +1,38 @@
 package eu.jonahbauer.raytracing.scene;
 
+import eu.jonahbauer.raytracing.math.Range;
+import eu.jonahbauer.raytracing.math.Ray;
 import eu.jonahbauer.raytracing.math.Vec3;
 import eu.jonahbauer.raytracing.render.material.Material;
+import eu.jonahbauer.raytracing.render.texture.Texture;
 import org.jetbrains.annotations.NotNull;
 
 import java.util.Objects;
 
+/**
+ * The result of a {@linkplain Hittable#hit(Ray, Range) hit}.
+ * @param t the {@code t} value at which the hit occurs
+ * @param position the position of the hit
+ * @param normal the surface normal at the hit position
+ * @param target the hit target (for debug purposes only)
+ * @param material the material of the surface
+ * @param u the texture u coordinate (or {@code Double.NaN} if the {@linkplain Material#texture() material's texture} does {@linkplain Texture#isUVRequired() not depend} on the uv-coordinates)
+ * @param v the texture v coordinate (or {@code Double.NaN} if the {@linkplain Material#texture() material's texture} does {@linkplain Texture#isUVRequired() not depend} on the uv-coordinates)
+ * @param isFrontFace whether the front or the back of the surface was it
+ */
 public record HitResult(
-        double t,
+        double t, @NotNull Vec3 position, @NotNull Vec3 normal, @NotNull Hittable target,
-        @NotNull Vec3 position,
+        @NotNull Material material, double u, double v, boolean isFrontFace
-        @NotNull Vec3 normal,
-        @NotNull Material material,
-        boolean frontFace
 ) implements Comparable<HitResult> {
     public HitResult {
         Objects.requireNonNull(position, "position");
         normal = normal.unit();
     }
 
+    public @NotNull HitResult withPositionAndNormal(@NotNull Vec3 position, @NotNull Vec3 normal) {
+        return new HitResult(t, position, normal, target, material, u, v, isFrontFace);
+    }
+
     @Override
     public int compareTo(@NotNull HitResult o) {
         return Double.compare(t, o.t);

src/main/java/eu/jonahbauer/raytracing/scene/Hittable.java

@@ -11,21 +11,38 @@ import org.jetbrains.annotations.NotNull;
 import java.util.Optional;
 
 public interface Hittable {
+    @NotNull Range FORWARD = new Range(0.001, Double.POSITIVE_INFINITY);
 
     /**
-     * {@return the value <code>t</code> such that <code>ray.at(t)</code> is the intersection of this shaped closest to
+     * @see #hit(Ray, Range)
-     * the ray origin, or <code>Double.NaN</code> if the ray does not intersect this shape}
+     */
+    default @NotNull Optional<HitResult> hit(@NotNull Ray ray) {
+        return hit(ray, FORWARD);
+    }
+
+    /**
+     * Tests whether the {@code ray} intersects {@code this} hittable.
+     * <p>
+     * The second parameter {@code range} allows the implementation to skip unnecessary calculations if it can
+     * determine that a hit (if any) will fall outside the valid range of {@code t}s. The returned hit may still be
+     * outside the valid range and has to be checked by the caller.
      * @param ray a ray
+     * @param range the range of valid {@code t}s
+     * @return the result of the hit test, containing (among others) the value {@code t} such that {@code ray.at(t)} is
+     *         a point on {@code this} hittable
      */
     @NotNull Optional<HitResult> hit(@NotNull Ray ray, @NotNull Range range);
 
+    /**
+     * {@return the axis-aligned bounding box of this hittable}
+     */
     @NotNull AABB getBoundingBox();
 
     default @NotNull Hittable translate(@NotNull Vec3 offset) {
-        return new Translate(this, offset);
+        return Translate.create(this, offset);
     }
 
     default @NotNull Hittable rotateY(double angle) {
-        return new RotateY(this, angle);
+        return RotateY.create(this, angle);
     }
 }

src/main/java/eu/jonahbauer/raytracing/scene/Scene.java

@@ -2,11 +2,13 @@ package eu.jonahbauer.raytracing.scene;
 
 import eu.jonahbauer.raytracing.math.AABB;
 import eu.jonahbauer.raytracing.math.Ray;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Color;
 import eu.jonahbauer.raytracing.scene.util.HittableBinaryTree;
 import eu.jonahbauer.raytracing.scene.util.HittableCollection;
 import org.jetbrains.annotations.NotNull;
+import org.jetbrains.annotations.Nullable;
 
+import java.util.ArrayList;
 import java.util.List;
 import java.util.Objects;
 
@@ -14,29 +16,28 @@ public final class Scene extends HittableCollection {
     private final @NotNull HittableCollection objects;
     private final @NotNull SkyBox background;
 
+    private final @Nullable List<@NotNull Target> targets;
+
     public Scene(@NotNull List<? extends @NotNull Hittable> objects) {
-        this(Color.BLACK, objects);
+        this(objects, null);
     }
 
-    public Scene(@NotNull Color background, @NotNull List<? extends @NotNull Hittable> objects) {
+    public Scene(@NotNull List<? extends @NotNull Hittable> objects, @Nullable List<? extends @NotNull Target> targets) {
-        this(SkyBox.solid(background), objects);
+        this(Color.BLACK, objects, targets);
     }
 
     public Scene(@NotNull SkyBox background, @NotNull List<? extends @NotNull Hittable> objects) {
-        this.objects = new HittableBinaryTree(objects);
+        this(background, objects, null);
+    }
+
+    public Scene(@NotNull SkyBox background, @NotNull List<? extends @NotNull Hittable> objects, @Nullable List<? extends @NotNull Target> targets) {
+        var list = new ArrayList<Hittable>(objects.size() + (targets != null ? targets.size() : 0));
+        list.addAll(objects);
+        if (targets != null) list.addAll(targets);
+        this.objects = new HittableBinaryTree(list);
         this.background = Objects.requireNonNull(background);
-    }
 
-    public Scene(@NotNull Hittable @NotNull... objects) {
+        this.targets = targets != null ? List.copyOf(targets) : null;
-        this(List.of(objects));
-    }
-
-    public Scene(@NotNull Color background, @NotNull Hittable @NotNull... objects) {
-        this(background, List.of(objects));
-    }
-
-    public Scene(@NotNull SkyBox background, @NotNull Hittable @NotNull... objects) {
-        this(background, List.of(objects));
     }
 
     @Override
@@ -49,6 +50,10 @@ public final class Scene extends HittableCollection {
         return objects.getBoundingBox();
     }
 
+    public @Nullable List<@NotNull Target> getTargets() {
+        return targets;
+    }
+
     public @NotNull Color getBackgroundColor(@NotNull Ray ray) {
         return background.getColor(ray);
     }

src/main/java/eu/jonahbauer/raytracing/scene/SkyBox.java

@@ -1,7 +1,7 @@
 package eu.jonahbauer.raytracing.scene;
 
 import eu.jonahbauer.raytracing.math.Ray;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Color;
 import org.jetbrains.annotations.NotNull;
 
 @FunctionalInterface
@@ -18,8 +18,4 @@ public interface SkyBox {
             return Color.lerp(bottom, top, alt / Math.PI + 0.5);
         };
     }
-
-    static @NotNull SkyBox solid(@NotNull Color color) {
-        return _ -> color;
-    }
 }

src/main/java/eu/jonahbauer/raytracing/scene/Target.java

@@ -0,0 +1,39 @@
+package eu.jonahbauer.raytracing.scene;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import eu.jonahbauer.raytracing.render.renderer.pdf.TargetingProbabilityDensityFunction;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.random.RandomGenerator;
+
+/**
+ * An interface for objects that can be targeted. A target can construct randomly distributed directions in which
+ * it will be hit from a given origin.
+ * @see TargetingProbabilityDensityFunction
+ */
+public interface Target extends Hittable {
+    /**
+     * Returns the probability density for a direction as sampled by {@link #getTargetingDirection(Vec3, RandomGenerator)}.
+     * @param origin the origin
+     * @param direction the direction
+     * @return the probability density for a direction as sampled by {@link #getTargetingDirection(Vec3, RandomGenerator)}
+     */
+    double getProbabilityDensity(@NotNull Vec3 origin, @NotNull Vec3 direction);
+
+    /**
+     * {@return a vector targeting this hittable from the <code>origin</code>} The vector is chosen randomly.
+     * @param origin the origin
+     * @param random a random number generator
+     */
+    @NotNull Vec3 getTargetingDirection(@NotNull Vec3 origin, @NotNull RandomGenerator random);
+
+    @Override
+    default @NotNull Target translate(@NotNull Vec3 offset) {
+        return (Target) Hittable.super.translate(offset);
+    }
+
+    @Override
+    default @NotNull Target rotateY(double angle) {
+        return (Target) Hittable.super.rotateY(angle);
+    }
+}

src/main/java/eu/jonahbauer/raytracing/scene/hittable2d/Hittable2D.java

@@ -51,8 +51,41 @@ public abstract class Hittable2D implements Hittable {
         if (!isInterior(alpha, beta)) return Optional.empty();
 
         var frontFace = denominator < 0;
-        return Optional.of(new HitResult(t, position, frontFace ? normal : normal.neg(), material, frontFace));
+        return Optional.of(new HitResult(
+                t, position, frontFace ? normal : normal.neg(), this,
+                material, alpha, beta, frontFace
+        ));
+    }
+
+    protected double hit0(@NotNull Ray ray, @NotNull Range range) {
+        var denominator = ray.direction().times(normal);
+        if (Math.abs(denominator) < 1e-8) return Double.NaN; // parallel
+
+        var t = (d - ray.origin().times(normal)) / denominator;
+        if (!range.surrounds(t)) return Double.NaN;
+
+        var position = ray.at(t);
+        var p = position.minus(origin);
+
+        var alpha = Vec3.tripleProduct(w, p, v);
+        var beta = Vec3.tripleProduct(w, u, p);
+        if (!isInterior(alpha, beta)) return Double.NaN;
+
+        return t;
+    }
+
+    protected @NotNull Vec3 get(double alpha, double beta) {
+        return new Vec3(
+                Math.fma(beta, v.x(), Math.fma(alpha, u.x(), origin.x())),
+                Math.fma(beta, v.y(), Math.fma(alpha, u.y(), origin.y())),
+                Math.fma(beta, v.z(), Math.fma(alpha, u.z(), origin.z()))
+        );
     }
 
     protected abstract boolean isInterior(double alpha, double beta);
+
+    @Override
+    public @NotNull String toString() {
+        return this.getClass().getSimpleName() + "(origin=" + origin + ", u=" + u + ", v=" + v + ")";
+    }
 }

src/main/java/eu/jonahbauer/raytracing/scene/hittable2d/Parallelogram.java

@@ -1,11 +1,16 @@
 package eu.jonahbauer.raytracing.scene.hittable2d;
 
 import eu.jonahbauer.raytracing.math.AABB;
+import eu.jonahbauer.raytracing.math.Ray;
 import eu.jonahbauer.raytracing.math.Vec3;
 import eu.jonahbauer.raytracing.render.material.Material;
+import eu.jonahbauer.raytracing.scene.Target;
+import eu.jonahbauer.raytracing.scene.util.PdfUtil;
 import org.jetbrains.annotations.NotNull;
 
-public final class Parallelogram extends Hittable2D {
+import java.util.random.RandomGenerator;
+
+public final class Parallelogram extends Hittable2D implements Target {
     private final @NotNull AABB bbox;
 
     public Parallelogram(@NotNull Vec3 origin, @NotNull Vec3 u, @NotNull Vec3 v, @NotNull Material material) {
@@ -22,4 +27,24 @@ public final class Parallelogram extends Hittable2D {
     public @NotNull AABB getBoundingBox() {
         return bbox;
     }
+
+    @Override
+    public double getProbabilityDensity(@NotNull Vec3 origin, @NotNull Vec3 direction) {
+        if (Double.isNaN(hit0(new Ray(origin, direction), FORWARD))) return 0;
+
+        var o = this.origin.minus(origin);
+        var a = o.unit();
+        var b = o.plus(u).unit();
+        var c = o.plus(v).unit();
+        var d = o.plus(u).plus(v).unit();
+        var angle = PdfUtil.getSolidAngle(a, b, d) + PdfUtil.getSolidAngle(c, b, d);
+        return 1 / angle;
+    }
+
+    @Override
+    public @NotNull Vec3 getTargetingDirection(@NotNull Vec3 origin, @NotNull RandomGenerator random) {
+        var alpha = random.nextDouble();
+        var beta = random.nextDouble();
+        return get(alpha, beta).minus(origin);
+    }
 }

src/main/java/eu/jonahbauer/raytracing/scene/hittable3d/Box.java

@@ -0,0 +1,304 @@
+package eu.jonahbauer.raytracing.scene.hittable3d;
+
+import eu.jonahbauer.raytracing.math.AABB;
+import eu.jonahbauer.raytracing.math.Range;
+import eu.jonahbauer.raytracing.math.Ray;
+import eu.jonahbauer.raytracing.math.Vec3;
+import eu.jonahbauer.raytracing.render.material.Material;
+import eu.jonahbauer.raytracing.scene.HitResult;
+import eu.jonahbauer.raytracing.scene.Hittable;
+import eu.jonahbauer.raytracing.scene.Target;
+import eu.jonahbauer.raytracing.scene.util.PdfUtil;
+import org.jetbrains.annotations.NotNull;
+import org.jetbrains.annotations.Nullable;
+
+import java.util.Objects;
+import java.util.Optional;
+import java.util.random.RandomGenerator;
+
+public final class Box implements Hittable, Target {
+    private final @NotNull AABB box;
+    private final @Nullable Material @NotNull[] materials;
+
+    public Box(@NotNull Vec3 a, @NotNull Vec3 b, @NotNull Material material) {
+        this(new AABB(a, b), material);
+    }
+
+    public Box(@NotNull AABB box, @NotNull Material material) {
+        this(box, Objects.requireNonNull(material, "material"), material, material, material, material, material);
+    }
+
+    public Box(
+            @NotNull Vec3 a, @NotNull Vec3 b,
+            @Nullable Material top, @Nullable Material bottom,
+            @Nullable Material left, @Nullable Material right,
+            @Nullable Material front, @Nullable Material back
+    ) {
+        this(new AABB(a, b), top, bottom, left, right, front, back);
+    }
+
+    public Box(
+            @NotNull AABB box,
+            @Nullable Material top, @Nullable Material bottom,
+            @Nullable Material left, @Nullable Material right,
+            @Nullable Material front, @Nullable Material back
+    ) {
+        this.box = Objects.requireNonNull(box, "box");
+        this.materials = new Material[] { left, bottom, back, right, top, front };
+    }
+
+    @Override
+    public @NotNull Optional<HitResult> hit(@NotNull Ray ray, @NotNull Range range) {
+        // based on AABB#hit with additional detection of the side hit
+        var origin = ray.origin();
+        var direction = ray.direction();
+        var invDirection = direction.inv();
+
+        var tmin = AABB.intersect(box.min(), origin, invDirection);
+        var tmax = AABB.intersect(box.max(), origin, invDirection);
+
+        double tlmax = Double.NEGATIVE_INFINITY;
+        double tumin = Double.POSITIVE_INFINITY;
+
+        Side entry = null;
+        Side exit = null;
+
+        for (int i = 0; i < 3; i++) {
+            if (direction.get(i) >= 0) {
+                if (tmin[i] > tlmax) {
+                    tlmax = tmin[i];
+                    entry = Side.NEGATIVE[i];
+                }
+                if (tmax[i] < tumin) {
+                    tumin = tmax[i];
+                    exit = Side.POSITIVE[i];
+                }
+            } else {
+                if (tmax[i] > tlmax) {
+                    tlmax = tmax[i];
+                    entry = Side.POSITIVE[i];
+                }
+                if (tmin[i] < tumin) {
+                    tumin = tmin[i];
+                    exit = Side.NEGATIVE[i];
+                }
+            }
+        }
+
+        if (tlmax < tumin && tumin >= range.min() && tlmax <= range.max()) {
+            assert entry != null && exit != null;
+            return hit0(tlmax, tumin, entry, exit, ray, range);
+        } else {
+            return Optional.empty();
+        }
+    }
+
+    private @NotNull Optional<HitResult> hit0(double tmin, double tmax, @NotNull Side entry, @NotNull Side exit, @NotNull Ray ray, @NotNull Range range) {
+        double t;
+        Side side;
+        boolean frontFace;
+        Material material;
+        Vec3 normal;
+        if (range.surrounds(tmin) && materials[entry.ordinal()] != null) {
+            t = tmin;
+            side = entry;
+            frontFace = true;
+            material = materials[side.ordinal()];
+            normal = side.normal;
+        } else if (range.surrounds(tmax) && materials[exit.ordinal()] != null) {
+            t = tmax;
+            side = exit;
+            frontFace = false;
+            material = materials[side.ordinal()];
+            normal = side.normal.neg();
+        } else {
+            return Optional.empty();
+        }
+
+        var position = ray.at(t);
+        var uv = material.texture().isUVRequired();
+        var u = uv ? side.getTextureU(box, position) : Double.NaN;
+        var v = uv ? side.getTextureV(box, position) : Double.NaN;
+        return Optional.of(new HitResult(t, position, normal, this, material, u, v, frontFace));
+    }
+
+    @Override
+    public @NotNull AABB getBoundingBox() {
+        return box;
+    }
+
+    @Override
+    public double getProbabilityDensity(@NotNull Vec3 origin, @NotNull Vec3 direction) {
+        if (contains(origin)) return 1 / (4 * Math.PI);
+        if (hit(new Ray(origin, direction)).isEmpty()) return 0;
+
+        var solidAngle = 0d;
+        for (var s : Side.values()) {
+            if (!s.isExterior(box, origin)) continue;
+            solidAngle += s.getSolidAngle(box, origin);
+        }
+
+        return 1 / solidAngle;
+    }
+
+    @Override
+    public @NotNull Vec3 getTargetingDirection(@NotNull Vec3 origin, @NotNull RandomGenerator random) {
+        if (contains(origin)) return Vec3.random(random);
+
+        // determine sides facing the origin and their solid angles
+        int visible = 0;
+
+        // at most three faces are visible
+        Side[] sides = new Side[3];
+        double[] solidAngle = new double[3];
+
+        double accumSolidAngle = 0;
+        for (var s : Side.values()) {
+            if (!s.isExterior(box, origin)) continue;
+
+            var sa = s.getSolidAngle(box, origin);
+            accumSolidAngle += sa;
+            sides[visible] = s;
+            solidAngle[visible] = accumSolidAngle;
+            visible++;
+        }
+
+        // choose a random side facing the origin based on their relative solid angles
+        var r = random.nextDouble() * solidAngle[visible - 1];
+        for (int j = 0; j < visible; j++) {
+            if (r < solidAngle[j]) {
+                // choose a random point on that side
+                var target = sides[j].random(box, random);
+                return target.minus(origin);
+            }
+        }
+
+        throw new AssertionError();
+    }
+
+    private boolean contains(@NotNull Vec3 point) {
+        return box.min().x() < point.x() && point.x() < box.max().x()
+               && box.min().y() < point.y() && point.y() < box.max().y()
+               && box.min().z() < point.z() && point.z() < box.max().z();
+    }
+
+    @Override
+    public @NotNull String toString() {
+        return "Box(min=" + box.min() + ", max=" + box.max() + ")";
+    }
+
+    private enum Side {
+        NEG_X(Vec3.UNIT_X.neg()),
+        NEG_Y(Vec3.UNIT_Y.neg()),
+        NEG_Z(Vec3.UNIT_Z.neg()),
+        POS_X(Vec3.UNIT_X),
+        POS_Y(Vec3.UNIT_Y),
+        POS_Z(Vec3.UNIT_Z),
+        ;
+
+        private static final Side[] NEGATIVE = new Side[] {Side.NEG_X, Side.NEG_Y, Side.NEG_Z};
+        private static final Side[] POSITIVE = new Side[] {Side.POS_X, Side.POS_Y, Side.POS_Z};
+
+        private final @NotNull Vec3 normal;
+
+        Side(@NotNull Vec3 normal) {
+            this.normal = Objects.requireNonNull(normal, "normal");
+        }
+
+        /**
+         * {@return the texture u coordinate for a position on this side of the box}
+         */
+        public double getTextureU(@NotNull AABB box, @NotNull Vec3 pos) {
+            return switch (this) {
+                case NEG_X -> (pos.z() - box.min().z()) / (box.max().z() - box.min().z());
+                case POS_X -> (box.max().z() - pos.z()) / (box.max().z() - box.min().z());
+                case NEG_Y, POS_Y, POS_Z -> (pos.x() - box.min().x()) / (box.max().x() - box.min().x());
+                case NEG_Z -> (box.max().x() - pos.x()) / (box.max().x() - box.min().x());
+            };
+        }
+
+        /**
+         * {@return the texture v coordinate for a position on this side of the box}
+         */
+        public double getTextureV(@NotNull AABB box, @NotNull Vec3 pos) {
+            return switch (this) {
+                case NEG_X, POS_X, NEG_Z, POS_Z -> (pos.y() - box.min().y()) / (box.max().y() - box.min().y());
+                case NEG_Y -> (pos.z() - box.min().z()) / (box.max().z() - box.min().z());
+                case POS_Y -> (box.max().z() - pos.z()) / (box.max().z() - box.min().z());
+            };
+        }
+
+        /**
+         * {@return whether the given position is outside of the box only considering <code>this</code> side}
+         */
+        public boolean isExterior(@NotNull AABB box, @NotNull Vec3 pos) {
+            return switch (this) {
+                case NEG_X -> pos.x() < box.min().x();
+                case NEG_Y -> pos.y() < box.min().y();
+                case NEG_Z -> pos.z() < box.min().z();
+                case POS_X -> pos.x() > box.max().x();
+                case POS_Y -> pos.y() > box.max().y();
+                case POS_Z -> pos.z() > box.max().z();
+            };
+        }
+
+        /**
+         * {@return the point on <code>this</code> side of the <code>box</code> with the given <code>u</code>-<code>v</code>-coordinates}
+         */
+        public @NotNull Vec3 get(@NotNull AABB box, double u, double v) {
+            return switch (this) {
+                case NEG_X -> new Vec3(
+                        box.min().x(),
+                        Math.fma(v, box.max().y() - box.min().y(), box.min().y()),
+                        Math.fma(u, box.max().z() - box.min().z(), box.min().z())
+                );
+                case NEG_Y -> new Vec3(
+                        Math.fma(u, box.max().x() - box.min().x(), box.min().x()),
+                        box.min().y(),
+                        Math.fma(v, box.max().z() - box.min().z(), box.min().z())
+                );
+                case NEG_Z -> new Vec3(
+                        Math.fma(u, box.min().x() - box.max().x(), box.max().x()),
+                        Math.fma(v, box.max().y() - box.min().y(), box.min().y()),
+                        box.min().z()
+                );
+                case POS_X -> new Vec3(
+                        box.max().x(),
+                        Math.fma(v, box.max().y() - box.min().y(), box.min().y()),
+                        Math.fma(u, box.min().z() - box.max().z(), box.max().z())
+                );
+                case POS_Y -> new Vec3(
+                        Math.fma(u, box.max().x() - box.min().x(), box.min().x()),
+                        box.max().y(),
+                        Math.fma(v, box.min().z() - box.max().z(), box.max().z())
+                );
+                case POS_Z -> new Vec3(
+                        Math.fma(u, box.max().x() - box.min().x(), box.min().x()),
+                        Math.fma(v, box.max().y() - box.min().y(), box.min().y()),
+                        box.max().z()
+                );
+            };
+        }
+
+        /**
+         * {@return a random point on <code>this</code> side of the <code>box</code>}
+         */
+        public @NotNull Vec3 random(@NotNull AABB box, @NotNull RandomGenerator random) {
+            var u = random.nextDouble();
+            var v = random.nextDouble();
+            return get(box, u, v);
+        }
+
+        /**
+         * {@return the solid angle covered by <code>this</code> side of the <code>box</code> when viewed from <code>pos</code>}
+         */
+        public double getSolidAngle(@NotNull AABB box, @NotNull Vec3 pos) {
+            var a = get(box, 0, 0).minus(pos).unit();
+            var b = get(box, 0, 1).minus(pos).unit();
+            var c = get(box, 1, 1).minus(pos).unit();
+            var d = get(box, 1, 0).minus(pos).unit();
+
+            return PdfUtil.getSolidAngle(a, b, d) + PdfUtil.getSolidAngle(c, b, d);
+        }
+    }
+}

src/main/java/eu/jonahbauer/raytracing/scene/hittable3d/ConstantMedium.java

@@ -32,7 +32,7 @@ public record ConstantMedium(@NotNull Hittable boundary, double density, @NotNul
         if (hitDistance > distance) return Optional.empty();
 
         var t = tmin + hitDistance / length;
-        return Optional.of(new HitResult(t, ray.at(t), Vec3.UNIT_X, material, true)); // arbitrary normal and frontFace
+        return Optional.of(new HitResult(t, ray.at(t), Vec3.UNIT_X, this, material, 0, 0, true)); // arbitrary normal, u, v and isFrontFace
     }
 
     @Override

src/main/java/eu/jonahbauer/raytracing/scene/hittable3d/Sphere.java

@@ -7,24 +7,32 @@ import eu.jonahbauer.raytracing.math.Ray;
 import eu.jonahbauer.raytracing.math.Vec3;
 import eu.jonahbauer.raytracing.scene.HitResult;
 import eu.jonahbauer.raytracing.scene.Hittable;
+import eu.jonahbauer.raytracing.scene.Target;
 import org.jetbrains.annotations.NotNull;
 
 import java.util.Objects;
 import java.util.Optional;
+import java.util.random.RandomGenerator;
 
-public final class Sphere implements Hittable {
+public final class Sphere implements Hittable, Target {
     private final @NotNull Vec3 center;
     private final double radius;
     private final @NotNull Material material;
 
     private final @NotNull AABB bbox;
 
+    private final @NotNull Vec3 normalizedCenter;
+    private final double invRadius;
+
     public Sphere(@NotNull Vec3 center, double radius, @NotNull Material material) {
         this.center = Objects.requireNonNull(center, "center");
         this.material = Objects.requireNonNull(material, "material");
         if (radius <= 0 || !Double.isFinite(radius)) throw new IllegalArgumentException("radius must be positive");
         this.radius = radius;
 
+        this.invRadius = 1 / radius;
+        this.normalizedCenter = this.center.times(-this.invRadius);
+
         this.bbox = new AABB(
                 center.minus(radius, radius, radius),
                 center.plus(radius, radius, radius)
@@ -33,6 +41,32 @@ public final class Sphere implements Hittable {
 
     @Override
     public @NotNull Optional<HitResult> hit(@NotNull Ray ray, @NotNull Range range) {
+        var t = hit0(ray, range);
+        if (Double.isNaN(t)) return Optional.empty();
+
+        var position = ray.at(t);
+        var normal = Vec3.fma(invRadius, position, normalizedCenter);
+        var frontFace = normal.times(ray.direction()) < 0;
+
+        double u;
+        double v;
+        if (material.texture().isUVRequired()) {
+            var theta = Math.acos(-normal.y());
+            var phi = Math.atan2(-normal.z(), normal.x()) + Math.PI;
+            u = phi / (2 * Math.PI);
+            v = theta / Math.PI;
+        } else {
+            u = Double.NaN;
+            v = Double.NaN;
+        }
+
+        return Optional.of(new HitResult(
+                t, position, frontFace ? normal : normal.neg(), this,
+                material, u, v, frontFace
+        ));
+    }
+
+    private double hit0(@NotNull Ray ray, @NotNull Range range) {
         var oc = ray.origin().minus(center);
 
         var a = ray.direction().squared();
@@ -40,22 +74,44 @@ public final class Sphere implements Hittable {
         var c = oc.squared() - radius * radius;
 
         var discriminant = h * h - a * c;
-        if (discriminant < 0) return Optional.empty();
+        if (discriminant < 0) return Double.NaN;
 
         var sd = Math.sqrt(discriminant);
 
         double t = (- h - sd) / a;
         if (!range.surrounds(t)) t = (- h + sd) / a;
-        if (!range.surrounds(t)) return Optional.empty();
+        if (!range.surrounds(t)) return Double.NaN;
 
-        var position = ray.at(t);
+        return t;
-        var normal = position.minus(center);
-        var frontFace = normal.times(ray.direction()) < 0;
-        return Optional.of(new HitResult(t, position, frontFace ? normal : normal.times(-1), material, frontFace));
     }
 
     @Override
     public @NotNull AABB getBoundingBox() {
         return bbox;
     }
+
+    @Override
+    public double getProbabilityDensity(@NotNull Vec3 origin, @NotNull Vec3 direction) {
+        if (Double.isNaN(hit0(new Ray(origin, direction), FORWARD))) return 0;
+
+        var cos = Math.sqrt(1 - radius * radius / (center.minus(origin).squared()));
+        var solidAngle = 2 * Math.PI * (1 - cos);
+        return 1 / solidAngle;
+    }
+
+    @Override
+    public @NotNull Vec3 getTargetingDirection(@NotNull Vec3 origin, @NotNull RandomGenerator random) {
+        var direction = center.minus(origin);
+        var out = Vec3.randomOppositeHemisphere(random, direction);
+        return new Vec3(
+                Math.fma(radius, out.x(), center.x() - origin.x()),
+                Math.fma(radius, out.y(), center.y() - origin.y()),
+                Math.fma(radius, out.z(), center.z() - origin.z())
+        );
+    }
+
+    @Override
+    public @NotNull String toString() {
+        return "Sphere(center=" + center + ", radius=" + radius + ")";
+    }
 }

src/main/java/eu/jonahbauer/raytracing/scene/transform/RotateY.java

@@ -5,15 +5,26 @@ import eu.jonahbauer.raytracing.math.Ray;
 import eu.jonahbauer.raytracing.math.Vec3;
 import eu.jonahbauer.raytracing.scene.HitResult;
 import eu.jonahbauer.raytracing.scene.Hittable;
+import eu.jonahbauer.raytracing.scene.Target;
 import org.jetbrains.annotations.NotNull;
 
-public final class RotateY extends Transform {
+import java.util.random.RandomGenerator;
+
+public sealed class RotateY extends Transform {
     private final double cos;
     private final double sin;
 
     private final @NotNull AABB bbox;
 
-    public RotateY(@NotNull Hittable object, double angle) {
+    public static @NotNull RotateY create(@NotNull Hittable object, double angle) {
+        if (object instanceof Target) {
+            return new RotateYTarget(object, angle);
+        } else {
+            return new RotateY(object, angle);
+        }
+    }
+
+    private RotateY(@NotNull Hittable object, double angle) {
         super(object);
         this.cos = Math.cos(angle);
         this.sin = Math.sin(angle);
@@ -45,45 +56,58 @@ public final class RotateY extends Transform {
     }
 
     @Override
-    protected @NotNull Ray transform(@NotNull Ray ray) {
+    protected final @NotNull Ray transform(@NotNull Ray ray) {
         var origin = ray.origin();
         var direction = ray.direction();
 
-        var newOrigin = new Vec3(
+        var newOrigin = transform(origin);
-                cos * origin.x() - sin * origin.z(),
+        var newDirection = transform(direction);
-                origin.y(),
-                sin * origin.x() + cos * origin.z()
-        );
-        var newDirection = new Vec3(
-                cos * direction.x() - sin * direction.z(),
-                direction.y(),
-                sin * direction.x() + cos * direction.z()
-        );
-
         return new Ray(newOrigin, newDirection);
     }
 
     @Override
-    protected @NotNull HitResult transform(@NotNull HitResult result) {
+    protected final @NotNull HitResult transform(@NotNull HitResult result) {
         var position = result.position();
-        var newPosition = new Vec3(
+        var newPosition = untransform(position);
-                cos * position.x() + sin * position.z(),
-                position.y(),
-                - sin * position.x() + cos * position.z()
-        );
 
         var normal = result.normal();
-        var newNormal = new Vec3(
+        var newNormal = untransform(normal);
-                cos * normal.x() + sin * normal.z(),
-                normal.y(),
-                -sin * normal.x() + cos * normal.z()
-        );
 
-        return new HitResult(result.t(), newPosition, newNormal, result.material(), result.frontFace());
+        return result.withPositionAndNormal(newPosition, newNormal);
+    }
+
+    protected final @NotNull Vec3 transform(@NotNull Vec3 vec) {
+        return new Vec3(cos * vec.x() - sin * vec.z(), vec.y(), sin * vec.x() + cos * vec.z());
+    }
+
+    protected final @NotNull Vec3 untransform(@NotNull Vec3 vec) {
+        return new Vec3(cos * vec.x() + sin * vec.z(), vec.y(), - sin * vec.x() + cos * vec.z());
     }
 
     @Override
     public @NotNull AABB getBoundingBox() {
         return bbox;
     }
+
+    @Override
+    public @NotNull String toString() {
+        return object + " rotated by " + Math.toDegrees(Math.atan2(sin, cos)) + "° around the y axis";
+    }
+
+    private static final class RotateYTarget extends RotateY implements Target {
+
+        private RotateYTarget(@NotNull Hittable object, double angle) {
+            super(object, angle);
+        }
+
+        @Override
+        public double getProbabilityDensity(@NotNull Vec3 origin, @NotNull Vec3 direction) {
+            return ((Target) object).getProbabilityDensity(transform(origin), transform(direction));
+        }
+
+        @Override
+        public @NotNull Vec3 getTargetingDirection(@NotNull Vec3 origin, @NotNull RandomGenerator random) {
+            return untransform(((Target) object).getTargetingDirection(transform(origin), random));
+        }
+    }
 }

src/main/java/eu/jonahbauer/raytracing/scene/transform/Transform.java

@@ -2,12 +2,15 @@ package eu.jonahbauer.raytracing.scene.transform;
 
 import eu.jonahbauer.raytracing.math.Range;
 import eu.jonahbauer.raytracing.math.Ray;
+import eu.jonahbauer.raytracing.math.Vec3;
 import eu.jonahbauer.raytracing.scene.HitResult;
 import eu.jonahbauer.raytracing.scene.Hittable;
+import eu.jonahbauer.raytracing.scene.Target;
 import org.jetbrains.annotations.NotNull;
 
 import java.util.Objects;
 import java.util.Optional;
+import java.util.random.RandomGenerator;
 
 public abstract class Transform implements Hittable {
     protected final @NotNull Hittable object;

src/main/java/eu/jonahbauer/raytracing/scene/transform/Translate.java

@@ -5,13 +5,24 @@ import eu.jonahbauer.raytracing.math.Ray;
 import eu.jonahbauer.raytracing.math.Vec3;
 import eu.jonahbauer.raytracing.scene.HitResult;
 import eu.jonahbauer.raytracing.scene.Hittable;
+import eu.jonahbauer.raytracing.scene.Target;
 import org.jetbrains.annotations.NotNull;
 
-public final class Translate extends Transform {
+import java.util.random.RandomGenerator;
-    private final @NotNull Vec3 offset;
+
+public sealed class Translate extends Transform {
+    protected final @NotNull Vec3 offset;
     private final @NotNull AABB bbox;
 
-    public Translate(@NotNull Hittable object, @NotNull Vec3 offset) {
+    public static @NotNull Translate create(@NotNull Hittable object, @NotNull Vec3 offset) {
+        if (object instanceof Target) {
+            return new TranslateTarget(object, offset);
+        } else {
+            return new Translate(object, offset);
+        }
+    }
+
+    private Translate(@NotNull Hittable object, @NotNull Vec3 offset) {
         super(object);
         this.offset = offset;
 
@@ -23,23 +34,40 @@ public final class Translate extends Transform {
     }
 
     @Override
-    protected @NotNull Ray transform(@NotNull Ray ray) {
+    protected final @NotNull Ray transform(@NotNull Ray ray) {
         return new Ray(ray.origin().minus(offset), ray.direction());
     }
 
     @Override
-    protected @NotNull HitResult transform(@NotNull HitResult result) {
+    protected final @NotNull HitResult transform(@NotNull HitResult result) {
-        return new HitResult(
+        return result.withPositionAndNormal(result.position().plus(offset), result.normal());
-                result.t(),
-                result.position().plus(offset),
-                result.normal(),
-                result.material(),
-                result.frontFace()
-        );
     }
 
     @Override
-    public @NotNull AABB getBoundingBox() {
+    public final @NotNull AABB getBoundingBox() {
         return bbox;
     }
+
+    @Override
+    public @NotNull String toString() {
+        return object + " translated by " + offset;
+    }
+
+    private static final class TranslateTarget extends Translate implements Target {
+        private TranslateTarget(@NotNull Hittable object, @NotNull Vec3 offset) {
+            super(object, offset);
+        }
+
+        @Override
+        public double getProbabilityDensity(@NotNull Vec3 origin, @NotNull Vec3 direction) {
+            if (!(object instanceof Target target)) throw new UnsupportedOperationException();
+            return target.getProbabilityDensity(origin.minus(offset), direction);
+        }
+
+        @Override
+        public @NotNull Vec3 getTargetingDirection(@NotNull Vec3 origin, @NotNull RandomGenerator random) {
+            if (!(object instanceof Target target)) throw new UnsupportedOperationException();
+            return target.getTargetingDirection(origin.minus(offset), random);
+        }
+    }
 }

src/main/java/eu/jonahbauer/raytracing/scene/util/HittableBinaryTree.java

@@ -47,7 +47,7 @@ public final class HittableBinaryTree extends HittableCollection {
 
     @Override
     public void hit(@NotNull Ray ray, @NotNull State state) {
-        if (!bbox.hit(ray)) return;
+        if (!bbox.hit(ray, state.getRange())) return;
         if (left instanceof HittableCollection coll) {
             coll.hit(ray, state);
         } else if (left != null) {

src/main/java/eu/jonahbauer/raytracing/scene/util/HittableCollection.java

@@ -41,6 +41,10 @@ public abstract class HittableCollection implements Hittable {
             this.range = Objects.requireNonNull(range);
         }
 
+        public @NotNull Range getRange() {
+            return range;
+        }
+
         private @NotNull Optional<HitResult> getResult() {
             return Optional.ofNullable(result);
         }

src/main/java/eu/jonahbauer/raytracing/scene/util/HittableOctree.java

@@ -1,253 +0,0 @@
-package eu.jonahbauer.raytracing.scene.util;
-
-import eu.jonahbauer.raytracing.math.AABB;
-import eu.jonahbauer.raytracing.math.Range;
-import eu.jonahbauer.raytracing.math.Ray;
-import eu.jonahbauer.raytracing.math.Vec3;
-import eu.jonahbauer.raytracing.scene.Hittable;
-import org.jetbrains.annotations.NotNull;
-import org.jetbrains.annotations.Nullable;
-
-import java.util.*;
-import java.util.function.Predicate;
-import java.util.stream.IntStream;
-
-public final class HittableOctree extends HittableCollection {
-    private static final int LIST_SIZE_LIMIT = 16;
-
-    private final @Nullable Storage storage;
-    private final @NotNull AABB bbox;
-
-    public HittableOctree(@NotNull List<? extends @NotNull Hittable> objects) {
-        bbox = AABB.getBoundingBox(objects).orElse(AABB.EMPTY);
-        storage = newStorage(bbox, objects);
-    }
-
-    private static @NotNull AABB[] getBoundingBoxes(@NotNull AABB aabb, @NotNull Vec3 center) {
-        return new AABB[] {
-                new AABB(new Range(aabb.x().min(), center.x()), new Range(aabb.y().min(), center.y()), new Range(aabb.z().min(), center.z())),
-                new AABB(new Range(center.x(), aabb.x().max()), new Range(aabb.y().min(), center.y()), new Range(aabb.z().min(), center.z())),
-                new AABB(new Range(aabb.x().min(), center.x()), new Range(center.y(), aabb.y().max()), new Range(aabb.z().min(), center.z())),
-                new AABB(new Range(center.x(), aabb.x().max()), new Range(center.y(), aabb.y().max()), new Range(aabb.z().min(), center.z())),
-                new AABB(new Range(aabb.x().min(), center.x()), new Range(aabb.y().min(), center.y()), new Range(center.z(), aabb.z().max())),
-                new AABB(new Range(center.x(), aabb.x().max()), new Range(aabb.y().min(), center.y()), new Range(center.z(), aabb.z().max())),
-                new AABB(new Range(aabb.x().min(), center.x()), new Range(center.y(), aabb.y().max()), new Range(center.z(), aabb.z().max())),
-                new AABB(new Range(center.x(), aabb.x().max()), new Range(center.y(), aabb.y().max()), new Range(center.z(), aabb.z().max())),
-        };
-    }
-
-    private static @Nullable Storage newStorage(@NotNull AABB aabb, @NotNull List<? extends @NotNull Hittable> objects) {
-        if (objects.isEmpty()) return null;
-        if (objects.size() < LIST_SIZE_LIMIT) {
-            return new ListStorage(aabb, objects);
-        } else {
-            var center = aabb.center();
-            var octants = (List<Hittable>[]) new List<?>[8];
-            for (int i = 0; i < 8; i++) octants[i] = new ArrayList<>();
-            var bboxes = getBoundingBoxes(aabb, center);
-            var list = new ArrayList<Hittable>();
-
-            for (var object : objects) {
-                var bbox = object.getBoundingBox();
-                var imin = getOctantIndex(center, bbox.min());
-                var imax = getOctantIndex(center, bbox.max());
-                if (imin == imax) {
-                    octants[imin].add(object);
-                } else {
-                    list.add(object);
-                }
-            }
-
-            return new NodeStorage(aabb, center, list, IntStream.range(0, 8).mapToObj(i -> newStorage(bboxes[i], octants[i])).toArray(Storage[]::new));
-        }
-    }
-
-    @Override
-    public void hit(@NotNull Ray ray, @NotNull State state) {
-        hit(ray, object -> hit(state, ray, object));
-    }
-
-    @Override
-    public @NotNull AABB getBoundingBox() {
-        return bbox;
-    }
-
-    /**
-     * Use HERO algorithms to find all elements that could possibly be hit by the given ray.
-     * @see <a href="https://doi.org/10.1007/978-3-642-76298-7_3">
-     *      Agate, M., Grimsdale, R.L., Lister, P.F. (1991).
-     *      The HERO Algorithm for Ray-Tracing Octrees.
-     *      In: Grimsdale, R.L., Straßer, W. (eds) Advances in Computer Graphics Hardware IV. Eurographic Seminars. Springer, Berlin, Heidelberg.</a>
-     */
-    private void hit(@NotNull Ray ray, @NotNull Predicate<? super Hittable> action) {
-        if (storage != null) storage.hit(ray, action);
-    }
-
-    private static int getOctantIndex(@NotNull Vec3 center, @NotNull Vec3 pos) {
-        return (pos.x() < center.x() ? 0 : 1)
-               | (pos.y() < center.y() ? 0 : 2)
-               | (pos.z() < center.z() ? 0 : 4);
-
-    }
-
-    private abstract static sealed class Storage {
-        protected final @NotNull AABB bbox;
-
-        public Storage(@NotNull AABB bbox) {
-            this.bbox = Objects.requireNonNull(bbox);
-        }
-
-        protected boolean hit(@NotNull Ray ray, @NotNull Predicate<? super Hittable> action) {
-            var range = bbox.intersect(ray);
-            if (range.isEmpty()) return false;
-
-            int vmask = ray.vmask();
-            return hit0(ray, vmask, range.get().min(), range.get().max(), action);
-        }
-
-        protected abstract boolean hit0(@NotNull Ray ray, int vmask, double tmin, double tmax, @NotNull Predicate<? super Hittable> action);
-    }
-
-    private static final class ListStorage extends Storage {
-        private final @NotNull List<Hittable> list;
-
-        public ListStorage(@NotNull AABB bbox, @NotNull List<? extends @NotNull Hittable> entries) {
-            super(bbox);
-            this.list = List.copyOf(entries);
-        }
-
-        @Override
-        protected boolean hit0(@NotNull Ray ray, int vmask, double tmin, double tmax, @NotNull Predicate<? super Hittable> action) {
-            var hit = false;
-            for (Hittable hittable : list) {
-                hit |= action.test(hittable);
-            }
-            return hit;
-        }
-    }
-
-    private static final class NodeStorage extends Storage {
-        private final @Nullable Storage @NotNull[] octants;
-        private final @NotNull Vec3 center;
-        private final int degenerate;
-
-        private final @NotNull List<Hittable> list; // track elements spanning multiple octants separately
-
-        public NodeStorage(@NotNull AABB bbox, @NotNull Vec3 center, @NotNull List<? extends @NotNull Hittable> list, @Nullable Storage @NotNull[] octants) {
-            super(bbox);
-            this.octants = octants;
-            this.center = center;
-
-            this.list = List.copyOf(list);
-
-            int count = 0;
-            int degenerate = 0;
-            for (int i = 0; i < octants.length; i++) {
-                if (octants[i] != null) {
-                    count++;
-                    degenerate = i;
-                }
-            }
-            this.degenerate = count == 1 ? degenerate : -1;
-        }
-
-        @Override
-        protected boolean hit(@NotNull Ray ray, @NotNull Predicate<? super Hittable> action) {
-            if (degenerate >= 0 && list.isEmpty()) {
-                return octants[degenerate].hit(ray, action);
-            } else {
-                return super.hit(ray, action);
-            }
-        }
-
-        @Override
-        protected boolean hit0(@NotNull Ray ray, int vmask, double tmin, double tmax, @NotNull Predicate<? super Hittable> action) {
-            if (tmax < 0) return false;
-
-            // check for hit
-            var hit = false;
-
-            // process entries spanning multiple children
-            for (Hittable object : list) {
-                hit |= action.test(object);
-            }
-
-            // t values for intersection points of ray with planes through center
-            var tmid = AABB.intersect(center, ray);
-            // masks of planes in the order of intersection, e.g. [2, 1, 4] for a ray intersection y = center.y() then x = center.x() then z = center.z()
-            var masklist = calculateMasklist(tmid);
-            // the first child to be hit by the ray assuming a ray with positive x, y and z coordinates
-            var childmask = (tmid[0] < tmin ? 1 : 0)
-                            | (tmid[1] < tmin ? 2 : 0)
-                            | (tmid[2] < tmin ? 4 : 0);
-            // the last child to be hit by the ray assuming a ray with positive x, y and z coordinates
-            var lastmask = (tmid[0] < tmax ? 1 : 0)
-                           | (tmid[1] < tmax ? 2 : 0)
-                           | (tmid[2] < tmax ? 4 : 0);
-
-            var childTmin = tmin;
-
-            int i = 0;
-            while (true) {
-                // use vmask to nullify the assumption of a positive ray made for childmask
-                var child = octants[childmask ^ vmask];
-
-                // calculate t value for exit of child
-                double childTmax;
-                if (childmask == lastmask) {
-                    // last child shares tmax
-                    childTmax = tmax;
-                } else {
-                    // determine next child
-                    while ((masklist[i] & childmask) != 0) {
-                        i++;
-                    }
-                    childmask = childmask | masklist[i];
-                    // tmax of current child is the t value for the intersection with the plane dividing the current and next child
-                    childTmax = tmid[Integer.numberOfTrailingZeros(masklist[i])];
-                }
-
-                // process child
-                var childHit = child != null && child.hit0(ray, vmask, childTmin, childTmax, action);
-                hit |= childHit;
-
-                // break after last child has been processed or a hit has been found
-                if (childTmax == tmax || childHit) break;
-
-                // tmin of next child is tmax of current child
-                childTmin = childTmax;
-            }
-
-            return hit;
-        }
-
-        private static final int[][] MASKLISTS = new int[][] {
-                {1, 2, 4},
-                {1, 4, 2},
-                {4, 1, 2},
-                {2, 1, 4},
-                {2, 4, 1},
-                {4, 2, 1}
-        };
-
-        private static int @NotNull [] calculateMasklist(double @NotNull[] tmid) {
-            if (tmid[0] < tmid[1]) {
-                if (tmid[1] < tmid[2]) {
-                    return MASKLISTS[0]; // {1, 2, 4}
-                } else if (tmid[0] < tmid[2]) {
-                    return MASKLISTS[1]; // {1, 4, 2}
-                } else {
-                    return MASKLISTS[2]; // {4, 1, 2}
-                }
-            } else {
-                if (tmid[0] < tmid[2]) {
-                    return MASKLISTS[3]; // {2, 1, 4}
-                } else if (tmid[1] < tmid[2]) {
-                    return MASKLISTS[4]; // {2, 4, 1}
-                } else {
-                    return MASKLISTS[5]; // {4, 2, 1}
-                }
-            }
-        }
-    }
-}

src/main/java/eu/jonahbauer/raytracing/scene/util/Hittables.java

@@ -1,35 +0,0 @@
-package eu.jonahbauer.raytracing.scene.util;
-
-import eu.jonahbauer.raytracing.math.Vec3;
-import eu.jonahbauer.raytracing.render.material.Material;
-import eu.jonahbauer.raytracing.scene.Hittable;
-import eu.jonahbauer.raytracing.scene.hittable2d.Parallelogram;
-import org.jetbrains.annotations.NotNull;
-
-import java.util.ArrayList;
-
-public final class Hittables {
-    private Hittables() {
-        throw new UnsupportedOperationException();
-    }
-
-    public static @NotNull Hittable box(@NotNull Vec3 a, @NotNull Vec3 b, @NotNull Material material) {
-        var sides = new ArrayList<Hittable>();
-
-        var min = Vec3.min(a, b);
-        var max = Vec3.max(a, b);
-
-        var dx = new Vec3(max.x() - min.x(), 0, 0);
-        var dy = new Vec3(0, max.y() - min.y(), 0);
-        var dz = new Vec3(0, 0, max.z() - min.z());
-
-        sides.add(new Parallelogram(new Vec3(min.x(), min.y(), max.z()), dx, dy, material)); // front
-        sides.add(new Parallelogram(new Vec3(max.x(), min.y(), max.z()), dz.neg(), dy, material)); // right
-        sides.add(new Parallelogram(new Vec3(max.x(), min.y(), min.z()), dx.neg(), dy, material)); // back
-        sides.add(new Parallelogram(new Vec3(min.x(), min.y(), min.z()), dz, dy, material)); // left
-        sides.add(new Parallelogram(new Vec3(min.x(), max.y(), max.z()), dx, dz.neg(), material)); // top
-        sides.add(new Parallelogram(new Vec3(min.x(), min.y(), min.z()), dx, dz, material)); // bottom
-
-        return new HittableList(sides);
-    }
-}

src/main/java/eu/jonahbauer/raytracing/scene/util/PdfUtil.java

@@ -0,0 +1,19 @@
+package eu.jonahbauer.raytracing.scene.util;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import org.jetbrains.annotations.NotNull;
+
+public final class PdfUtil {
+    private PdfUtil() {
+        throw new UnsupportedOperationException();
+    }
+
+    /**
+     * {@return the solid angle of the triangle abc as seen from the origin} The vectors {@code a}, {@code b} and {@code c}
+     * must be unit vectors.
+     */
+    public static double getSolidAngle(@NotNull Vec3 a, @NotNull Vec3 b, @NotNull Vec3 c) {
+        var angle = 2 * Math.atan(Math.abs(Vec3.tripleProduct(a, b, c)) / (1 + a.times(b) + b.times(c) + c.times(a)));
+        return angle < 0 ? 2 * Math.PI + angle : angle;
+    }
+}

src/test/java/eu/jonahbauer/raytracing/render/canvas/ImageTest.java

@@ -1,6 +1,6 @@
 package eu.jonahbauer.raytracing.render.canvas;
 
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Color;
 import eu.jonahbauer.raytracing.render.ImageFormat;
 import org.junit.jupiter.api.Test;
 import org.junit.jupiter.api.io.TempDir;

src/test/java/eu/jonahbauer/raytracing/scene/hittable3d/SphereTest.java

@@ -3,7 +3,7 @@ package eu.jonahbauer.raytracing.scene.hittable3d;
 import eu.jonahbauer.raytracing.math.Range;
 import eu.jonahbauer.raytracing.math.Ray;
 import eu.jonahbauer.raytracing.math.Vec3;
-import eu.jonahbauer.raytracing.render.Color;
+import eu.jonahbauer.raytracing.render.texture.Color;
 import eu.jonahbauer.raytracing.render.material.LambertianMaterial;
 import org.junit.jupiter.api.Test;