add total internal reflection

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

@@ -17,7 +17,7 @@ public class Main {
         var scene = new Scene(
                 new Sphere(0, -100.5, 1, 100, new LambertianMaterial(new Color(0.8, 0.8, 0.0))),
                 new Sphere(0, 0, 1.2, 0.5, new LambertianMaterial(new Color(0.1, 0.2, 0.5))),
-                new Sphere(-1, 0, 1, 0.5, new DielectricMaterial(1.5)),
+                new Sphere(-1, 0, 1, 0.5, new DielectricMaterial(0.75)),
                 new Sphere(1, 0, 1, 0.5, new MetallicMaterial(new Color(0.8, 0.6, 0.2), 1.0))
         );
         var camera = new Camera(512, 2, 16 / 9d);

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

@@ -12,7 +12,21 @@ public record DielectricMaterial(double refractionIndex) implements Material {
     @Override
     public @NotNull Optional<ScatterResult> scatter(@NotNull Ray ray, @NotNull HitResult hit) {
         var ri = hit.frontFace() ? (1 / refractionIndex) : refractionIndex;
-        var refracted = Vec3.refract(ray.direction(), hit.normal(), ri);
+
-        return Optional.of(new ScatterResult(new Ray(hit.position(), refracted), Color.WHITE));
+        var cosTheta = Math.min(- ray.direction().unit().times(hit.normal()), 1.0);
+        var reflectance = reflectance(cosTheta);
+        var reflect = reflectance > Math.random();
+
+        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), Color.WHITE));
+    }
+
+    private double reflectance(double cos) {
+        // use schlick's approximation for reflectance
+        var r0 = (1 - refractionIndex) / (1 + refractionIndex);
+        r0 = r0 * r0;
+        return r0 + (1 - r0) * (1 - cos) * (1 - cos) * (1 - cos) * (1 - cos) * (1 - cos);
     }
 }

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

@@ -2,6 +2,8 @@ package eu.jonahbauer.raytracing.math;
 
 import org.jetbrains.annotations.NotNull;
 
+import java.util.Optional;
+
 public record Vec3(double x, double y, double z) {
     public static final Vec3 ZERO = new Vec3(0, 0, 0);
     public static final Vec3 UNIT_X = new Vec3(1, 0, 0);
@@ -31,12 +33,15 @@ public record Vec3(double x, double y, double z) {
         return vec.minus(normal.times(2 * normal.times(vec)));
     }
 
-    public static @NotNull Vec3 refract(@NotNull Vec3 vec, @NotNull Vec3 normal, double index) {
+    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);
-        var rOutPerp = vec.plus(normal.times(cosTheta)).times(index);
+        var sinTheta = Math.sqrt(1 - cosTheta * cosTheta);
+        if (ri * sinTheta > 1) return Optional.empty();
+
+        var rOutPerp = vec.plus(normal.times(cosTheta)).times(ri);
         var rOutParallel = normal.times(- Math.sqrt(Math.abs(1 - rOutPerp.squared())));
-        return rOutPerp.plus(rOutParallel);
+        return Optional.of(rOutPerp.plus(rOutParallel));
     }
 
     public @NotNull Vec3 plus(@NotNull Vec3 b) {