wip

https://pbr-book.org/4ed/Radiometry,_Spectra,_and_Color/Color

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

@@ -1,6 +1,5 @@
 package eu.jonahbauer.raytracing;
 
-import eu.jonahbauer.raytracing.math.AABB;
 import eu.jonahbauer.raytracing.math.Vec3;
 import eu.jonahbauer.raytracing.render.texture.CheckerTexture;
 import eu.jonahbauer.raytracing.render.texture.Color;
@@ -293,7 +292,7 @@ public class Examples {
 
         return new Example(
                 new Scene(getSkyBox(), List.of(
-                        new Sphere(Vec3.ZERO, 2, new LambertianMaterial(new ImageTexture("/earthmap.jpg")))
+                        new Sphere(Vec3.ZERO, 2, new LambertianMaterial(new ImageTexture("/eu/jonahbauer/raytracing/textures/earthmap.jpg")))
                 )),
                 SimpleCamera.builder()
                         .withImage(height * 16 / 9, height)
@@ -369,7 +368,7 @@ public class Examples {
         ));
 
         // textures spheres
-        objects.add(new Sphere(new Vec3(400, 200, 400), 100, new LambertianMaterial(new ImageTexture("/earthmap.jpg"))));
+        objects.add(new Sphere(new Vec3(400, 200, 400), 100, new LambertianMaterial(new ImageTexture("/eu/jonahbauer/raytracing/textures/earthmap.jpg"))));
         objects.add(new Sphere(new Vec3(220, 280, 300), 80, new LambertianMaterial(new PerlinTexture(0.2))));
 
         // box from spheres

src/main/java/eu/jonahbauer/raytracing/math/Matrix3.java

@@ -0,0 +1,72 @@
+package eu.jonahbauer.raytracing.math;
+
+import org.jetbrains.annotations.NotNull;
+
+public record Matrix3(
+        double a11, double a12, double a13,
+        double a21, double a22, double a23,
+        double a31, double a32, double a33
+) {
+
+    public Matrix3() {
+        this(1, 1, 1);
+    }
+
+    public Matrix3(double a11, double a22, double a33) {
+        this(a11, 0, 0, 0, a22, 0, 0, 0, a33);
+    }
+
+    public @NotNull Matrix3 times(@NotNull Matrix3 other) {
+        return new Matrix3(
+                a11 * other.a11 + a12 * other.a21 + a13 * other.a31,
+                a11 * other.a12 + a12 * other.a22 + a13 * other.a32,
+                a11 * other.a13 + a12 * other.a23 + a13 * other.a33,
+                a21 * other.a11 + a22 * other.a21 + a23 * other.a31,
+                a21 * other.a12 + a22 * other.a22 + a23 * other.a32,
+                a21 * other.a13 + a22 * other.a23 + a23 * other.a33,
+                a31 * other.a11 + a32 * other.a21 + a33 * other.a31,
+                a31 * other.a12 + a32 * other.a22 + a33 * other.a32,
+                a31 * other.a13 + a32 * other.a23 + a33 * other.a33
+        );
+    }
+
+    public @NotNull Matrix3 times(double other) {
+        return new Matrix3(
+                a11 * other, a12 * other, a13 * other,
+                a21 * other, a22 * other, a23 * other,
+                a31 * other, a32 * other, a33 * other
+        );
+    }
+
+    public @NotNull Vec3 times(@NotNull Vec3 other) {
+        return new Vec3(
+                a11 * other.x() + a12 * other.y() + a13 * other.z(),
+                a21 * other.x() + a22 * other.y() + a23 * other.z(),
+                a31 * other.x() + a32 * other.y() + a33 * other.z()
+        );
+    }
+
+    public @NotNull Matrix3 plus(@NotNull Matrix3 other) {
+        return new Matrix3(
+                a11 + other.a11, a12 + other.a12, a13 + other.a13,
+                a21 + other.a21, a22 + other.a22, a23 + other.a23,
+                a31 + other.a31, a32 + other.a32, a33 + other.a33
+        );
+    }
+
+    public double det() {
+        return a11 * a22 * a33 + a12 * a23 * a31 + a13 * a21 * a32
+                - a13 * a22 * a31 - a23 * a32 * a11 - a33 * a12 * a21;
+    }
+
+    public @NotNull Matrix3 invert() {
+        var det = det();
+        if (det == 0) throw new IllegalStateException();
+        var t = 1 / det;
+        return new Matrix3(
+                t * (a22 * a33 - a23 * a32), t * (-a12 * a33 + a13 * a32), t * (a12 * a23 - a13 * a22),
+                t * (-a21 * a33 + a23 * a31), t * (a11 * a33 - a13 * a31), t * (-a11 * a23 + a13 * a21),
+                t * (a21 * a32 - a22 * a31), t * (a11 * a32 + a12 * a31), t * (a11 * a22 - a12 * a21)
+        );
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/SampledSpectrum.java

@@ -0,0 +1,76 @@
+package eu.jonahbauer.raytracing.render.spectral;
+
+import eu.jonahbauer.raytracing.render.spectral.colors.ColorSpace;
+import eu.jonahbauer.raytracing.render.spectral.colors.ColorXYZ;
+import eu.jonahbauer.raytracing.render.spectral.spectrum.Spectrum;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import org.jetbrains.annotations.NotNull;
+
+public final class SampledSpectrum {
+    private final double @NotNull[] values;
+
+
+    public static void main(String[] args) {
+        System.out.println();
+    }
+
+    public SampledSpectrum(@NotNull SampledWavelengths lambdas, @NotNull Spectrum spectrum) {
+        var values = new double[lambdas.size()];
+        for (int i = 0; i < values.length; i++) {
+            values[i] = spectrum.get(lambdas.get(i));
+        }
+        this.values = values;
+    }
+
+    private SampledSpectrum(double @NotNull[] values) {
+        this.values = values;
+    }
+
+    public static @NotNull SampledSpectrum multiply(@NotNull SampledSpectrum a, @NotNull SampledSpectrum b) {
+        var out = new double[a.values.length];
+        for (int i = 0; i < a.values.length; i++) {
+            out[i] = a.values[i] * b.values[i];
+        }
+        return new SampledSpectrum(out);
+    }
+
+    public static @NotNull SampledSpectrum multiply(@NotNull SampledSpectrum a, double b) {
+        var out = new double[a.values.length];
+        for (int i = 0; i < a.values.length; i++) {
+            out[i] = a.values[i] * b;
+        }
+        return new SampledSpectrum(out);
+    }
+
+    public static @NotNull SampledSpectrum add(@NotNull SampledSpectrum a, @NotNull SampledSpectrum b) {
+        var out = new double[a.values.length];
+        for (int i = 0; i < a.values.length; i++) {
+            out[i] = a.values[i] + b.values[i];
+        }
+        return new SampledSpectrum(out);
+    }
+
+    public double get(int index) {
+        return values[index];
+    }
+
+    public int size() {
+        return values.length;
+    }
+
+    public double average() {
+        double avg = 0;
+        for (int i = 0; i < values.length; i++) {
+            avg = Math.fma(1d / (i + 1), values[i] - avg, avg);
+        }
+        return avg;
+    }
+
+    public @NotNull ColorXYZ toXYZ(@NotNull SampledWavelengths lambdas) {
+        return lambdas.toXYZ(this);
+    }
+
+    public @NotNull Color toRGB(@NotNull SampledWavelengths lambdas, @NotNull ColorSpace cs) {
+        return cs.toRGB(toXYZ(lambdas));
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/SampledWavelengths.java

@@ -0,0 +1,91 @@
+package eu.jonahbauer.raytracing.render.spectral;
+
+import eu.jonahbauer.raytracing.render.spectral.colors.ColorXYZ;
+import eu.jonahbauer.raytracing.render.spectral.spectrum.Spectra;
+import eu.jonahbauer.raytracing.render.spectral.spectrum.Spectrum;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.Arrays;
+
+/**
+ * A set of sampled wavelength that can be tracked together.
+ */
+public final class SampledWavelengths {
+    private final double @NotNull[] lambdas;
+    private final double @NotNull[] pdf;
+
+    public static @NotNull SampledWavelengths uniform(double rng) {
+        return uniform(rng, Spectrum.LAMBDA_MIN, Spectrum.LAMBDA_MAX);
+    }
+
+    public static @NotNull SampledWavelengths uniform(double rng, double min, double max) {
+        var lambdas = new double[Spectrum.SAMPLES];
+
+        // choose first sample at random
+        lambdas[0] = (1 - rng) * min + rng * max;
+
+        // choose next samples in equal intervals, wrapping if necessary
+        var delta = (max - min) / Spectrum.SAMPLES;
+        for (int i = 1; i < Spectrum.SAMPLES; i++) {
+            lambdas[i] = lambdas[i - 1] + delta;
+            if (lambdas[i] > max) {
+                lambdas[i] = min + (lambdas[i] - max);
+            }
+        }
+
+        var pdf = new double[Spectrum.SAMPLES];
+        Arrays.fill(pdf, 1 / (max - min));
+        return new SampledWavelengths(lambdas, pdf);
+    }
+
+    private SampledWavelengths(double @NotNull[] lambdas, double @NotNull[] pdf) {
+        this.lambdas = lambdas;
+        this.pdf = pdf;
+    }
+
+    public double get(int index) {
+        return lambdas[index];
+    }
+
+    public int size() {
+        return lambdas.length;
+    }
+
+    /**
+     * Terminates the secondary wavelengths. This method should be called after a wavelength-dependent operation like
+     * refraction that makes it incorrect to track multiple wavelengths together.
+     */
+    public void terminateSecondary() {
+        if (pdf.length < 2 || pdf[1] == 0) return;
+        Arrays.fill(pdf, 1, pdf.length, 0d);
+        pdf[0] /= pdf.length;
+    }
+
+    @NotNull
+    ColorXYZ toXYZ(@NotNull SampledSpectrum spectrum) {
+        var x = Spectra.X.sample(this);
+        var y = Spectra.Y.sample(this);
+        var z = Spectra.Z.sample(this);
+
+        return new ColorXYZ(
+                toXYZ0(spectrum, x) / ColorXYZ.CIE_Y_INTEGRAL,
+                toXYZ0(spectrum, y) / ColorXYZ.CIE_Y_INTEGRAL,
+                toXYZ0(spectrum, z) / ColorXYZ.CIE_Y_INTEGRAL
+        );
+    }
+
+    private double toXYZ0(@NotNull SampledSpectrum spectrum, @NotNull SampledSpectrum cie) {
+        var avg = 0d;
+        for (int i = 0; i < spectrum.size(); i++) {
+            var pdf = this.pdf[i];
+            double value;
+            if (pdf == 0) {
+                value = 0;
+            } else {
+                value = spectrum.get(i) * cie.get(i) / pdf;
+            }
+            avg = Math.fma(1d / (i + 1), value - avg, avg);
+        }
+        return avg;
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/colors/Chromaticity.java

@@ -0,0 +1,4 @@
+package eu.jonahbauer.raytracing.render.spectral.colors;
+
+public record Chromaticity(double x, double y) {
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/colors/ColorSpace.java

@@ -0,0 +1,90 @@
+package eu.jonahbauer.raytracing.render.spectral.colors;
+
+import eu.jonahbauer.raytracing.math.Matrix3;
+import eu.jonahbauer.raytracing.render.spectral.spectrum.DenselySampledSpectrum;
+import eu.jonahbauer.raytracing.render.spectral.spectrum.Spectrum;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.NoSuchElementException;
+import java.util.Objects;
+
+/**
+ * An RGB color space.
+ */
+public final class ColorSpace {
+    private final @NotNull Chromaticity r;
+    private final @NotNull Chromaticity g;
+    private final @NotNull Chromaticity b;
+    private final @NotNull Chromaticity w;
+    private final @NotNull DenselySampledSpectrum illuminant;
+
+    private final @NotNull Matrix3 XYZfromRGB;
+    private final @NotNull Matrix3 RGBfromXYZ;
+    private final @NotNull SpectrumTable RGBtoSpectrumTable;
+
+    public ColorSpace(
+            @NotNull Chromaticity r, @NotNull Chromaticity g, @NotNull Chromaticity b,
+            @NotNull Spectrum illuminant, @NotNull SpectrumTable table
+    ) {
+        this.r = Objects.requireNonNull(r, "r");
+        this.g = Objects.requireNonNull(r, "g");
+        this.b = Objects.requireNonNull(r, "b");
+        this.illuminant = new DenselySampledSpectrum(illuminant);
+        this.RGBtoSpectrumTable = table;
+
+        var W = illuminant.toXYZ();
+        this.w = W.xy();
+
+        var R = new ColorXYZ(r);
+        var G = new ColorXYZ(g);
+        var B = new ColorXYZ(b);
+        var rgb = new Matrix3(
+                R.x(), G.x(), B.x(),
+                R.y(), G.y(), B.y(),
+                R.z(), G.z(), B.z()
+        );
+        var C = rgb.invert().times(W.toVec3());
+
+        this.XYZfromRGB = rgb.times(new Matrix3(C.x(), C.y(), C.z()));
+        this.RGBfromXYZ = XYZfromRGB.invert();
+    }
+
+    public @NotNull Color toRGB(@NotNull ColorXYZ xyz) {
+        var out = RGBfromXYZ.times(xyz.toVec3());
+        return new Color(out.x(), out.y(), out.z());
+    }
+
+    public @NotNull ColorXYZ toXYZ(@NotNull Color rgb) {
+        var out = XYZfromRGB.times(rgb.toVec3());
+        return new ColorXYZ(out);
+    }
+
+    public @NotNull SigmoidPolynomial toSpectrum(@NotNull Color rgb) {
+        return RGBtoSpectrumTable.get(new Color(
+                Math.max(0, rgb.r()),
+                Math.max(0, rgb.g()),
+                Math.max(0, rgb.b())
+        ));
+    }
+
+    public @NotNull Chromaticity r() {
+        return r;
+    }
+
+    public @NotNull Chromaticity g() {
+        return g;
+    }
+
+    public @NotNull Chromaticity b() {
+        return b;
+    }
+
+    public @NotNull Chromaticity w() {
+        return w;
+    }
+
+    public @NotNull DenselySampledSpectrum illuminant() {
+        return illuminant;
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/colors/ColorSpaces.java

@@ -0,0 +1,29 @@
+package eu.jonahbauer.raytracing.render.spectral.colors;
+
+import eu.jonahbauer.raytracing.render.spectral.spectrum.Spectra;
+import org.jetbrains.annotations.NotNull;
+
+public final class ColorSpaces {
+    public static final @NotNull ColorSpace sRGB = new ColorSpace(
+            new Chromaticity(0.6400, 0.3300),
+            new Chromaticity(0.3000, 0.6000),
+            new Chromaticity(0.1500, 0.0600),
+            Spectra.D65, null
+    );
+    public static final @NotNull ColorSpace DCI_P3 = new ColorSpace(
+            new Chromaticity(0.680, 0.320),
+            new Chromaticity(0.265, 0.690),
+            new Chromaticity(0.150, 0.060),
+            Spectra.D65, null
+    );
+    public static final @NotNull ColorSpace Rec2020 = new ColorSpace(
+            new Chromaticity(0.708, 0.292),
+            new Chromaticity(0.170, 0.797),
+            new Chromaticity(0.131, 0.046),
+            Spectra.D65, null
+    );
+
+    private ColorSpaces() {
+        throw new UnsupportedOperationException();
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/colors/ColorXYZ.java

@@ -0,0 +1,52 @@
+package eu.jonahbauer.raytracing.render.spectral.colors;
+
+import eu.jonahbauer.raytracing.math.Vec3;
+import org.jetbrains.annotations.NotNull;
+
+/**
+ * A CIE XYZ color
+ */
+public record ColorXYZ(double x, double y, double z) {
+    public static final double CIE_Y_INTEGRAL = 106.85689500000002;
+
+    public ColorXYZ(@NotNull Chromaticity chromaticity) {
+        this(chromaticity, 1);
+    }
+
+    public ColorXYZ(@NotNull Chromaticity chromaticity, double Y) {
+        this(
+                chromaticity.y() == 0 ? 0 : Y * chromaticity.x() / chromaticity.y(),
+                chromaticity.y() == 0 ? 0 : Y,
+                chromaticity.y() == 0 ? 0 : Y * (1 - chromaticity.x() - chromaticity.y()) / chromaticity.y()
+        );
+    }
+
+    public ColorXYZ(@NotNull Vec3 vec) {
+        this(vec.x(), vec.y(), vec.z());
+    }
+
+    public double average() {
+        return (x + y + z) / 3;
+    }
+
+    public @NotNull Chromaticity xy() {
+        var factor = 1 / (x + y + z);
+        return new Chromaticity(factor * x, factor * y);
+    }
+
+    public @NotNull Vec3 toVec3() {
+        return new Vec3(x, y, z);
+    }
+
+    public static @NotNull ColorXYZ multiply(@NotNull ColorXYZ a, @NotNull ColorXYZ b) {
+        return new ColorXYZ(a.x * b.x, a.y * b.y, a.z * b.z);
+    }
+
+    public static @NotNull ColorXYZ multiply(@NotNull ColorXYZ a, double b) {
+        return new ColorXYZ(a.x * b, a.y * b, a.z * b);
+    }
+
+    public static @NotNull ColorXYZ add(@NotNull ColorXYZ a, @NotNull ColorXYZ b) {
+        return new ColorXYZ(a.x + b.x, a.y + b.y, a.z + b.z);
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/colors/SigmoidPolynomial.java

@@ -0,0 +1,34 @@
+package eu.jonahbauer.raytracing.render.spectral.colors;
+
+import eu.jonahbauer.raytracing.render.spectral.spectrum.Spectrum;
+
+/**
+ * A function of the form {@code s(p(x))} where {@code p} is a polynomial of second degree and {@code s} is the sigmoid
+ * function <code>s(x) = 0.5 + x / (2 * sqrt(1 + x^2))</code>.
+ * <p>
+ * A function of this form is used to generate a {@link Spectrum} from an RGB value.
+ *
+ * @param c0 the coefficient of the quadratic term
+ * @param c1 the coefficient of the linear term
+ * @param c2 the coefficient of the constant term
+ */
+public record SigmoidPolynomial(double c0, double c1, double c2) {
+
+    public double get(double x) {
+        var p = Math.fma(x, Math.fma(x, c0, c1), c2);
+        if (!Double.isFinite(p)) return p > 0 ? 1 : 0;
+        return .5 + x / (p * Math.sqrt(1 + p * p));
+    }
+
+    public double max() {
+        // evaluate at the edges
+        var result = Math.max(get(Spectrum.LAMBDA_MIN), get(Spectrum.LAMBDA_MAX));
+        var lambda = -c1 / (2 * c0);
+        if (lambda >= 360 && lambda <= 830) {
+            // evaluate at the vertex
+            return Math.max(result, get(lambda));
+        } else {
+            return result;
+        }
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/colors/SpectrumTable.java

@@ -0,0 +1,91 @@
+package eu.jonahbauer.raytracing.render.spectral.colors;
+
+import eu.jonahbauer.raytracing.render.texture.Color;
+import org.jetbrains.annotations.NotNull;
+
+import java.util.Arrays;
+
+/**
+ * A table of sigmoid polynomials used to convert between RGB values and spectra.
+ * <p>
+ * The rgb values are renormalized to xyz coordinates with {@code z} being the largest of the rgb components, and
+ * {@code x} and {@code y} being the other two rgb components divided by {@code z}. By this construction, {@code x},
+ * {@code y} and {@code z} are all in the range [0, 1] which allows for better use of the samples in a fixed grid.
+ * The {@code z} coordinate is additionally remapped using {@link #zNodes} to improve sampling at both ends of the scale.
+ * <p>
+ * The coefficients of the sigmoid functions are stored in a five-dimensional array with indices as described in
+ * {@link #coefficients}.
+ */
+public final class SpectrumTable {
+    private static final int RESOLUTION = 64;
+
+    /**
+     * the remapped {@code z} values
+     */
+    private final double[] zNodes;
+
+    /**
+     * the stored coefficients, with the following indices
+     * <ol>
+     *     <li>the component index of the biggest rgb component</li>
+     *     <li>the {@code z} coordinate</li>
+     *     <li>the {@code y} coordinate</li>
+     *     <li>the {@code x} coordinate</li>
+     *     <li>the coefficient index</li>
+     * </ol>
+     */
+    private final double[][][][][] coefficients;
+
+    public SpectrumTable(double[] zNodes, double[][][][][] coefficients) {
+        this.zNodes = zNodes;
+        this.coefficients = coefficients;
+    }
+
+    public @NotNull SigmoidPolynomial get(@NotNull Color color) {
+        // handle uniform rgb values
+        if (color.r() == color.g() && color.g() == color.b()) {
+            return new SigmoidPolynomial(0, 0, (color.r() - .5) / Math.sqrt(color.r() * (1 - color.r())));
+        }
+
+        // find maximum component and compute remapped component values
+        var max = color.r() > color.g()
+                ? (color.r() > color.b() ? 0 : 2)
+                : (color.g() > color.b() ? 1 : 2);
+
+        var z = color.component(max);
+        var x = color.component((max + 1) % 3) * (RESOLUTION - 1) / z;
+        var y = color.component((max + 2) % 3) * (RESOLUTION - 1) / z;
+
+        // compute integer indices and offsets for coefficient interpolation
+        int xi = Math.min((int) x, RESOLUTION - 2);
+        int yi = Math.min((int) y, RESOLUTION - 2);
+        int zi = Arrays.binarySearch(zNodes, z);
+        if (zi < 0) zi = -zi - 1;
+        zi++;
+
+        var dx = x - xi;
+        var dy = y -yi;
+        var dz = (z - zNodes[zi]) / (zNodes[zi + 1] - zNodes[zi]);
+
+        // trilinearly interpolate sigmoid polynomial coefficients
+        var c = new double[3];
+        for (int i = 0; i < 3; i++) {
+            c[i] = lerp(dz,
+                        lerp(dy,
+                             lerp(dx, coefficients[max][zi + 0][yi + 0][xi + 0][i], coefficients[max][zi + 0][yi + 0][xi + 1][i]),
+                             lerp(dx, coefficients[max][zi + 0][yi + 1][xi + 0][i], coefficients[max][zi + 0][yi + 1][xi + 1][i])
+                        ),
+                        lerp(dy,
+                             lerp(dx, coefficients[max][zi + 1][yi + 0][xi + 0][i], coefficients[max][zi + 1][yi + 0][xi + 1][i]),
+                             lerp(dx, coefficients[max][zi + 1][yi + 1][xi + 0][i], coefficients[max][zi + 1][yi + 1][xi + 1][i])
+                        )
+            );
+        }
+
+        return new SigmoidPolynomial(c[0], c[1], c[2]);
+    }
+
+    private static double lerp(double t, double a, double b) {
+        return Math.fma(t, b, Math.fma(-t, a, a));
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/spectrum/BlackbodySpectrum.java

@@ -0,0 +1,45 @@
+package eu.jonahbauer.raytracing.render.spectral.spectrum;
+
+public final class BlackbodySpectrum implements Spectrum {
+    /**
+     * the speed of light in m/s
+     */
+    private static final double c = 299792458d;
+
+    /**
+     * the planck constant in m^2*kg/s
+     */
+    private static final double h = 6.62607015E-34;
+
+    /**
+     * the boltzmann constant in m^2*kg/s^2/K
+     */
+    private static final double k = 1.380649E-23;
+
+    /**
+     * wien's displacement constant in m*K
+     */
+    private static final double b = 2.897771995E-3;
+
+    private final double T;
+    private final double factor;
+
+    public BlackbodySpectrum(double T) {
+        if (T < 0) throw new IllegalArgumentException("T must be non-negative");
+        this.T = T;
+        this.factor = 1 / get(b / T);
+    }
+
+    @Override
+    public double max() {
+        return 1;
+    }
+
+    @Override
+    public double get(double lambda) {
+        lambda *= 1E-9;
+        var l2 = lambda * lambda;
+        var x = h * c / (lambda * k * T);
+        return 2 * h * c * c / (l2 * l2 * lambda) / (Math.exp(x) - 1) * factor;
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/spectrum/ConstantSpectrum.java

@@ -0,0 +1,17 @@
+package eu.jonahbauer.raytracing.render.spectral.spectrum;
+
+/**
+ * A constant spectrum.
+ * @param c the constant value
+ */
+public record ConstantSpectrum(double c) implements Spectrum {
+    @Override
+    public double max() {
+        return c;
+    }
+
+    @Override
+    public double get(double lambda) {
+        return c;
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/spectrum/DenselySampledSpectrum.java

@@ -0,0 +1,51 @@
+package eu.jonahbauer.raytracing.render.spectral.spectrum;
+
+import org.jetbrains.annotations.NotNull;
+
+import java.util.Arrays;
+
+/**
+ * A spectrum sampled in one nanometer intervals.
+ */
+public final class DenselySampledSpectrum implements Spectrum {
+    private final double[] samples;
+    private final int min;
+
+    private final double max;
+
+    public DenselySampledSpectrum(@NotNull Spectrum spectrum) {
+        this(spectrum, LAMBDA_MIN, LAMBDA_MAX);
+    }
+
+    public DenselySampledSpectrum(@NotNull Spectrum spectrum, int min, int max) {
+        if (max - min + 1 <= 0) throw new IllegalArgumentException("samples must not be empty");
+        this.samples = new double[max - min + 1];
+        var maxValue = 0d;
+        for (int lambda = min; lambda <= max; lambda++) {
+            var sample = spectrum.get(lambda);
+            if (sample > maxValue) maxValue = sample;
+            this.samples[lambda] = sample;
+        }
+        this.min = min;
+        this.max = maxValue;
+    }
+
+    public DenselySampledSpectrum(double @NotNull[] samples, int lambdaMin) {
+        if (samples.length == 0) throw new IllegalArgumentException("samples must not be empty");
+        this.samples = Arrays.copyOf(samples, samples.length);
+        this.min = lambdaMin;
+        this.max = Arrays.stream(this.samples).max().orElseThrow();
+    }
+
+    @Override
+    public double max() {
+        return max;
+    }
+
+    @Override
+    public double get(double lambda) {
+        int offset = (int) Math.round(lambda) - min;
+        if (offset < 0 || offset >= samples.length) return 0;
+        return samples[offset];
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/spectrum/PiecewiseLinearSpectrum.java

@@ -0,0 +1,48 @@
+package eu.jonahbauer.raytracing.render.spectral.spectrum;
+
+import java.util.Arrays;
+
+public final class PiecewiseLinearSpectrum implements Spectrum {
+    private final double[] lambdas;
+    private final double[] values;
+    private final double max;
+
+    public PiecewiseLinearSpectrum(double[] lambdas, double[] values) {
+        if (lambdas.length != values.length) {
+            throw new IllegalArgumentException("lambdas and values must have the same length");
+        }
+
+        this.lambdas = Arrays.copyOf(lambdas, lambdas.length);
+        this.values = Arrays.copyOf(values, values.length);
+
+        var max = 0d;
+        for (int i = 1; i < this.lambdas.length; i++) {
+            if (this.lambdas[i] <= this.lambdas[i - 1]) {
+                throw new IllegalArgumentException("lambdas must be in increasing order");
+            }
+            if (this.values[i] < 0) {
+                throw new IllegalArgumentException("values must be non-negative");
+            } else if (this.values[i] > max) {
+                max = this.values[i];
+            }
+        }
+        this.max = max;
+    }
+
+    @Override
+    public double max() {
+        return max;
+    }
+
+    @Override
+    public double get(double lambda) {
+        if (lambdas.length == 0 || lambda < lambdas[0] || lambda > lambdas[lambdas.length - 1]) return 0;
+        if (lambda == lambdas[lambdas.length - 1]) return values[values.length - 1];
+
+        var i = Arrays.binarySearch(lambdas, lambda);
+        if (i < 0) i = -i - 1;
+
+        var t = (lambda - lambdas[i]) / (lambdas[i + 1] - lambdas[i]);
+        return (1 - t) * values[i] + t * values[i + 1];
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/spectrum/RGBAlbedoSpectrum.java

@@ -0,0 +1,27 @@
+package eu.jonahbauer.raytracing.render.spectral.spectrum;
+
+import eu.jonahbauer.raytracing.render.spectral.colors.ColorSpace;
+import eu.jonahbauer.raytracing.render.spectral.colors.SigmoidPolynomial;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import org.jetbrains.annotations.NotNull;
+
+public final class RGBAlbedoSpectrum implements Spectrum {
+    private final @NotNull SigmoidPolynomial polynomial;
+
+    public RGBAlbedoSpectrum(@NotNull ColorSpace cs, @NotNull Color rgb) {
+        if (rgb.r() < 0 || rgb.r() > 1 || rgb.g() < 0 || rgb.g() > 1 || rgb.b() < 0 || rgb.b() > 1) {
+            throw new IllegalArgumentException();
+        }
+        this.polynomial = cs.toSpectrum(rgb);
+    }
+
+    @Override
+    public double max() {
+        return polynomial.max();
+    }
+
+    @Override
+    public double get(double lambda) {
+        return polynomial.get(lambda);
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/spectrum/RGBIlluminantSpectrum.java

@@ -0,0 +1,32 @@
+package eu.jonahbauer.raytracing.render.spectral.spectrum;
+
+import eu.jonahbauer.raytracing.render.spectral.colors.ColorSpace;
+import eu.jonahbauer.raytracing.render.spectral.colors.SigmoidPolynomial;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import org.jetbrains.annotations.NotNull;
+
+public final class RGBIlluminantSpectrum implements Spectrum {
+    private final double scale;
+    private final @NotNull SigmoidPolynomial polynomial;
+    private final @NotNull DenselySampledSpectrum illuminant;
+
+    public RGBIlluminantSpectrum(@NotNull ColorSpace cs, @NotNull Color rgb) {
+        if (rgb.r() < 0 || rgb.g() < 0 || rgb.b() < 0) {
+            throw new IllegalArgumentException();
+        }
+        var max = Math.max(rgb.r(), Math.max(rgb.g(), rgb.b()));
+        this.scale = 2 * max;
+        this.polynomial = cs.toSpectrum(scale == 0 ? Color.multiply(rgb, scale) : Color.BLACK);
+        this.illuminant = cs.illuminant();
+    }
+
+    @Override
+    public double max() {
+        return scale * polynomial.max() * illuminant.max();
+    }
+
+    @Override
+    public double get(double lambda) {
+        return scale * polynomial.get(lambda) * illuminant.get(lambda);
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/spectrum/RGBUnboundedSpectrum.java

@@ -0,0 +1,30 @@
+package eu.jonahbauer.raytracing.render.spectral.spectrum;
+
+import eu.jonahbauer.raytracing.render.spectral.colors.ColorSpace;
+import eu.jonahbauer.raytracing.render.spectral.colors.SigmoidPolynomial;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import org.jetbrains.annotations.NotNull;
+
+public final class RGBUnboundedSpectrum implements Spectrum {
+    private final double scale;
+    private final @NotNull SigmoidPolynomial polynomial;
+
+    public RGBUnboundedSpectrum(@NotNull ColorSpace cs, @NotNull Color rgb) {
+        if (rgb.r() < 0 || rgb.g() < 0 || rgb.b() < 0) {
+            throw new IllegalArgumentException();
+        }
+        var max = Math.max(rgb.r(), Math.max(rgb.g(), rgb.b()));
+        this.scale = 2 * max;
+        this.polynomial = cs.toSpectrum(scale == 0 ? Color.multiply(rgb, scale) : Color.BLACK);
+    }
+
+    @Override
+    public double max() {
+        return scale * polynomial.max();
+    }
+
+    @Override
+    public double get(double lambda) {
+        return scale * polynomial.get(lambda);
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/spectrum/Spectra.java

@@ -0,0 +1,86 @@
+package eu.jonahbauer.raytracing.render.spectral.spectrum;
+
+import org.jetbrains.annotations.NotNull;
+
+import java.io.BufferedReader;
+import java.io.IOException;
+import java.io.InputStreamReader;
+import java.io.UncheckedIOException;
+import java.nio.charset.StandardCharsets;
+import java.util.ArrayList;
+import java.util.List;
+
+public final class Spectra {
+    /**
+     * the CIE XYZ color matching curve for X
+     */
+    public static final Spectrum X;
+    /**
+     * the CIE XYZ color matching curve for Y
+     */
+    public static final Spectrum Y;
+    /**
+     * the CIE XYZ color matching curve for Z
+     */
+    public static final Spectrum Z;
+    /**
+     * the CIE standard illuminant D50
+     */
+    public static final Spectrum D50;
+    /**
+     * the CIE standard illuminant D65
+     */
+    public static final Spectrum D65;
+
+    static {
+        var xyz = read("/eu/jonahbauer/raytracing/spectrum/CIE_xyz_1931_2deg.csv");
+        X = xyz[0];
+        Y = xyz[1];
+        Z = xyz[2];
+        D50 = read("/eu/jonahbauer/raytracing/spectrum/CIE_std_illum_D50.csv")[0];
+        D65 = read("/eu/jonahbauer/raytracing/spectrum/CIE_std_illum_D65.csv")[0];
+    }
+
+    private static @NotNull DenselySampledSpectrum[] read(@NotNull String path) {
+        var lambda = new ArrayList<Double>();
+        var values = new ArrayList<List<Double>>();
+
+        try (
+                var is = Spectra.class.getResourceAsStream(path);
+                var in = new BufferedReader(new InputStreamReader(is, StandardCharsets.US_ASCII))
+        ) {
+            int count = -1;
+            String line;
+            while ((line = in.readLine()) != null) {
+                var parts = line.split(",");
+                if (count == -1) {
+                    count = parts.length - 1;
+                    for (int i = 0; i < count; i++) values.add(new ArrayList<>());
+                } else if (count != parts.length - 1) {
+                    throw new IllegalStateException("invalid spectrum file: " + path);
+                }
+
+                lambda.add(Double.parseDouble(parts[0]));
+                for (int i = 0; i < count; i++) {
+                    values.get(i).add(Double.parseDouble(parts[i + 1]));
+                }
+            }
+        } catch (IOException e) {
+            throw new UncheckedIOException(e);
+        }
+
+        var out = new DenselySampledSpectrum[values.size()];
+        var lambdaArray = lambda.stream().mapToDouble(Double::doubleValue).toArray();
+        for (int i = 0; i < values.size(); i++) {
+            var valueArray = values.get(i).stream().mapToDouble(Double::doubleValue).toArray();
+            var s = new PiecewiseLinearSpectrum(lambdaArray, valueArray);
+            out[i] = new DenselySampledSpectrum(s);
+        }
+
+        return out;
+    }
+
+    private Spectra() {
+        throw new UnsupportedOperationException();
+    }
+}

src/main/java/eu/jonahbauer/raytracing/render/spectral/spectrum/Spectrum.java

@@ -0,0 +1,49 @@
+package eu.jonahbauer.raytracing.render.spectral.spectrum;
+
+import eu.jonahbauer.raytracing.render.spectral.colors.ColorSpace;
+import eu.jonahbauer.raytracing.render.spectral.colors.ColorXYZ;
+import eu.jonahbauer.raytracing.render.spectral.SampledSpectrum;
+import eu.jonahbauer.raytracing.render.spectral.SampledWavelengths;
+import eu.jonahbauer.raytracing.render.texture.Color;
+import org.jetbrains.annotations.NotNull;
+
+public interface Spectrum {
+    int LAMBDA_MIN = 360;
+    int LAMBDA_MAX = 830;
+    int SAMPLES = 4;
+
+    /**
+     * {@return the maximum value of <code>this</code> spectrum over the range of wavelengths}
+     */
+    double max();
+
+    /**
+     * {@return the value of <code>this</code> spectrum at a given wavelength}
+     * @param lambda the wavelength in nanometers
+     */
+    double get(double lambda);
+
+    default @NotNull SampledSpectrum sample(@NotNull SampledWavelengths lambdas) {
+        return new SampledSpectrum(lambdas, this);
+    }
+
+    default @NotNull ColorXYZ toXYZ() {
+        return new ColorXYZ(
+                innerProduct(Spectra.X, this) / ColorXYZ.CIE_Y_INTEGRAL,
+                innerProduct(Spectra.Y, this) / ColorXYZ.CIE_Y_INTEGRAL,
+                innerProduct(Spectra.Z, this) / ColorXYZ.CIE_Y_INTEGRAL
+        );
+    }
+
+    default @NotNull Color toRGB(@NotNull ColorSpace cs) {
+        return cs.toRGB(toXYZ());
+    }
+
+    private static double innerProduct(@NotNull Spectrum f, @NotNull Spectrum g) {
+        var integral = 0.0;
+        for (var lambda = LAMBDA_MIN; lambda <= LAMBDA_MAX; lambda++) {
+            integral += f.get(lambda) * g.get(lambda);
+        }
+        return integral;
+    }
+}

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

@@ -5,6 +5,7 @@ import eu.jonahbauer.raytracing.math.Vec3;
 import eu.jonahbauer.raytracing.scene.SkyBox;
 import org.jetbrains.annotations.NotNull;
 
+import java.util.Objects;
 import java.util.Random;
 
 import static eu.jonahbauer.raytracing.Main.DEBUG;
@@ -20,9 +21,9 @@ public record Color(double r, double g, double b) implements Texture, SkyBox {
         if (t < 0) return a;
         if (t > 1) return b;
         return new Color(
-                (1 - t) * a.r + t * b.r,
+                Math.fma(t, b.r, Math.fma(-t, a.r, a.r)),
-                (1 - t) * a.g + t * b.g,
+                Math.fma(t, b.g, Math.fma(-t, a.g, a.g)),
-                (1 - t) * a.b + t * b.b
+                Math.fma(t, b.b, Math.fma(-t, a.b, a.b))
         );
     }
 
@@ -86,6 +87,10 @@ public record Color(double r, double g, double b) implements Texture, SkyBox {
         this(red / 255f, green / 255f, blue / 255f);
     }
 
+    public Color(@NotNull Vec3 vec) {
+        this(vec.x(), vec.y(), vec.z());
+    }
+
     public Color {
         if (DEBUG) {
             if (!Double.isFinite(r) || !Double.isFinite(g) || !Double.isFinite(b)) {
@@ -109,6 +114,15 @@ public record Color(double r, double g, double b) implements Texture, SkyBox {
         return toInt(b);
     }
 
+    public double component(int i) {
+        return switch (i) {
+            case 0 -> r;
+            case 1 -> g;
+            case 2 -> b;
+            default -> throw new IndexOutOfBoundsException(i);
+        };
+    }
+
     @Override
     public @NotNull Color get(double u, double v, @NotNull Vec3 p) {
         return this;
@@ -124,6 +138,10 @@ public record Color(double r, double g, double b) implements Texture, SkyBox {
         return false;
     }
 
+    public @NotNull Vec3 toVec3() {
+        return new Vec3(r, g, b);
+    }
+
     private static int toInt(double value) {
         return Math.clamp((int) (255.99 * value), 0, 255);
     }

src/main/resources/eu/jonahbauer/raytracing/spectrum/CIE_std_illum_D50.csv

@@ -0,0 +1,531 @@
+300,0.01922
+301,0.222348
+302,0.425476
+303,0.628604
+304,0.831732
+305,1.03486
+306,1.23799
+307,1.44112
+308,1.64424
+309,1.84737
+310,2.0505
+311,2.62329
+312,3.19608
+313,3.76887
+314,4.34166
+315,4.91445
+316,5.48724
+317,6.06003
+318,6.63282
+319,7.20561
+320,7.7784
+321,8.47531
+322,9.17222
+323,9.86913
+324,10.566
+325,11.263
+326,11.9599
+327,12.6568
+328,13.3537
+329,14.0506
+330,14.7475
+331,15.0676
+332,15.3876
+333,15.7076
+334,16.0277
+335,16.3478
+336,16.6678
+337,16.9878
+338,17.3079
+339,17.628
+340,17.948
+341,18.2542
+342,18.5603
+343,18.8665
+344,19.1727
+345,19.4788
+346,19.785
+347,20.0912
+348,20.3974
+349,20.7035
+350,21.0097
+351,21.3029
+352,21.5961
+353,21.8894
+354,22.1826
+355,22.4758
+356,22.769
+357,23.0622
+358,23.3555
+359,23.6487
+360,23.9419
+361,24.2438
+362,24.5457
+363,24.8475
+364,25.1494
+365,25.4513
+366,25.7532
+367,26.0551
+368,26.3569
+369,26.6588
+370,26.9607
+371,26.7134
+372,26.4661
+373,26.2187
+374,25.9714
+375,25.7241
+376,25.4768
+377,25.2295
+378,24.9821
+379,24.7348
+380,24.4875
+381,25.0258
+382,25.5641
+383,26.1024
+384,26.6407
+385,27.179
+386,27.7174
+387,28.2557
+388,28.794
+389,29.3323
+390,29.8706
+391,31.8144
+392,33.7581
+393,35.7018
+394,37.6456
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+398,45.4206
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