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 +1,71 @@
+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 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 +1,95 @@
+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 {
+    public static final @NotNull ColorSpace sRGB;
+    public static final @NotNull ColorSpace DCI_P3;
+    public static final @NotNull ColorSpace Rec2020;
+
+    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 Object RGBtoSpectrumTable;
+
+    public static ColorSpace getNamed(@NotNull String name) {
+        return switch (name) {
+            case "sRGB" -> sRGB;
+            case "DCI-P3" -> DCI_P3;
+            case "Rec2020" -> Rec2020;
+            default -> throw new NoSuchElementException("unknown color space " + name);
+        };
+    }
+
+    public ColorSpace(
+            @NotNull Chromaticity r, @NotNull Chromaticity g, @NotNull Chromaticity b,
+            @NotNull Spectrum illuminant, @NotNull Object 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 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/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/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, (int) LAMBDA_MIN, (int) 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/Spectra.java

@@ -0,0 +1,78 @@
+package eu.jonahbauer.raytracing.render.spectral.spectrum;
+
+import eu.jonahbauer.raytracing.render.spectral.ColorMatchingFunction;
+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;
+
+public final class Spectra {
+    private static final Spectrum X;
+    private static final Spectrum Y;
+    private static final Spectrum Z;
+
+    static {
+        var count = Spectrum.LAMBDA_MAX - Spectrum.LAMBDA_MIN + 1;
+        var x = new double[count];
+        var y = new double[count];
+        var z = new double[count];
+
+        try (
+                var is = Spectra.class.getResourceAsStream("/eu/jonahbauer/raytracing/spectrum/CIE_xyz_1931_2deg.csv");
+                var in = new BufferedReader(new InputStreamReader(is, StandardCharsets.US_ASCII))
+        ) {
+            for (int i = 0; i < count; i++) {
+                var line = in.readLine().split(",");
+                x[i] = Double.parseDouble(line[1]);
+                y[i] = Double.parseDouble(line[2]);
+                z[i] = Double.parseDouble(line[3]);
+            }
+        } catch (IOException e) {
+            throw new UncheckedIOException(e);
+        }
+
+        X = new DenselySampledSpectrum(x, Spectrum.LAMBDA_MIN);
+        Y = new DenselySampledSpectrum(y, Spectrum.LAMBDA_MIN);
+        Z = new DenselySampledSpectrum(z, Spectrum.LAMBDA_MIN);
+    }
+
+    /**
+     * {@return the X color matching curve}
+     */
+    public static @NotNull Spectrum X() {
+        return X;
+    }
+
+    /**
+     * {@return the Y color matching curve}
+     */
+    public static @NotNull Spectrum Y() {
+        return Y;
+    }
+
+    /**
+     * {@return the Z color matching curve}
+     */
+    public static @NotNull Spectrum Z() {
+        return Z;
+    }
+
+    /**
+     * {@return the D illuminant at the given temperature}
+     * @param T the temperature
+     */
+    public static @NotNull Spectrum D(double T) {
+
+    }
+
+    public static @NotNull Spectrum getNamed(@NotNull String name) {
+
+    }
+
+    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

@@ -20,9 +20,9 @@ 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 +86,10 @@ 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)) {
@@ -124,6 +128,10 @@ 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_xyz_1931_2deg.csv

@@ -0,0 +1,471 @@
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