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,
-                (1 - t) * a.g + t * b.g,
-                (1 - t) * a.b + t * b.b
+                Math.fma(t, b.r, Math.fma(-t, a.r, a.r)),
+                Math.fma(t, b.g, Math.fma(-t, a.g, a.g)),
+                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
+395,39.5894
+396,41.5331
+397,43.4768
+398,45.4206
+399,47.3644
+400,49.3081
+401,50.0286
+402,50.749
+403,51.4695
+404,52.19
+405,52.9104
+406,53.6309
+407,54.3514
+408,55.0719
+409,55.7923
+410,56.5128
+411,56.8649
+412,57.217
+413,57.5691
+414,57.9212
+415,58.2733
+416,58.6254
+417,58.9775
+418,59.3296
+419,59.6817
+420,60.0338
+421,59.8122
+422,59.5905
+423,59.3689
+424,59.1473
+425,58.9256
+426,58.704
+427,58.4824
+428,58.2608
+429,58.0391
+430,57.8175
+431,59.5182
+432,61.219
+433,62.9197
+434,64.6205
+435,66.3212
+436,68.0219
+437,69.7227
+438,71.4234
+439,73.1242
+440,74.8249
+441,76.0671
+442,77.3094
+443,78.5516
+444,79.7938
+445,81.036
+446,82.2783
+447,83.5205
+448,84.7627
+449,86.005
+450,87.2472
+451,87.5837
+452,87.9202
+453,88.2567
+454,88.5932
+455,88.9297
+456,89.2662
+457,89.6027
+458,89.9392
+459,90.2757
+460,90.6122
+461,90.6878
+462,90.7634
+463,90.839
+464,90.9146
+465,90.9902
+466,91.0657
+467,91.1413
+468,91.2169
+469,91.2925
+470,91.3681
+471,91.7421
+472,92.1162
+473,92.4902
+474,92.8643
+475,93.2383
+476,93.6123
+477,93.9864
+478,94.3604
+479,94.7345
+480,95.1085
+481,94.7939
+482,94.4793
+483,94.1648
+484,93.8502
+485,93.5356
+486,93.221
+487,92.9064
+488,92.5919
+489,92.2773
+490,91.9627
+491,92.3388
+492,92.7149
+493,93.091
+494,93.4671
+495,93.8432
+496,94.2193
+497,94.5954
+498,94.9715
+499,95.3476
+500,95.7237
+501,95.8127
+502,95.9016
+503,95.9906
+504,96.0795
+505,96.1685
+506,96.2575
+507,96.3464
+508,96.4354
+509,96.5243
+510,96.6133
+511,96.6649
+512,96.7164
+513,96.768
+514,96.8196
+515,96.8712
+516,96.9227
+517,96.9743
+518,97.0259
+519,97.0774
+520,97.129
+521,97.626
+522,98.123
+523,98.62
+524,99.117
+525,99.614
+526,100.111
+527,100.608
+528,101.105
+529,101.602
+530,102.099
+531,101.965
+532,101.83
+533,101.696
+534,101.561
+535,101.427
+536,101.292
+537,101.158
+538,101.024
+539,100.889
+540,100.755
+541,100.911
+542,101.067
+543,101.223
+544,101.38
+545,101.536
+546,101.692
+547,101.848
+548,102.005
+549,102.161
+550,102.317
+551,102.085
+552,101.854
+553,101.622
+554,101.39
+555,101.158
+556,100.927
+557,100.695
+558,100.463
+559,100.232
+560,100
+561,99.7735
+562,99.547
+563,99.3205
+564,99.094
+565,98.8675
+566,98.641
+567,98.4145
+568,98.188
+569,97.9615
+570,97.735
+571,97.8533
+572,97.9716
+573,98.0899
+574,98.2082
+575,98.3265
+576,98.4448
+577,98.5631
+578,98.6814
+579,98.7997
+580,98.918
+581,98.3761
+582,97.8342
+583,97.2922
+584,96.7503
+585,96.2084
+586,95.6665
+587,95.1246
+588,94.5826
+589,94.0407
+590,93.4988
+591,93.9177
+592,94.3366
+593,94.7555
+594,95.1744
+595,95.5933
+596,96.0122
+597,96.4311
+598,96.85
+599,97.2689
+600,97.6878
+601,97.8459
+602,98.0041
+603,98.1622
+604,98.3203
+605,98.4784
+606,98.6366
+607,98.7947
+608,98.9528
+609,99.111
+610,99.2691
+611,99.2463
+612,99.2236
+613,99.2008
+614,99.1781
+615,99.1553
+616,99.1325
+617,99.1098
+618,99.087
+619,99.0643
+620,99.0415
+621,98.7095
+622,98.3776
+623,98.0456
+624,97.7136
+625,97.3816
+626,97.0497
+627,96.7177
+628,96.3857
+629,96.0538
+630,95.7218
+631,96.0353
+632,96.3489
+633,96.6624
+634,96.976
+635,97.2895
+636,97.603
+637,97.9166
+638,98.2301
+639,98.5437
+640,98.8572
+641,98.5382
+642,98.2192
+643,97.9002
+644,97.5812
+645,97.2622
+646,96.9432
+647,96.6242
+648,96.3052
+649,95.9862
+650,95.6672
+651,95.9195
+652,96.1717
+653,96.424
+654,96.6762
+655,96.9285
+656,97.1808
+657,97.433
+658,97.6853
+659,97.9375
+660,98.1898
+661,98.6712
+662,99.1525
+663,99.6339
+664,100.115
+665,100.597
+666,101.078
+667,101.559
+668,102.041
+669,102.522
+670,103.003
+671,102.616
+672,102.229
+673,101.842
+674,101.455
+675,101.068
+676,100.681
+677,100.294
+678,99.9071
+679,99.52
+680,99.133
+681,97.9578
+682,96.7826
+683,95.6074
+684,94.4322
+685,93.257
+686,92.0817
+687,90.9065
+688,89.7313
+689,88.5561
+690,87.3809
+691,87.8032
+692,88.2254
+693,88.6477
+694,89.0699
+695,89.4922
+696,89.9145
+697,90.3367
+698,90.759
+699,91.1812
+700,91.6035
+701,91.732
+702,91.8605
+703,91.989
+704,92.1175
+705,92.246
+706,92.3746
+707,92.5031
+708,92.6316
+709,92.7601
+710,92.8886
+711,91.2852
+712,89.6818
+713,88.0783
+714,86.4749
+715,84.8715
+716,83.2681
+717,81.6647
+718,80.0612
+719,78.4578
+720,76.8544
+721,77.8201
+722,78.7858
+723,79.7514
+724,80.7171
+725,81.6828
+726,82.6485
+727,83.6142
+728,84.5798
+729,85.5455
+730,86.5112
+731,87.1181
+732,87.7249
+733,88.3318
+734,88.9386
+735,89.5455
+736,90.1524
+737,90.7592
+738,91.3661
+739,91.9729
+740,92.5798
+741,91.1448
+742,89.7098
+743,88.2748
+744,86.8398
+745,85.4048
+746,83.9699
+747,82.5349
+748,81.0999
+749,79.6649
+750,78.2299
+751,76.1761
+752,74.1223
+753,72.0685
+754,70.0147
+755,67.9608
+756,65.907
+757,63.8532
+758,61.7994
+759,59.7456
+760,57.6918
+761,60.2149
+762,62.738
+763,65.2612
+764,67.7843
+765,70.3074
+766,72.8305
+767,75.3536
+768,77.8768
+769,80.3999
+770,82.923
+771,82.4581
+772,81.9932
+773,81.5283
+774,81.0634
+775,80.5985
+776,80.1336
+777,79.6687
+778,79.2038
+779,78.7389
+780,78.274
+781,78.402
+782,78.5301
+783,78.6581
+784,78.7862
+785,78.9142
+786,79.0422
+787,79.1703
+788,79.2983
+789,79.4264
+790,79.5544
+791,78.9391
+792,78.3238
+793,77.7085
+794,77.0932
+795,76.478
+796,75.8627
+797,75.2474
+798,74.6321
+799,74.0168
+800,73.4015
+801,72.4534
+802,71.5052
+803,70.5571
+804,69.609
+805,68.6608
+806,67.7127
+807,66.7646
+808,65.8165
+809,64.8683
+810,63.9202
+811,64.6059
+812,65.2916
+813,65.9772
+814,66.6629
+815,67.3486
+816,68.0343
+817,68.72
+818,69.4056
+819,70.0913
+820,70.777
+821,71.1435
+822,71.5099
+823,71.8764
+824,72.2429
+825,72.6094
+826,72.9758
+827,73.3423
+828,73.7088
+829,74.0752
+830,74.4417

src/main/resources/eu/jonahbauer/raytracing/spectrum/CIE_std_illum_D65.csv

@@ -0,0 +1,531 @@
+300,0.0341
+301,0.36014
+302,0.68618
+303,1.01222
+304,1.33826
+305,1.6643
+306,1.99034
+307,2.31638
+308,2.64242
+309,2.96846
+310,3.2945
+311,4.98865
+312,6.6828
+313,8.37695
+314,10.0711
+315,11.7652
+316,13.4594
+317,15.1535
+318,16.8477
+319,18.5418
+320,20.236
+321,21.9177
+322,23.5995
+323,25.2812
+324,26.963
+325,28.6447
+326,30.3265
+327,32.0082
+328,33.69
+329,35.3717
+330,37.0535
+331,37.343
+332,37.6326
+333,37.9221
+334,38.2116
+335,38.5011
+336,38.7907
+337,39.0802
+338,39.3697
+339,39.6593
+340,39.9488
+341,40.4451
+342,40.9414
+343,41.4377
+344,41.934
+345,42.4302
+346,42.9265
+347,43.4228
+348,43.9191
+349,44.4154
+350,44.9117
+351,45.0844
+352,45.257
+353,45.4297
+354,45.6023
+355,45.775
+356,45.9477
+357,46.1203
+358,46.293
+359,46.4656
+360,46.6383
+361,47.1834
+362,47.7285
+363,48.2735
+364,48.8186
+365,49.3637
+366,49.9088
+367,50.4539
+368,50.9989
+369,51.544
+370,52.0891
+371,51.8777
+372,51.6664
+373,51.455
+374,51.2437
+375,51.0323
+376,50.8209
+377,50.6096
+378,50.3982
+379,50.1869
+380,49.9755
+381,50.4428
+382,50.91
+383,51.3773
+384,51.8446
+385,52.3118
+386,52.7791
+387,53.2464
+388,53.7137
+389,54.1809
+390,54.6482
+391,57.4589
+392,60.2695
+393,63.0802
+394,65.8909
+395,68.7015
+396,71.5122
+397,74.3229
+398,77.1336
+399,79.9442
+400,82.7549
+401,83.628
+402,84.5011
+403,85.3742
+404,86.2473
+405,87.1204
+406,87.9936
+407,88.8667
+408,89.7398
+409,90.6129
+410,91.486
+411,91.6806
+412,91.8752
+413,92.0697
+414,92.2643
+415,92.4589
+416,92.6535
+417,92.8481
+418,93.0426
+419,93.2372
+420,93.4318
+421,92.7568
+422,92.0819
+423,91.4069
+424,90.732
+425,90.057
+426,89.3821
+427,88.7071
+428,88.0322
+429,87.3572
+430,86.6823
+431,88.5006
+432,90.3188
+433,92.1371
+434,93.9554
+435,95.7736
+436,97.5919
+437,99.4102
+438,101.228
+439,103.047
+440,104.865
+441,106.079
+442,107.294
+443,108.508
+444,109.722
+445,110.936
+446,112.151
+447,113.365
+448,114.579
+449,115.794
+450,117.008
+451,117.088
+452,117.169
+453,117.249
+454,117.33
+455,117.41
+456,117.49
+457,117.571
+458,117.651
+459,117.732
+460,117.812
+461,117.517
+462,117.222
+463,116.927
+464,116.632
+465,116.336
+466,116.041
+467,115.746
+468,115.451
+469,115.156
+470,114.861
+471,114.967
+472,115.073
+473,115.18
+474,115.286
+475,115.392
+476,115.498
+477,115.604
+478,115.711
+479,115.817
+480,115.923
+481,115.212
+482,114.501
+483,113.789
+484,113.078
+485,112.367
+486,111.656
+487,110.945
+488,110.233
+489,109.522
+490,108.811
+491,108.865
+492,108.92
+493,108.974
+494,109.028
+495,109.082
+496,109.137
+497,109.191
+498,109.245
+499,109.3
+500,109.354
+501,109.199
+502,109.044
+503,108.888
+504,108.733
+505,108.578
+506,108.423
+507,108.268
+508,108.112
+509,107.957
+510,107.802
+511,107.501
+512,107.2
+513,106.898
+514,106.597
+515,106.296
+516,105.995
+517,105.694
+518,105.392
+519,105.091
+520,104.79
+521,105.08
+522,105.37
+523,105.66
+524,105.95
+525,106.239
+526,106.529
+527,106.819
+528,107.109
+529,107.399
+530,107.689
+531,107.361
+532,107.032
+533,106.704
+534,106.375
+535,106.047
+536,105.719
+537,105.39
+538,105.062
+539,104.733
+540,104.405
+541,104.369
+542,104.333
+543,104.297
+544,104.261
+545,104.225
+546,104.19
+547,104.154
+548,104.118
+549,104.082
+550,104.046
+551,103.641
+552,103.237
+553,102.832
+554,102.428
+555,102.023
+556,101.618
+557,101.214
+558,100.809
+559,100.405
+560,100
+561,99.6334
+562,99.2668
+563,98.9003
+564,98.5337
+565,98.1671
+566,97.8005
+567,97.4339
+568,97.0674
+569,96.7008
+570,96.3342
+571,96.2796
+572,96.225
+573,96.1703
+574,96.1157
+575,96.0611
+576,96.0065
+577,95.9519
+578,95.8972
+579,95.8426
+580,95.788
+581,95.0778
+582,94.3675
+583,93.6573
+584,92.947
+585,92.2368
+586,91.5266
+587,90.8163
+588,90.1061
+589,89.3958
+590,88.6856
+591,88.8177
+592,88.9497
+593,89.0818
+594,89.2138
+595,89.3459
+596,89.478
+597,89.61
+598,89.7421
+599,89.8741
+600,90.0062
+601,89.9655
+602,89.9248
+603,89.8841
+604,89.8434
+605,89.8026
+606,89.7619
+607,89.7212
+608,89.6805
+609,89.6398
+610,89.5991
+611,89.4091
+612,89.219
+613,89.029
+614,88.8389
+615,88.6489
+616,88.4589
+617,88.2688
+618,88.0788
+619,87.8887
+620,87.6987
+621,87.2577
+622,86.8167
+623,86.3757
+624,85.9347
+625,85.4936
+626,85.0526
+627,84.6116
+628,84.1706
+629,83.7296
+630,83.2886
+631,83.3297
+632,83.3707
+633,83.4118
+634,83.4528
+635,83.4939
+636,83.535
+637,83.576
+638,83.6171
+639,83.6581
+640,83.6992
+641,83.332
+642,82.9647
+643,82.5975
+644,82.2302
+645,81.863
+646,81.4958
+647,81.1285
+648,80.7613
+649,80.394
+650,80.0268
+651,80.0456
+652,80.0644
+653,80.0831
+654,80.1019
+655,80.1207
+656,80.1395
+657,80.1583
+658,80.177
+659,80.1958
+660,80.2146
+661,80.4209
+662,80.6272
+663,80.8336
+664,81.0399
+665,81.2462
+666,81.4525
+667,81.6588
+668,81.8652
+669,82.0715
+670,82.2778
+671,81.8784
+672,81.4791
+673,81.0797
+674,80.6804
+675,80.281
+676,79.8816
+677,79.4823
+678,79.0829
+679,78.6836
+680,78.2842
+681,77.4279
+682,76.5716
+683,75.7153
+684,74.859
+685,74.0027
+686,73.1465
+687,72.2902
+688,71.4339
+689,70.5776
+690,69.7213
+691,69.9101
+692,70.0989
+693,70.2876
+694,70.4764
+695,70.6652
+696,70.854
+697,71.0428
+698,71.2315
+699,71.4203
+700,71.6091
+701,71.8831
+702,72.1571
+703,72.4311
+704,72.7051
+705,72.979
+706,73.253
+707,73.527
+708,73.801
+709,74.075
+710,74.349
+711,73.0745
+712,71.8
+713,70.5255
+714,69.251
+715,67.9765
+716,66.702
+717,65.4275
+718,64.153
+719,62.8785
+720,61.604
+721,62.4322
+722,63.2603
+723,64.0885
+724,64.9166
+725,65.7448
+726,66.573
+727,67.4011
+728,68.2293
+729,69.0574
+730,69.8856
+731,70.4057
+732,70.9259
+733,71.446
+734,71.9662
+735,72.4863
+736,73.0064
+737,73.5266
+738,74.0467
+739,74.5669
+740,75.087
+741,73.9376
+742,72.7881
+743,71.6387
+744,70.4893
+745,69.3398
+746,68.1904
+747,67.041
+748,65.8916
+749,64.7421
+750,63.5927
+751,61.8752
+752,60.1578
+753,58.4403
+754,56.7229
+755,55.0054
+756,53.288
+757,51.5705
+758,49.8531
+759,48.1356
+760,46.4182
+761,48.4569
+762,50.4956
+763,52.5344
+764,54.5731
+765,56.6118
+766,58.6505
+767,60.6892
+768,62.728
+769,64.7667
+770,66.8054
+771,66.4631
+772,66.1209
+773,65.7786
+774,65.4364
+775,65.0941
+776,64.7518
+777,64.4096
+778,64.0673
+779,63.7251
+780,63.3828
+781,63.4749
+782,63.567
+783,63.6592
+784,63.7513
+785,63.8434
+786,63.9355
+787,64.0276
+788,64.1198
+789,64.2119
+790,64.304
+791,63.8188
+792,63.3336
+793,62.8484
+794,62.3632
+795,61.8779
+796,61.3927
+797,60.9075
+798,60.4223
+799,59.9371
+800,59.4519
+801,58.7026
+802,57.9533
+803,57.204
+804,56.4547
+805,55.7054
+806,54.9562
+807,54.2069
+808,53.4576
+809,52.7083
+810,51.959
+811,52.5072
+812,53.0553
+813,53.6035
+814,54.1516
+815,54.6998
+816,55.248
+817,55.7961
+818,56.3443
+819,56.8924
+820,57.4406
+821,57.7278
+822,58.015
+823,58.3022
+824,58.5894
+825,58.8765
+826,59.1637
+827,59.4509
+828,59.7381
+829,60.0253
+830,60.3125

src/main/resources/eu/jonahbauer/raytracing/spectrum/CIE_xyz_1931_2deg.csv

@@ -0,0 +1,471 @@
+360,0.000129900000,0.0000039170000,0.000606100000
+361,0.000145847000,0.0000043935810,0.000680879200
+362,0.000163802100,0.0000049296040,0.000765145600
+363,0.000184003700,0.0000055321360,0.000860012400
+364,0.000206690200,0.0000062082450,0.000966592800
+365,0.000232100000,0.0000069650000,0.001086000000
+366,0.000260728000,0.0000078132190,0.001220586000
+367,0.000293075000,0.0000087673360,0.001372729000
+368,0.000329388000,0.0000098398440,0.001543579000
+369,0.000369914000,0.0000110432300,0.001734286000
+370,0.000414900000,0.0000123900000,0.001946000000
+371,0.000464158700,0.0000138864100,0.002177777000
+372,0.000518986000,0.0000155572800,0.002435809000
+373,0.000581854000,0.0000174429600,0.002731953000
+374,0.000655234700,0.0000195837500,0.003078064000
+375,0.000741600000,0.0000220200000,0.003486000000
+376,0.000845029600,0.0000248396500,0.003975227000
+377,0.000964526800,0.0000280412600,0.004540880000
+378,0.001094949000,0.0000315310400,0.005158320000
+379,0.001231154000,0.0000352152100,0.005802907000
+380,0.001368000000,0.0000390000000,0.006450001000
+381,0.001502050000,0.0000428264000,0.007083216000
+382,0.001642328000,0.0000469146000,0.007745488000
+383,0.001802382000,0.0000515896000,0.008501152000
+384,0.001995757000,0.0000571764000,0.009414544000
+385,0.002236000000,0.0000640000000,0.010549990000
+386,0.002535385000,0.0000723442100,0.011965800000
+387,0.002892603000,0.0000822122400,0.013655870000
+388,0.003300829000,0.0000935081600,0.015588050000
+389,0.003753236000,0.0001061361000,0.017730150000
+390,0.004243000000,0.0001200000000,0.020050010000
+391,0.004762389000,0.0001349840000,0.022511360000
+392,0.005330048000,0.0001514920000,0.025202880000
+393,0.005978712000,0.0001702080000,0.028279720000
+394,0.006741117000,0.0001918160000,0.031897040000
+395,0.007650000000,0.0002170000000,0.036210000000
+396,0.008751373000,0.0002469067000,0.041437710000
+397,0.010028880000,0.0002812400000,0.047503720000
+398,0.011421700000,0.0003185200000,0.054119880000
+399,0.012869010000,0.0003572667000,0.060998030000
+400,0.014310000000,0.0003960000000,0.067850010000
+401,0.015704430000,0.0004337147000,0.074486320000
+402,0.017147440000,0.0004730240000,0.081361560000
+403,0.018781220000,0.0005178760000,0.089153640000
+404,0.020748010000,0.0005722187000,0.098540480000
+405,0.023190000000,0.0006400000000,0.110200000000
+406,0.026207360000,0.0007245600000,0.124613300000
+407,0.029782480000,0.0008255000000,0.141701700000
+408,0.033880920000,0.0009411600000,0.161303500000
+409,0.038468240000,0.0010698800000,0.183256800000
+410,0.043510000000,0.0012100000000,0.207400000000
+411,0.048995600000,0.0013620910000,0.233692100000
+412,0.055022600000,0.0015307520000,0.262611400000
+413,0.061718800000,0.0017203680000,0.294774600000
+414,0.069212000000,0.0019353230000,0.330798500000
+415,0.077630000000,0.0021800000000,0.371300000000
+416,0.086958110000,0.0024548000000,0.416209100000
+417,0.097176720000,0.0027640000000,0.465464200000
+418,0.108406300000,0.0031178000000,0.519694800000
+419,0.120767200000,0.0035264000000,0.579530300000
+420,0.134380000000,0.0040000000000,0.645600000000
+421,0.149358200000,0.0045462400000,0.718483800000
+422,0.165395700000,0.0051593200000,0.796713300000
+423,0.181983100000,0.0058292800000,0.877845900000
+424,0.198611000000,0.0065461600000,0.959439000000
+425,0.214770000000,0.0073000000000,1.039050100000
+426,0.230186800000,0.0080865070000,1.115367300000
+427,0.244879700000,0.0089087200000,1.188497100000
+428,0.258777300000,0.0097676800000,1.258123300000
+429,0.271807900000,0.0106644300000,1.323929600000
+430,0.283900000000,0.0116000000000,1.385600000000
+431,0.294943800000,0.0125731700000,1.442635200000
+432,0.304896500000,0.0135827200000,1.494803500000
+433,0.313787300000,0.0146296800000,1.542190300000
+434,0.321645400000,0.0157150900000,1.584880700000
+435,0.328500000000,0.0168400000000,1.622960000000
+436,0.334351300000,0.0180073600000,1.656404800000
+437,0.339210100000,0.0192144800000,1.685295900000
+438,0.343121300000,0.0204539200000,1.709874500000
+439,0.346129600000,0.0217182400000,1.730382100000
+440,0.348280000000,0.0230000000000,1.747060000000
+441,0.349599900000,0.0242946100000,1.760044600000
+442,0.350147400000,0.0256102400000,1.769623300000
+443,0.350013000000,0.0269585700000,1.776263700000
+444,0.349287000000,0.0283512500000,1.780433400000
+445,0.348060000000,0.0298000000000,1.782600000000
+446,0.346373300000,0.0313108300000,1.782968200000
+447,0.344262400000,0.0328836800000,1.781699800000
+448,0.341808800000,0.0345211200000,1.779198200000
+449,0.339094100000,0.0362257100000,1.775867100000
+450,0.336200000000,0.0380000000000,1.772110000000
+451,0.333197700000,0.0398466700000,1.768258900000
+452,0.330041100000,0.0417680000000,1.764039000000
+453,0.326635700000,0.0437660000000,1.758943800000
+454,0.322886800000,0.0458426700000,1.752466300000
+455,0.318700000000,0.0480000000000,1.744100000000
+456,0.314025100000,0.0502436800000,1.733559500000
+457,0.308884000000,0.0525730400000,1.720858100000
+458,0.303290400000,0.0549805600000,1.705936900000
+459,0.297257900000,0.0574587200000,1.688737200000
+460,0.290800000000,0.0600000000000,1.669200000000
+461,0.283970100000,0.0626019700000,1.647528700000
+462,0.276721400000,0.0652775200000,1.623412700000
+463,0.268917800000,0.0680420800000,1.596022300000
+464,0.260422700000,0.0709110900000,1.564528000000
+465,0.251100000000,0.0739000000000,1.528100000000
+466,0.240847500000,0.0770160000000,1.486111400000
+467,0.229851200000,0.0802664000000,1.439521500000
+468,0.218407200000,0.0836668000000,1.389879900000
+469,0.206811500000,0.0872328000000,1.338736200000
+470,0.195360000000,0.0909800000000,1.287640000000
+471,0.184213600000,0.0949175500000,1.237422300000
+472,0.173327300000,0.0990458400000,1.187824300000
+473,0.162688100000,0.1033674000000,1.138761100000
+474,0.152283300000,0.1078846000000,1.090148000000
+475,0.142100000000,0.1126000000000,1.041900000000
+476,0.132178600000,0.1175320000000,0.994197600000
+477,0.122569600000,0.1226744000000,0.947347300000
+478,0.113275200000,0.1279928000000,0.901453100000
+479,0.104297900000,0.1334528000000,0.856619300000
+480,0.095640000000,0.1390200000000,0.812950100000
+481,0.087299550000,0.1446764000000,0.770517300000
+482,0.079308040000,0.1504693000000,0.729444800000
+483,0.071717760000,0.1564619000000,0.689913600000
+484,0.064580990000,0.1627177000000,0.652104900000
+485,0.057950010000,0.1693000000000,0.616200000000
+486,0.051862110000,0.1762431000000,0.582328600000
+487,0.046281520000,0.1835581000000,0.550416200000
+488,0.041150880000,0.1912735000000,0.520337600000
+489,0.036412830000,0.1994180000000,0.491967300000
+490,0.032010000000,0.2080200000000,0.465180000000
+491,0.027917200000,0.2171199000000,0.439924600000
+492,0.024144400000,0.2267345000000,0.416183600000
+493,0.020687000000,0.2368571000000,0.393882200000
+494,0.017540400000,0.2474812000000,0.372945900000
+495,0.014700000000,0.2586000000000,0.353300000000
+496,0.012161790000,0.2701849000000,0.334857800000
+497,0.009919960000,0.2822939000000,0.317552100000
+498,0.007967240000,0.2950505000000,0.301337500000
+499,0.006296346000,0.3085780000000,0.286168600000
+500,0.004900000000,0.3230000000000,0.272000000000
+501,0.003777173000,0.3384021000000,0.258817100000
+502,0.002945320000,0.3546858000000,0.246483800000
+503,0.002424880000,0.3716986000000,0.234771800000
+504,0.002236293000,0.3892875000000,0.223453300000
+505,0.002400000000,0.4073000000000,0.212300000000
+506,0.002925520000,0.4256299000000,0.201169200000
+507,0.003836560000,0.4443096000000,0.190119600000
+508,0.005174840000,0.4633944000000,0.179225400000
+509,0.006982080000,0.4829395000000,0.168560800000
+510,0.009300000000,0.5030000000000,0.158200000000
+511,0.012149490000,0.5235693000000,0.148138300000
+512,0.015535880000,0.5445120000000,0.138375800000
+513,0.019477520000,0.5656900000000,0.128994200000
+514,0.023992770000,0.5869653000000,0.120075100000
+515,0.029100000000,0.6082000000000,0.111700000000
+516,0.034814850000,0.6293456000000,0.103904800000
+517,0.041120160000,0.6503068000000,0.096667480000
+518,0.047985040000,0.6708752000000,0.089982720000
+519,0.055378610000,0.6908424000000,0.083845310000
+520,0.063270000000,0.7100000000000,0.078249990000
+521,0.071635010000,0.7281852000000,0.073208990000
+522,0.080462240000,0.7454636000000,0.068678160000
+523,0.089739960000,0.7619694000000,0.064567840000
+524,0.099456450000,0.7778368000000,0.060788350000
+525,0.109600000000,0.7932000000000,0.057250010000
+526,0.120167400000,0.8081104000000,0.053904350000
+527,0.131114500000,0.8224962000000,0.050746640000
+528,0.142367900000,0.8363068000000,0.047752760000
+529,0.153854200000,0.8494916000000,0.044898590000
+530,0.165500000000,0.8620000000000,0.042160000000
+531,0.177257100000,0.8738108000000,0.039507280000
+532,0.189140000000,0.8849624000000,0.036935640000
+533,0.201169400000,0.8954936000000,0.034458360000
+534,0.213365800000,0.9054432000000,0.032088720000
+535,0.225749900000,0.9148501000000,0.029840000000
+536,0.238320900000,0.9237348000000,0.027711810000
+537,0.251066800000,0.9320924000000,0.025694440000
+538,0.263992200000,0.9399226000000,0.023787160000
+539,0.277101700000,0.9472252000000,0.021989250000
+540,0.290400000000,0.9540000000000,0.020300000000
+541,0.303891200000,0.9602561000000,0.018718050000
+542,0.317572600000,0.9660074000000,0.017240360000
+543,0.331438400000,0.9712606000000,0.015863640000
+544,0.345482800000,0.9760225000000,0.014584610000
+545,0.359700000000,0.9803000000000,0.013400000000
+546,0.374083900000,0.9840924000000,0.012307230000
+547,0.388639600000,0.9874182000000,0.011301880000
+548,0.403378400000,0.9903128000000,0.010377920000
+549,0.418311500000,0.9928116000000,0.009529306000
+550,0.433449900000,0.9949501000000,0.008749999000
+551,0.448795300000,0.9967108000000,0.008035200000
+552,0.464336000000,0.9980983000000,0.007381600000
+553,0.480064000000,0.9991120000000,0.006785400000
+554,0.495971300000,0.9997482000000,0.006242800000
+555,0.512050100000,1.0000000000000,0.005749999000
+556,0.528295900000,0.9998567000000,0.005303600000
+557,0.544691600000,0.9993046000000,0.004899800000
+558,0.561209400000,0.9983255000000,0.004534200000
+559,0.577821500000,0.9968987000000,0.004202400000
+560,0.594500000000,0.9950000000000,0.003900000000
+561,0.611220900000,0.9926005000000,0.003623200000
+562,0.627975800000,0.9897426000000,0.003370600000
+563,0.644760200000,0.9864444000000,0.003141400000
+564,0.661569700000,0.9827241000000,0.002934800000
+565,0.678400000000,0.9786000000000,0.002749999000
+566,0.695239200000,0.9740837000000,0.002585200000
+567,0.712058600000,0.9691712000000,0.002438600000
+568,0.728828400000,0.9638568000000,0.002309400000
+569,0.745518800000,0.9581349000000,0.002196800000
+570,0.762100000000,0.9520000000000,0.002100000000
+571,0.778543200000,0.9454504000000,0.002017733000
+572,0.794825600000,0.9384992000000,0.001948200000
+573,0.810926400000,0.9311628000000,0.001889800000
+574,0.826824800000,0.9234576000000,0.001840933000
+575,0.842500000000,0.9154000000000,0.001800000000
+576,0.857932500000,0.9070064000000,0.001766267000
+577,0.873081600000,0.8982772000000,0.001737800000
+578,0.887894400000,0.8892048000000,0.001711200000
+579,0.902318100000,0.8797816000000,0.001683067000
+580,0.916300000000,0.8700000000000,0.001650001000
+581,0.929799500000,0.8598613000000,0.001610133000
+582,0.942798400000,0.8493920000000,0.001564400000
+583,0.955277600000,0.8386220000000,0.001513600000
+584,0.967217900000,0.8275813000000,0.001458533000
+585,0.978600000000,0.8163000000000,0.001400000000
+586,0.989385600000,0.8047947000000,0.001336667000
+587,0.999548800000,0.7930820000000,0.001270000000
+588,1.009089200000,0.7811920000000,0.001205000000
+589,1.018006400000,0.7691547000000,0.001146667000
+590,1.026300000000,0.7570000000000,0.001100000000
+591,1.033982700000,0.7447541000000,0.001068800000
+592,1.040986000000,0.7324224000000,0.001049400000
+593,1.047188000000,0.7200036000000,0.001035600000
+594,1.052466700000,0.7074965000000,0.001021200000
+595,1.056700000000,0.6949000000000,0.001000000000
+596,1.059794400000,0.6822192000000,0.000968640000
+597,1.061799200000,0.6694716000000,0.000929920000
+598,1.062806800000,0.6566744000000,0.000886880000
+599,1.062909600000,0.6438448000000,0.000842560000
+600,1.062200000000,0.6310000000000,0.000800000000
+601,1.060735200000,0.6181555000000,0.000760960000
+602,1.058443600000,0.6053144000000,0.000723680000
+603,1.055224400000,0.5924756000000,0.000685920000
+604,1.050976800000,0.5796379000000,0.000645440000
+605,1.045600000000,0.5668000000000,0.000600000000
+606,1.039036900000,0.5539611000000,0.000547866700
+607,1.031360800000,0.5411372000000,0.000491600000
+608,1.022666200000,0.5283528000000,0.000435400000
+609,1.013047700000,0.5156323000000,0.000383466700
+610,1.002600000000,0.5030000000000,0.000340000000
+611,0.991367500000,0.4904688000000,0.000307253300
+612,0.979331400000,0.4780304000000,0.000283160000
+613,0.966491600000,0.4656776000000,0.000265440000
+614,0.952847900000,0.4534032000000,0.000251813300
+615,0.938400000000,0.4412000000000,0.000240000000
+616,0.923194000000,0.4290800000000,0.000229546700
+617,0.907244000000,0.4170360000000,0.000220640000
+618,0.890502000000,0.4050320000000,0.000211960000
+619,0.872920000000,0.3930320000000,0.000202186700
+620,0.854449900000,0.3810000000000,0.000190000000
+621,0.835084000000,0.3689184000000,0.000174213300
+622,0.814946000000,0.3568272000000,0.000155640000
+623,0.794186000000,0.3447768000000,0.000135960000
+624,0.772954000000,0.3328176000000,0.000116853300
+625,0.751400000000,0.3210000000000,0.000100000000
+626,0.729583600000,0.3093381000000,0.000086133330
+627,0.707588800000,0.2978504000000,0.000074600000
+628,0.685602200000,0.2865936000000,0.000065000000
+629,0.663810400000,0.2756245000000,0.000056933330
+630,0.642400000000,0.2650000000000,0.000049999990
+631,0.621514900000,0.2547632000000,0.000044160000
+632,0.601113800000,0.2448896000000,0.000039480000
+633,0.581105200000,0.2353344000000,0.000035720000
+634,0.561397700000,0.2260528000000,0.000032640000
+635,0.541900000000,0.2170000000000,0.000030000000
+636,0.522599500000,0.2081616000000,0.000027653330
+637,0.503546400000,0.1995488000000,0.000025560000
+638,0.484743600000,0.1911552000000,0.000023640000
+639,0.466193900000,0.1829744000000,0.000021813330
+640,0.447900000000,0.1750000000000,0.000020000000
+641,0.429861300000,0.1672235000000,0.000018133330
+642,0.412098000000,0.1596464000000,0.000016200000
+643,0.394644000000,0.1522776000000,0.000014200000
+644,0.377533300000,0.1451259000000,0.000012133330
+645,0.360800000000,0.1382000000000,0.000010000000
+646,0.344456300000,0.1315003000000,0.000007733333
+647,0.328516800000,0.1250248000000,0.000005400000
+648,0.313019200000,0.1187792000000,0.000003200000
+649,0.298001100000,0.1127691000000,0.000001333333
+650,0.283500000000,0.1070000000000,0.000000000000
+651,0.269544800000,0.1014762000000,0.000000000000
+652,0.256118400000,0.0961886400000,0.000000000000
+653,0.243189600000,0.0911229600000,0.000000000000
+654,0.230727200000,0.0862648500000,0.000000000000
+655,0.218700000000,0.0816000000000,0.000000000000
+656,0.207097100000,0.0771206400000,0.000000000000
+657,0.195923200000,0.0728255200000,0.000000000000
+658,0.185170800000,0.0687100800000,0.000000000000
+659,0.174832300000,0.0647697600000,0.000000000000
+660,0.164900000000,0.0610000000000,0.000000000000
+661,0.155366700000,0.0573962100000,0.000000000000
+662,0.146230000000,0.0539550400000,0.000000000000
+663,0.137490000000,0.0506737600000,0.000000000000
+664,0.129146700000,0.0475496500000,0.000000000000
+665,0.121200000000,0.0445800000000,0.000000000000
+666,0.113639700000,0.0417587200000,0.000000000000
+667,0.106465000000,0.0390849600000,0.000000000000
+668,0.099690440000,0.0365638400000,0.000000000000
+669,0.093330610000,0.0342004800000,0.000000000000
+670,0.087400000000,0.0320000000000,0.000000000000
+671,0.081900960000,0.0299626100000,0.000000000000
+672,0.076804280000,0.0280766400000,0.000000000000
+673,0.072077120000,0.0263293600000,0.000000000000
+674,0.067686640000,0.0247080500000,0.000000000000
+675,0.063600000000,0.0232000000000,0.000000000000
+676,0.059806850000,0.0218007700000,0.000000000000
+677,0.056282160000,0.0205011200000,0.000000000000
+678,0.052971040000,0.0192810800000,0.000000000000
+679,0.049818610000,0.0181206900000,0.000000000000
+680,0.046770000000,0.0170000000000,0.000000000000
+681,0.043784050000,0.0159037900000,0.000000000000
+682,0.040875360000,0.0148371800000,0.000000000000
+683,0.038072640000,0.0138106800000,0.000000000000
+684,0.035404610000,0.0128347800000,0.000000000000
+685,0.032900000000,0.0119200000000,0.000000000000
+686,0.030564190000,0.0110683100000,0.000000000000
+687,0.028380560000,0.0102733900000,0.000000000000
+688,0.026344840000,0.0095333110000,0.000000000000
+689,0.024452750000,0.0088461570000,0.000000000000
+690,0.022700000000,0.0082100000000,0.000000000000
+691,0.021084290000,0.0076237810000,0.000000000000
+692,0.019599880000,0.0070854240000,0.000000000000
+693,0.018237320000,0.0065914760000,0.000000000000
+694,0.016987170000,0.0061384850000,0.000000000000
+695,0.015840000000,0.0057230000000,0.000000000000
+696,0.014790640000,0.0053430590000,0.000000000000
+697,0.013831320000,0.0049957960000,0.000000000000
+698,0.012948680000,0.0046764040000,0.000000000000
+699,0.012129200000,0.0043800750000,0.000000000000
+700,0.011359160000,0.0041020000000,0.000000000000
+701,0.010629350000,0.0038384530000,0.000000000000
+702,0.009938846000,0.0035890990000,0.000000000000
+703,0.009288422000,0.0033542190000,0.000000000000
+704,0.008678854000,0.0031340930000,0.000000000000
+705,0.008110916000,0.0029290000000,0.000000000000
+706,0.007582388000,0.0027381390000,0.000000000000
+707,0.007088746000,0.0025598760000,0.000000000000
+708,0.006627313000,0.0023932440000,0.000000000000
+709,0.006195408000,0.0022372750000,0.000000000000
+710,0.005790346000,0.0020910000000,0.000000000000
+711,0.005409826000,0.0019535870000,0.000000000000
+712,0.005052583000,0.0018245800000,0.000000000000
+713,0.004717512000,0.0017035800000,0.000000000000
+714,0.004403507000,0.0015901870000,0.000000000000
+715,0.004109457000,0.0014840000000,0.000000000000
+716,0.003833913000,0.0013844960000,0.000000000000
+717,0.003575748000,0.0012912680000,0.000000000000
+718,0.003334342000,0.0012040920000,0.000000000000
+719,0.003109075000,0.0011227440000,0.000000000000
+720,0.002899327000,0.0010470000000,0.000000000000
+721,0.002704348000,0.0009765896000,0.000000000000
+722,0.002523020000,0.0009111088000,0.000000000000
+723,0.002354168000,0.0008501332000,0.000000000000
+724,0.002196616000,0.0007932384000,0.000000000000
+725,0.002049190000,0.0007400000000,0.000000000000
+726,0.001910960000,0.0006900827000,0.000000000000
+727,0.001781438000,0.0006433100000,0.000000000000
+728,0.001660110000,0.0005994960000,0.000000000000
+729,0.001546459000,0.0005584547000,0.000000000000
+730,0.001439971000,0.0005200000000,0.000000000000
+731,0.001340042000,0.0004839136000,0.000000000000
+732,0.001246275000,0.0004500528000,0.000000000000
+733,0.001158471000,0.0004183452000,0.000000000000
+734,0.001076430000,0.0003887184000,0.000000000000
+735,0.000999949300,0.0003611000000,0.000000000000
+736,0.000928735800,0.0003353835000,0.000000000000
+737,0.000862433200,0.0003114404000,0.000000000000
+738,0.000800750300,0.0002891656000,0.000000000000
+739,0.000743396000,0.0002684539000,0.000000000000
+740,0.000690078600,0.0002492000000,0.000000000000
+741,0.000640515600,0.0002313019000,0.000000000000
+742,0.000594502100,0.0002146856000,0.000000000000
+743,0.000551864600,0.0001992884000,0.000000000000
+744,0.000512429000,0.0001850475000,0.000000000000
+745,0.000476021300,0.0001719000000,0.000000000000
+746,0.000442453600,0.0001597781000,0.000000000000
+747,0.000411511700,0.0001486044000,0.000000000000
+748,0.000382981400,0.0001383016000,0.000000000000
+749,0.000356649100,0.0001287925000,0.000000000000
+750,0.000332301100,0.0001200000000,0.000000000000
+751,0.000309758600,0.0001118595000,0.000000000000
+752,0.000288887100,0.0001043224000,0.000000000000
+753,0.000269539400,0.0000973356000,0.000000000000
+754,0.000251568200,0.0000908458700,0.000000000000
+755,0.000234826100,0.0000848000000,0.000000000000
+756,0.000219171000,0.0000791466700,0.000000000000
+757,0.000204525800,0.0000738580000,0.000000000000
+758,0.000190840500,0.0000689160000,0.000000000000
+759,0.000178065400,0.0000643026700,0.000000000000
+760,0.000166150500,0.0000600000000,0.000000000000
+761,0.000155023600,0.0000559818700,0.000000000000
+762,0.000144621900,0.0000522256000,0.000000000000
+763,0.000134909800,0.0000487184000,0.000000000000
+764,0.000125852000,0.0000454474700,0.000000000000
+765,0.000117413000,0.0000424000000,0.000000000000
+766,0.000109551500,0.0000395610400,0.000000000000
+767,0.000102224500,0.0000369151200,0.000000000000
+768,0.000095394450,0.0000344486800,0.000000000000
+769,0.000089023900,0.0000321481600,0.000000000000
+770,0.000083075270,0.0000300000000,0.000000000000
+771,0.000077512690,0.0000279912500,0.000000000000
+772,0.000072313040,0.0000261135600,0.000000000000
+773,0.000067457780,0.0000243602400,0.000000000000
+774,0.000062928440,0.0000227246100,0.000000000000
+775,0.000058706520,0.0000212000000,0.000000000000
+776,0.000054770280,0.0000197785500,0.000000000000
+777,0.000051099180,0.0000184528500,0.000000000000
+778,0.000047676540,0.0000172168700,0.000000000000
+779,0.000044485670,0.0000160645900,0.000000000000
+780,0.000041509940,0.0000149900000,0.000000000000
+781,0.000038733240,0.0000139872800,0.000000000000
+782,0.000036142030,0.0000130515500,0.000000000000
+783,0.000033723520,0.0000121781800,0.000000000000
+784,0.000031464870,0.0000113625400,0.000000000000
+785,0.000029353260,0.0000106000000,0.000000000000
+786,0.000027375730,0.0000098858770,0.000000000000
+787,0.000025524330,0.0000092173040,0.000000000000
+788,0.000023793760,0.0000085923620,0.000000000000
+789,0.000022178700,0.0000080091330,0.000000000000
+790,0.000020673830,0.0000074657000,0.000000000000
+791,0.000019272260,0.0000069595670,0.000000000000
+792,0.000017966400,0.0000064879950,0.000000000000
+793,0.000016749910,0.0000060486990,0.000000000000
+794,0.000015616480,0.0000056393960,0.000000000000
+795,0.000014559770,0.0000052578000,0.000000000000
+796,0.000013573870,0.0000049017710,0.000000000000
+797,0.000012654360,0.0000045697200,0.000000000000
+798,0.000011797230,0.0000042601940,0.000000000000
+799,0.000010998440,0.0000039717390,0.000000000000
+800,0.000010253980,0.0000037029000,0.000000000000
+801,0.000009559646,0.0000034521630,0.000000000000
+802,0.000008912044,0.0000032183020,0.000000000000
+803,0.000008308358,0.0000030003000,0.000000000000
+804,0.000007745769,0.0000027971390,0.000000000000
+805,0.000007221456,0.0000026078000,0.000000000000
+806,0.000006732475,0.0000024312200,0.000000000000
+807,0.000006276423,0.0000022665310,0.000000000000
+808,0.000005851304,0.0000021130130,0.000000000000
+809,0.000005455118,0.0000019699430,0.000000000000
+810,0.000005085868,0.0000018366000,0.000000000000
+811,0.000004741466,0.0000017122300,0.000000000000
+812,0.000004420236,0.0000015962280,0.000000000000
+813,0.000004120783,0.0000014880900,0.000000000000
+814,0.000003841716,0.0000013873140,0.000000000000
+815,0.000003581652,0.0000012934000,0.000000000000
+816,0.000003339127,0.0000012058200,0.000000000000
+817,0.000003112949,0.0000011241430,0.000000000000
+818,0.000002902121,0.0000010480090,0.000000000000
+819,0.000002705645,0.0000009770578,0.000000000000
+820,0.000002522525,0.0000009109300,0.000000000000
+821,0.000002351726,0.0000008492513,0.000000000000
+822,0.000002192415,0.0000007917212,0.000000000000
+823,0.000002043902,0.0000007380904,0.000000000000
+824,0.000001905497,0.0000006881098,0.000000000000
+825,0.000001776509,0.0000006415300,0.000000000000
+826,0.000001656215,0.0000005980895,0.000000000000
+827,0.000001544022,0.0000005575746,0.000000000000
+828,0.000001439440,0.0000005198080,0.000000000000
+829,0.000001341977,0.0000004846123,0.000000000000
+830,0.000001251141,0.0000004518100,0.000000000000