Mixed gradient-value noise that generates it's values based on Minecraft biome data.

BiomeControlledGradValPerlinNoise.java

package io.github.opencubicchunks.cubicchunks.cubicgen.noise;

import com.flowpowered.noise.Utils;
import com.flowpowered.noise.module.Module;
import io.github.opencubicchunks.cubicchunks.cubicgen.math.Vec2d;
import net.minecraft.util.math.MathHelper;

public class BiomeControlledGradValPerlinNoise extends Module {
    private static final int X_NOISE_GEN = 1619;
    private static final int Y_NOISE_GEN = 31337;
    private static final int Z_NOISE_GEN = 6971;
    private static final int SEED_NOISE_GEN = 1013;
    private static final int SHIFT_NOISE_GEN = 8;

    private final double maxVal;
    private int octaves;
    private double fx;
    private double fy;
    private double fz;
    private double valleyDepthFactor;
    private final double scale;
    private final double offset;
    private final double fxi;
    private final double fyi;
    private final double fzi;
    private final int seed;

    private BiomeDataProvider data;

    /**
     * Generates a gradient-coherent-noise value from the coordinates of a three-dimensional input value.
     *
     * @param x                 The @a x coordinate of the input value.
     * @param y                 The @a y coordinate of the input value.
     * @param z                 The @a z coordinate of the input value.
     * @param seed              The random number seed.
     * @param valleyDepthFactor
     * @return The generated gradient-coherent-noise value.
     * <p/>
     * The return value ranges from 0 to 1.
     * <p/>
     * For an explanation of the difference between <i>gradient</i> noise and <i>value</i> noise, see the comments for the GradientNoise3D() function.
     */
    public static void gradientCoherentNoise3D(double x, double y, double z,
                                               double freqInvX, double freqInvY, double freqInvZ,
                                               int seed, BiomeDataProvider data, double valleyDepthFactor,
                                               Vec2d output) {

        // Create a unit-length cube aligned along an integer boundary.  This cube
        // surrounds the input point.

        int x0 = ((x > 0.0) ? (int) x : (int) x - 1);
        int x1 = x0 + 1;

        int y0 = ((y > 0.0) ? (int) y : (int) y - 1);
        int y1 = y0 + 1;

        int z0 = ((z > 0.0) ? (int) z : (int) z - 1);
        int z1 = z0 + 1;

        // world coordinates for biome data
        int wx0 = MathHelper.floor(x0 * freqInvX);
        int wy0 = MathHelper.floor(y0 * freqInvY);
        int wz0 = MathHelper.floor(z0 * freqInvZ);

        int wx1 = MathHelper.floor(x1 * freqInvX);
        int wy1 = MathHelper.floor(y1 * freqInvY);
        int wz1 = MathHelper.floor(z1 * freqInvZ);

        // Map the difference between the coordinates of the input value and the
        // coordinates of the cube's outer-lower-left vertex onto an S-curve.
        double xs = Utils.sCurve5(x - (double) x0);
        double ys = Utils.sCurve5(y - (double) y0);
        double zs = Utils.sCurve5(z - (double) z0);

        // Now calculate the noise values at each vertex of the cube.  To generate
        // the coherent-noise value at the input point, interpolate these eight
        // noise values using the S-curve value as the interpolant (trilinear
        // interpolation.)
        Vec2d n0 = new Vec2d(0, 0);
        Vec2d n1 = new Vec2d(0, 0);
        Vec2d ix0 = new Vec2d(0, 0);
        Vec2d ix1 = new Vec2d(0, 0);
        Vec2d iy0 = new Vec2d(0, 0);
        Vec2d iy1 = new Vec2d(0, 0);

        gradvalBiomeNoise3D(x, y, z, x0, y0, z0, wx0, wy0, wz0, seed, data, n0);
        gradvalBiomeNoise3D(x, y, z, x1, y0, z0, wx1, wy0, wz0, seed, data, n1);
        linearInterp(n0, n1, xs, ix0);

        gradvalBiomeNoise3D(x, y, z, x0, y1, z0, wx0, wy1, wz0, seed, data, n0);
        gradvalBiomeNoise3D(x, y, z, x1, y1, z0, wx1, wy1, wz0, seed, data, n1);
        linearInterp(n0, n1, xs, ix1);
        linearInterp(ix0, ix1, ys, iy0);

        gradvalBiomeNoise3D(x, y, z, x0, y0, z1, wx0, wy0, wz1, seed, data, n0);
        gradvalBiomeNoise3D(x, y, z, x1, y0, z1, wx1, wy0, wz1, seed, data, n1);
        linearInterp(n0, n1, xs, ix0);
        gradvalBiomeNoise3D(x, y, z, x0, y1, z1, wx0, wy1, wz1, seed, data, n0);
        gradvalBiomeNoise3D(x, y, z, x1, y1, z1, wx1, wy1, wz1, seed, data, n1);
        linearInterp(n0, n1, xs, ix1);
        linearInterp(ix0, ix1, ys, iy1);

        linearInterp(iy0, iy1, zs, output);
    }

    private static void linearInterp(Vec2d x0, Vec2d x1, double a, Vec2d out) {
        out.x = Utils.linearInterp(x0.x, x1.x, a);
        out.y = Utils.linearInterp(x0.y, x1.y, a);
    }

    /**
     * Generates mixed gradient and value noise using biome data basis for given coordinates,
     * specified as pair of integer and fractional parts.
     * <p>
     * The difference between fx and ix must be less than or equal to one.
     * The difference between @a fy and @a iy must be less than or equal to one.
     * The difference between @a fz and @a iz must be less than or equal to one.
     * <p/>
     * The noise gen
     * <p/>
     * The gradient part ranges from -1 to 1 multiplied by biome factor.
     * The value part is biome offset.
     * <p/>
     * This function generates a gradient-noise value by performing the following steps: - It first calculates a random normalized vector based on the nearby integer value passed to this function. -
     * It then calculates a new value by adding this vector to the nearby integer value passed to this function. - It then calculates the dot product of the above-generated value and the
     * floating-point input value passed to this function.
     * <p/>
     * A noise function differs from a random-number generator because it always returns the same output value if the same input value is passed to it.
     *
     * @param fx     The floating-point @a x coordinate of the input value.
     * @param fy     The floating-point @a y coordinate of the input value.
     * @param fz     The floating-point @a z coordinate of the input value.
     * @param ix     The integer @a x coordinate of a nearby value.
     * @param iy     The integer @a y coordinate of a nearby value.
     * @param iz     The integer @a z coordinate of a nearby value.
     * @param wx     World x coordinate for biome data
     * @param wy     World y coordinate for biome data
     * @param wz     World z coordinate for biome data
     * @param seed   The random number seed.
     * @param data   Source of biome data
     * @param output The output value. x is gradient component, y is value component
     */
    public static void gradvalBiomeNoise3D(double fx, double fy, double fz,
                                           int ix, int iy, int iz,
                                           int wx, int wy, int wz,
                                           int seed, BiomeDataProvider data, Vec2d output) {

        data.prepare(wx, wy, wz);
        double factor = data.variation() * 2; // * 2 because RANDOM_VECTORS is halved as an optimization

        // Randomly generate a gradient vector given the integer coordinates of the
        // input value.  This implementation generates a random number and uses it
        // as an index into a normalized-vector lookup table.
        int vectorIndex = (X_NOISE_GEN * ix + Y_NOISE_GEN * iy + Z_NOISE_GEN * iz + SEED_NOISE_GEN * seed);
        vectorIndex ^= (vectorIndex >> SHIFT_NOISE_GEN);
        vectorIndex &= 0xff;

        double xvGradient = Utils.RANDOM_VECTORS[(vectorIndex << 2)] * factor;
        double yvGradient = Utils.RANDOM_VECTORS[(vectorIndex << 2) + 1] * factor;
        double zvGradient = Utils.RANDOM_VECTORS[(vectorIndex << 2) + 2] * factor;

        // Set up us another vector equal to the distance between the two vectors
        // passed to this function.
        double xvPoint = (fx - ix);
        double yvPoint = (fy - iy);
        double zvPoint = (fz - iz);

        // Now compute the dot product of the gradient vector with the distance
        // vector.  The resulting value is gradient noise.  Apply a scaling and
        // offset value so that this noise value ranges from 0 to 1.
        output.x = (xvGradient * xvPoint) + (yvGradient * yvPoint) + (zvGradient * zvPoint);
        output.y = data.offset();
    }

    public BiomeControlledGradValPerlinNoise(BiomeDataProvider data, int octaves, long seed,
                                             boolean normalized, double minNorm, double maxNorm,
                                             double fx, double fy, double fz, double valleyDepthFactor) {
        super(0);
        this.data = data;

        this.fx = fx;
        this.fy = fy;
        this.fz = fz;

        fxi = 1.0/fx;
        fyi = 1.0/fy;
        fzi = 1.0/fz;

        maxVal = (Math.pow(0.5, octaves) - 1) / (0.5 - 1);
        scale = normalized ? (1.0/maxVal) * (maxNorm - minNorm) / 2 : 1;
        offset = normalized ? (maxNorm + minNorm) / 2 : 0;

        this.octaves = octaves;
        this.valleyDepthFactor = valleyDepthFactor;
        this.seed = (int) (seed ^ (seed >>> 32));
    }

    @Override
    public int getSourceModuleCount() {
        return 0;
    }

    @Override
    public double getValue(double x, double y, double z) {
        double x1 = x;
        double y1 = y;
        double z1 = z;

        double fxi = this.fxi;
        double fyi = this.fyi;
        double fzi = this.fzi;

        double curPersistence = 1.0;
        int seed;

        x1 *= fx;
        y1 *= fy;
        z1 *= fz;

        Vec2d out = new Vec2d(0, 0);
        Vec2d temp = new Vec2d(0, 0);

        for (int curOctave = 0; curOctave < octaves; curOctave++) {
            // Get the coherent-noise value from the input value and add it to the
            // final result.
            seed = this.seed + curOctave;
            BiomeControlledGradValPerlinNoise.gradientCoherentNoise3D(
                    x1, y1, z1, fxi, fyi, fzi,
                    seed, data, valleyDepthFactor, temp);
            out.add(temp.mul(curPersistence));

            // Prepare the next octave.
            x1 *= 2;
            y1 *= 2;
            z1 *= 2;
            fxi *= 0.5;
            fyi *= 0.5;
            fzi *= 0.5;
            curPersistence *= 0.5;
        }

        out.mul(scale).add(offset);
        
        if (y < out.y) {
            out.x *= valleyDepthFactor;
        }
        
        return out.x + out.y;
    }

    public interface BiomeDataProvider {
        void prepare(int x, int y, int z);

        double variation();

        double offset();
    }
}