Advanced mantle editing

src/main/java/com/volmit/iris/util/math/INode.java

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+/*
+ * Iris is a World Generator for Minecraft Bukkit Servers
+ * Copyright (c) 2021 Arcane Arts (Volmit Software)
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+package com.volmit.iris.util.math;
+
+import lombok.Data;
+import org.bukkit.util.Vector;
+
+@Data
+public class INode {
+
+    private Vector position;
+    private double tension;
+    private double bias;
+    private double continuity;
+
+    public INode() {
+        this(new Vector(0,0,0));
+    }
+
+    public INode(INode other) {
+        this.position = other.position;
+
+        this.tension = other.tension;
+        this.bias = other.bias;
+        this.continuity = other.continuity;
+    }
+
+    public INode(Vector position) {
+        this.position = position;
+    }
+}

src/main/java/com/volmit/iris/util/math/KochanekBartelsInterpolation.java

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+/*
+ * Iris is a World Generator for Minecraft Bukkit Servers
+ * Copyright (c) 2021 Arcane Arts (Volmit Software)
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+package com.volmit.iris.util.math;
+
+import org.bukkit.util.Vector;
+
+import java.util.Collections;
+import java.util.List;
+
+public class KochanekBartelsInterpolation implements PathInterpolation {
+
+    private List<INode> nodes;
+    private Vector[] coeffA;
+    private Vector[] coeffB;
+    private Vector[] coeffC;
+    private Vector[] coeffD;
+    private double scaling;
+
+    public KochanekBartelsInterpolation() {
+        setNodes(Collections.emptyList());
+    }
+
+    @Override
+    public void setNodes(List<INode> nodes) {
+        this.nodes = nodes;
+        recalc();
+    }
+
+    private void recalc() {
+        final int nNodes = nodes.size();
+        coeffA = new Vector[nNodes];
+        coeffB = new Vector[nNodes];
+        coeffC = new Vector[nNodes];
+        coeffD = new Vector[nNodes];
+
+        if (nNodes == 0) {
+            return;
+        }
+
+        INode nodeB = nodes.get(0);
+        double tensionB = nodeB.getTension();
+        double biasB = nodeB.getBias();
+        double continuityB = nodeB.getContinuity();
+        for (int i = 0; i < nNodes; ++i) {
+            final double tensionA = tensionB;
+            final double biasA = biasB;
+            final double continuityA = continuityB;
+
+            if (i + 1 < nNodes) {
+                nodeB = nodes.get(i + 1);
+                tensionB = nodeB.getTension();
+                biasB = nodeB.getBias();
+                continuityB = nodeB.getContinuity();
+            }
+
+            // Kochanek-Bartels tangent coefficients
+            final double ta = (1 - tensionA) * (1 + biasA) * (1 + continuityA) / 2; // Factor for lhs of d[i]
+            final double tb = (1 - tensionA) * (1 - biasA) * (1 - continuityA) / 2; // Factor for rhs of d[i]
+            final double tc = (1 - tensionB) * (1 + biasB) * (1 - continuityB) / 2; // Factor for lhs of d[i+1]
+            final double td = (1 - tensionB) * (1 - biasB) * (1 + continuityB) / 2; // Factor for rhs of d[i+1]
+
+            coeffA[i] = linearCombination(i, -ta, ta - tb - tc + 2, tb + tc - td - 2, td);
+            coeffB[i] = linearCombination(i, 2 * ta, -2 * ta + 2 * tb + tc - 3, -2 * tb - tc + td + 3, -td);
+            coeffC[i] = linearCombination(i, -ta, ta - tb, tb, 0);
+            //coeffD[i] = linearCombination(i,    0,               1,             0,   0);
+            coeffD[i] = retrieve(i); // this is an optimization
+        }
+
+        scaling = nodes.size() - 1;
+    }
+
+    /**
+     * Returns the linear combination of the given coefficients with the nodes adjacent to baseIndex.
+     *
+     * @param baseIndex node index
+     * @param f1 coefficient for baseIndex-1
+     * @param f2 coefficient for baseIndex
+     * @param f3 coefficient for baseIndex+1
+     * @param f4 coefficient for baseIndex+2
+     * @return linear combination of nodes[n-1..n+2] with f1..4
+     */
+    private Vector linearCombination(int baseIndex, double f1, double f2, double f3, double f4) {
+        final Vector r1 = retrieve(baseIndex - 1).multiply(f1);
+        final Vector r2 = retrieve(baseIndex    ).multiply(f2);
+        final Vector r3 = retrieve(baseIndex + 1).multiply(f3);
+        final Vector r4 = retrieve(baseIndex + 2).multiply(f4);
+
+        return r1.add(r2).add(r3).add(r4);
+    }
+
+    /**
+     * Retrieves a node. Indexes are clamped to the valid range.
+     *
+     * @param index node index to retrieve
+     * @return nodes[clamp(0, nodes.length-1)]
+     */
+    private Vector retrieve(int index) {
+        if (index < 0) {
+            return fastRetrieve(0);
+        }
+
+        if (index >= nodes.size()) {
+            return fastRetrieve(nodes.size() - 1);
+        }
+
+        return fastRetrieve(index);
+    }
+
+    private Vector fastRetrieve(int index) {
+        return nodes.get(index).getPosition();
+    }
+
+    @Override
+    public Vector getPosition(double position) {
+        if (coeffA == null) {
+            throw new IllegalStateException("Must call setNodes first.");
+        }
+
+        if (position > 1) {
+            return null;
+        }
+
+        position *= scaling;
+
+        final int index = (int) Math.floor(position);
+        final double remainder = position - index;
+
+        final Vector a = coeffA[index];
+        final Vector b = coeffB[index];
+        final Vector c = coeffC[index];
+        final Vector d = coeffD[index];
+
+        return a.multiply(remainder).add(b).multiply(remainder).add(c).multiply(remainder).add(d);
+    }
+
+    @Override
+    public Vector get1stDerivative(double position) {
+        if (coeffA == null) {
+            throw new IllegalStateException("Must call setNodes first.");
+        }
+
+        if (position > 1) {
+            return null;
+        }
+
+        position *= scaling;
+
+        final int index = (int) Math.floor(position);
+        //final double remainder = position - index;
+
+        final Vector a = coeffA[index];
+        final Vector b = coeffB[index];
+        final Vector c = coeffC[index];
+
+        return a.multiply(1.5 * position - 3.0 * index).add(b).multiply(2.0 * position).add(a.multiply(1.5 * index).subtract(b).multiply(2.0 * index)).add(c).multiply(scaling);
+    }
+
+    @Override
+    public double arcLength(double positionA, double positionB) {
+        if (coeffA == null) {
+            throw new IllegalStateException("Must call setNodes first.");
+        }
+
+        if (positionA > positionB) {
+            return arcLength(positionB, positionA);
+        }
+
+        positionA *= scaling;
+        positionB *= scaling;
+
+        final int indexA = (int) Math.floor(positionA);
+        final double remainderA = positionA - indexA;
+
+        final int indexB = (int) Math.floor(positionB);
+        final double remainderB = positionB - indexB;
+
+        return arcLengthRecursive(indexA, remainderA, indexB, remainderB);
+    }
+
+    /**
+     * Assumes a < b.
+     */
+    private double arcLengthRecursive(int indexLeft, double remainderLeft, int indexRight, double remainderRight) {
+        switch (indexRight - indexLeft) {
+            case 0:
+                return arcLengthRecursive(indexLeft, remainderLeft, remainderRight);
+
+            case 1:
+                // This case is merely a speed-up for a very common case
+                return arcLengthRecursive(indexLeft, remainderLeft, 1.0)
+                    + arcLengthRecursive(indexRight, 0.0, remainderRight);
+
+            default:
+                return arcLengthRecursive(indexLeft, remainderLeft, indexRight - 1, 1.0)
+                    + arcLengthRecursive(indexRight, 0.0, remainderRight);
+        }
+    }
+
+    private double arcLengthRecursive(int index, double remainderLeft, double remainderRight) {
+        final Vector a = coeffA[index].multiply(3.0);
+        final Vector b = coeffB[index].multiply(2.0);
+        final Vector c = coeffC[index];
+
+        final int nPoints = 8;
+
+        double accum = a.multiply(remainderLeft).add(b).multiply(remainderLeft).add(c).length() / 2.0;
+        for (int i = 1; i < nPoints - 1; ++i) {
+            double t = ((double) i) / nPoints;
+            t = (remainderRight - remainderLeft) * t + remainderLeft;
+            accum += a.multiply(t).add(b).multiply(t).add(c).length();
+        }
+
+        accum += a.multiply(remainderRight).add(b).multiply(remainderRight).add(c).length() / 2.0;
+        return accum * (remainderRight - remainderLeft) / nPoints;
+    }
+
+    @Override
+    public int getSegment(double position) {
+        if (coeffA == null) {
+            throw new IllegalStateException("Must call setNodes first.");
+        }
+
+        if (position > 1) {
+            return Integer.MAX_VALUE;
+        }
+
+        position *= scaling;
+
+        return (int) Math.floor(position);
+    }
+
+}

src/main/java/com/volmit/iris/util/math/PathInterpolation.java

@@ -0,0 +1,70 @@
+/*
+ * Iris is a World Generator for Minecraft Bukkit Servers
+ * Copyright (c) 2021 Arcane Arts (Volmit Software)
+ *
+ * This program is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program.  If not, see <https://www.gnu.org/licenses/>.
+ */
+
+package com.volmit.iris.util.math;
+
+import org.bukkit.util.Vector;
+
+import java.util.List;
+
+public interface PathInterpolation {
+
+    /**
+     * Sets nodes to be used by subsequent calls to
+     * {@link #getPosition(double)} and the other methods.
+     *
+     * @param nodes the nodes
+     */
+    void setNodes(List<INode> nodes);
+
+    /**
+     * Gets the result of f(position).
+     *
+     * @param position the position to interpolate
+     * @return the result
+     */
+    Vector getPosition(double position);
+
+    /**
+     * Gets the result of f'(position).
+     *
+     * @param position the position to interpolate
+     * @return the result
+     */
+    Vector get1stDerivative(double position);
+
+    /**
+     * Gets the result of &int;<sub>a</sub><sup style="position: relative; left: -1ex">b</sup>|f'(t)| dt.<br />
+     * That means it calculates the arc length (in meters) between positionA
+     * and positionB.
+     *
+     * @param positionA lower limit
+     * @param positionB upper limit
+     * @return the arc length
+     */
+    double arcLength(double positionA, double positionB);
+
+    /**
+     * Get the segment position.
+     *
+     * @param position the position
+     * @return the segment position
+     */
+    int getSegment(double position);
+
+}