Added /curve.

src/main/java/com/sk89q/worldedit/EditSession.java

@@ -41,6 +41,9 @@ import com.sk89q.worldedit.blocks.BlockType;
 import com.sk89q.worldedit.expression.Expression;
 import com.sk89q.worldedit.expression.ExpressionException;
 import com.sk89q.worldedit.expression.runtime.RValue;
+import com.sk89q.worldedit.interpolation.Interpolation;
+import com.sk89q.worldedit.interpolation.KochanekBartelsInterpolation;
+import com.sk89q.worldedit.interpolation.Node;
 import com.sk89q.worldedit.masks.Mask;
 import com.sk89q.worldedit.patterns.Pattern;
 import com.sk89q.worldedit.regions.CuboidRegion;
@@ -2999,10 +3002,10 @@ public class EditSession {
     /**
      * Draws a line (out of blocks) between two vectors.
      *
-     * @param pattern The block pattern used to draw the line
+     * @param pattern The block pattern used to draw the line.
      * @param pos1 One of the points that define the line.
      * @param pos2 The other point that defines the line.
-     * @param radius The radius of the line.
+     * @param radius The radius (thickness) of the line.
      * @param filled If false, only a shell will be generated.
      *
      * @return number of blocks affected
@@ -3012,25 +3015,15 @@ public class EditSession {
             throws MaxChangedBlocksException {
 
         Set<Vector> vset = new HashSet<Vector>();
-        int affected = 0;
         boolean notdrawn = true;
 
-        int ceilrad = (int) Math.ceil(radius);
         int x1 = pos1.getBlockX(), y1 = pos1.getBlockY(), z1 = pos1.getBlockZ();
         int x2 = pos2.getBlockX(), y2 = pos2.getBlockY(), z2 = pos2.getBlockZ();
         int tipx = x1, tipy = y1, tipz = z1;
         int dx = Math.abs(x2 - x1), dy = Math.abs(y2 - y1), dz = Math.abs(z2 - z1);
 
         if (dx + dy + dz == 0) {
-            for (int loopx = tipx - ceilrad; loopx <= tipx + ceilrad; loopx++) {
+            vset.add(new Vector(tipx, tipy, tipz));
-                for (int loopy = tipy - ceilrad; loopy <= tipy + ceilrad; loopy++) {
-                    for (int loopz = tipz - ceilrad; loopz <= tipz + ceilrad; loopz++) {
-                        if (hypot(loopx - tipx, loopy - tipy, loopz - tipz) <= radius) {
-                            vset.add(new Vector(loopx, loopy, loopz));
-                        }
-                    }
-                }
-            }
             notdrawn = false;
         }
 
@@ -3040,15 +3033,7 @@ public class EditSession {
                 tipy = (int) Math.round(y1 + domstep * ((double) dy) / ((double) dx) * (y2 - y1 > 0 ? 1 : -1));
                 tipz = (int) Math.round(z1 + domstep * ((double) dz) / ((double) dx) * (z2 - z1 > 0 ? 1 : -1));
 
-                for (int loopx = tipx - ceilrad; loopx <= tipx + ceilrad; loopx++) {
+                vset.add(new Vector(tipx, tipy, tipz));
-                    for (int loopy = tipy - ceilrad; loopy <= tipy + ceilrad; loopy++) {
-                        for (int loopz = tipz - ceilrad; loopz <= tipz + ceilrad; loopz++) {
-                            if (hypot(loopx - tipx, loopy - tipy, loopz - tipz) <= radius) {
-                                vset.add(new Vector(loopx, loopy, loopz));
-                            }
-                        }
-                    }
-                }
             }
             notdrawn = false;
         }
@@ -3059,15 +3044,7 @@ public class EditSession {
                 tipx = (int) Math.round(x1 + domstep * ((double) dx) / ((double) dy) * (x2 - x1 > 0 ? 1 : -1));
                 tipz = (int) Math.round(z1 + domstep * ((double) dz) / ((double) dy) * (z2 - z1 > 0 ? 1 : -1));
 
-                for (int loopx = tipx - ceilrad; loopx <= tipx + ceilrad; loopx++) {
+                vset.add(new Vector(tipx, tipy, tipz));
-                    for (int loopy = tipy - ceilrad; loopy <= tipy + ceilrad; loopy++) {
-                        for (int loopz = tipz - ceilrad; loopz <= tipz + ceilrad; loopz++) {
-                            if (hypot(loopx - tipx, loopy - tipy, loopz - tipz) <= radius) {
-                                vset.add(new Vector(loopx, loopy, loopz));
-                            }
-                        }
-                    }
-                }
             }
             notdrawn = false;
         }
@@ -3078,19 +3055,61 @@ public class EditSession {
                 tipy = (int) Math.round(y1 + domstep * ((double) dy) / ((double) dz) * (y2-y1>0 ? 1 : -1));
                 tipx = (int) Math.round(x1 + domstep * ((double) dx) / ((double) dz) * (x2-x1>0 ? 1 : -1));
 
-                for (int loopx = tipx - ceilrad; loopx <= tipx + ceilrad; loopx++) {
+                vset.add(new Vector(tipx, tipy, tipz));
-                    for (int loopy = tipy - ceilrad; loopy <= tipy + ceilrad; loopy++) {
-                        for (int loopz = tipz - ceilrad; loopz <= tipz + ceilrad; loopz++) {
-                            if (hypot(loopx - tipx, loopy - tipy, loopz - tipz) <= radius) {
-                                vset.add(new Vector(loopx, loopy, loopz));
-                            }
-                        }
-                    }
-                }
             }
             notdrawn = false;
         }
 
+        vset = getBallooned(vset, radius);
+        if (!filled) {
+            vset = getHollowed(vset);
+        }
+        return setBlocks(vset, pattern);
+    }
+
+    /**
+     * Draws a spline (out of blocks) between specified vectors.
+     *
+     * @param pattern The block pattern used to draw the spline.
+     * @param nodevectors The list of vectors to draw through.
+     * @param tension The tension of every node.
+     * @param bias The bias of every node.
+     * @param continuity The continuity of every node.
+     * @param quality The quality of the spline. Must be greater than 0.
+     * @param radius The radius (thickness) of the spline.
+     * @param filled If false, only a shell will be generated.
+     *
+     * @return number of blocks affected
+     * @throws MaxChangedBlocksException
+     */
+    public int drawSpline(Pattern pattern, List<Vector> nodevectors, double tension, double bias, double continuity, double quality, double radius, boolean filled)
+            throws MaxChangedBlocksException {
+
+        Set<Vector> vset = new HashSet<Vector>();
+        List<Node> nodes = new ArrayList(nodevectors.size());
+
+        Interpolation interpol = new KochanekBartelsInterpolation();
+
+        for (int loop = 0; loop < nodevectors.size(); loop++) {
+            Node n = new Node(nodevectors.get(loop));
+            n.setTension(tension);
+            n.setBias(bias);
+            n.setContinuity(continuity);
+            nodes.add(n);
+        }
+
+        interpol.setNodes(nodes);
+        double splinelength = interpol.arcLength(0, 1);
+        for (double loop = 0; loop <= 1; loop += 1D / splinelength / quality) {
+            Vector tipv = interpol.getPosition(loop);
+            int tipx = (int) Math.round(tipv.getX());
+            int tipy = (int) Math.round(tipv.getY());
+            int tipz = (int) Math.round(tipv.getZ());
+
+            vset.add(new Vector(tipx, tipy, tipz));
+        }
+
+        vset = getBallooned(vset, radius);
         if (!filled) {
             vset = getHollowed(vset);
         }
@@ -3105,6 +3124,26 @@ public class EditSession {
         return Math.sqrt(sum);
     }
 
+    private static Set<Vector> getBallooned(Set<Vector> vset, double radius) {
+        Set<Vector> returnset = new HashSet<Vector>();
+        int ceilrad = (int) Math.ceil(radius);
+
+        for (Vector v : vset) {
+            int tipx = v.getBlockX(), tipy = v.getBlockY(), tipz = v.getBlockZ();
+
+            for (int loopx = tipx - ceilrad; loopx <= tipx + ceilrad; loopx++) {
+                for (int loopy = tipy - ceilrad; loopy <= tipy + ceilrad; loopy++) {
+                    for (int loopz = tipz - ceilrad; loopz <= tipz + ceilrad; loopz++) {
+                        if (hypot(loopx - tipx, loopy - tipy, loopz - tipz) <= radius) {
+                            returnset.add(new Vector(loopx, loopy, loopz));
+                        }
+                    }
+                }
+            }
+        }
+        return returnset;
+    }
+
     private static Set<Vector> getHollowed(Set<Vector> vset) {
         Set<Vector> returnset = new HashSet<Vector>();
         for (Vector v : vset) {

src/main/java/com/sk89q/worldedit/commands/RegionCommands.java

@@ -23,6 +23,8 @@ import static com.sk89q.minecraft.util.commands.Logging.LogMode.ALL;
 import static com.sk89q.minecraft.util.commands.Logging.LogMode.ORIENTATION_REGION;
 import static com.sk89q.minecraft.util.commands.Logging.LogMode.REGION;
 
+import java.util.ArrayList;
+import java.util.List;
 import java.util.Set;
 
 import com.sk89q.minecraft.util.commands.Command;
@@ -44,6 +46,7 @@ import com.sk89q.worldedit.filtering.HeightMapFilter;
 import com.sk89q.worldedit.masks.Mask;
 import com.sk89q.worldedit.patterns.Pattern;
 import com.sk89q.worldedit.patterns.SingleBlockPattern;
+import com.sk89q.worldedit.regions.ConvexPolyhedralRegion;
 import com.sk89q.worldedit.regions.CuboidRegion;
 import com.sk89q.worldedit.regions.Region;
 import com.sk89q.worldedit.regions.RegionOperationException;
@@ -89,9 +92,10 @@ public class RegionCommands {
     @Command(
             aliases = { "/line" },
             usage = "<block> [thickness]",
-            desc = "Draws a line segment between selection corners",
+            desc = "Draws a line segment between cuboid selection corners",
             help =
-                "Draws a line segment between selection corners.\n" +
+                "Draws a line segment between cuboid selection corners.\n" +
+                "Can only be used with cuboid selections.\n" +
                 "Flags:\n" +
                 "  -h generates only a shell",
             flags = "h",
@@ -122,6 +126,43 @@ public class RegionCommands {
         player.print(blocksChanged + " block(s) have been changed.");
     }
 
+    @Command(
+            aliases = { "/curve" },
+            usage = "<block> [thickness]",
+            desc = "Draws a spline through selected points",
+            help =
+                "Draws a spline through selected points.\n" +
+                "Can only be uesd with convex polyhedral selections.\n" +
+                "Flags:\n" +
+                "  -h generates only a shell",
+            flags = "h",
+            min = 1,
+            max = 2
+    )
+    @CommandPermissions("worldedit.region.curve")
+    @Logging(REGION)
+    public void curve(CommandContext args, LocalSession session, LocalPlayer player,
+            EditSession editSession) throws WorldEditException {
+
+        Region region = session.getSelection(session.getSelectionWorld());
+        if (!(region instanceof ConvexPolyhedralRegion)) {
+            player.printError("Invalid region type");
+            return;
+        }
+        if (args.argsLength() < 2 ? false : args.getDouble(1) < 0) {
+            player.printError("Invalid thickness. Must not be negative");
+            return;
+        }
+
+        Pattern pattern = we.getBlockPattern(player, args.getString(0));
+        ConvexPolyhedralRegion cpregion = (ConvexPolyhedralRegion) region;
+        List<Vector> vectors = new ArrayList<Vector>(cpregion.getVertices());
+
+        int blocksChanged = editSession.drawSpline(pattern, vectors, 0, 0, 0, 10, args.argsLength() < 2 ? 0 : args.getDouble(1), !args.hasFlag('h'));
+
+        player.print(blocksChanged + " block(s) have been changed.");
+    }
+
     @Command(
         aliases = { "/replace", "/re", "/rep" },
         usage = "[from-block] <to-block>",

src/main/java/com/sk89q/worldedit/interpolation/Interpolation.java

@@ -0,0 +1,68 @@
+// $Id$
+/*
+ * WorldEditLibrary
+ * Copyright (C) 2010 sk89q <http://www.sk89q.com> and contributors
+ *
+ * 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 <http://www.gnu.org/licenses/>.
+ */
+package com.sk89q.worldedit.interpolation;
+
+import java.util.List;
+
+import com.sk89q.worldedit.Vector;
+
+/**
+ * Represents an arbitrary function in &#8477; &rarr; &#8477;<sup>3</sup>
+ *
+ * @author TomyLobo
+ *
+ */
+public interface Interpolation {
+    /**
+     * Sets nodes to be used by subsequent calls to
+     * {@link #getPosition(double)} and the other methods.
+     *
+     * @param nodes
+     */
+    public void setNodes(List<Node> nodes);
+
+    /**
+     * Gets the result of f(position)
+     *
+     * @param position
+     * @return
+     */
+    public Vector getPosition(double position);
+
+    /**
+     * Gets the result of f'(position).
+     *
+     * @param position
+     * @return
+     */
+    public 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
+     */
+    double arcLength(double positionA, double positionB);
+
+    int getSegment(double position);
+}

src/main/java/com/sk89q/worldedit/interpolation/KochanekBartelsInterpolation.java

@@ -0,0 +1,253 @@
+// $Id$
+/*
+ * WorldEditLibrary
+ * Copyright (C) 2010 sk89q <http://www.sk89q.com> and contributors
+ *
+ * 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 <http://www.gnu.org/licenses/>.
+ */
+package com.sk89q.worldedit.interpolation;
+
+import java.util.Collections;
+import java.util.List;
+
+import com.sk89q.worldedit.Vector;
+
+/**
+ * Kochanek-Bartels interpolation.<br />
+ * Continuous in the 2nd derivative.<br />
+ * Supports {@link Node#tension tension}, {@link Node#bias bias} and
+ * {@link Node#continuity continuity} parameters per {@link Node}
+ *
+ * @author TomyLobo
+ *
+ */
+public class KochanekBartelsInterpolation implements Interpolation {
+    private List<Node> nodes;
+    private Vector[] coeffA;
+    private Vector[] coeffB;
+    private Vector[] coeffC;
+    private Vector[] coeffD;
+    private double scaling;
+
+    public KochanekBartelsInterpolation() {
+        setNodes(Collections.<Node>emptyList());
+    }
+
+    @Override
+    public void setNodes(List<Node> 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;
+
+        Node 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
+     *
+     * @param indexLeft
+     * @param remainderLeft
+     * @param indexRight
+     * @param remainderRight
+     * @return
+     */
+    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;
+
+        final int index = (int) Math.floor(position);
+        return index;
+    }
+}

src/main/java/com/sk89q/worldedit/interpolation/LinearInterpolation.java

@@ -0,0 +1,158 @@
+// $Id$
+/*
+ * WorldEditLibrary
+ * Copyright (C) 2010 sk89q <http://www.sk89q.com> and contributors
+ *
+ * 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 <http://www.gnu.org/licenses/>.
+ */
+package com.sk89q.worldedit.interpolation;
+
+import java.util.List;
+
+import com.sk89q.worldedit.Vector;
+
+/**
+ * Simple linear interpolation. Mainly used for testing.
+ *
+ * @author TomyLobo
+ *
+ */
+public class LinearInterpolation implements Interpolation {
+    private List<Node> nodes;
+
+    @Override
+    public void setNodes(List<Node> nodes) {
+        this.nodes = nodes;
+    }
+
+    @Override
+    public Vector getPosition(double position) {
+        if (nodes == null)
+            throw new IllegalStateException("Must call setNodes first.");
+
+        if (position > 1)
+            return null;
+
+        position *= nodes.size() - 1;
+
+        final int index1 = (int) Math.floor(position);
+        final double remainder = position - index1;
+
+        final Vector position1 = nodes.get(index1).getPosition();
+        final Vector position2 = nodes.get(index1 + 1).getPosition();
+
+        return position1.multiply(1.0 - remainder).add(position2.multiply(remainder));
+    }
+
+    /*
+    Formula for position:
+        p1*(1-t) + p2*t
+    Formula for position in Horner/monomial form:
+        (p2-p1)*t + p1
+    1st Derivative:
+        p2-p1
+    2nd Derivative:
+        0
+    Integral:
+        (p2-p1)/2*t^2 + p1*t + constant
+    Integral in Horner form:
+        ((p2-p1)/2*t + p1)*t + constant
+    */
+
+    @Override
+    public Vector get1stDerivative(double position) {
+        if (nodes == null)
+            throw new IllegalStateException("Must call setNodes first.");
+
+        if (position > 1)
+            return null;
+
+        position *= nodes.size() - 1;
+
+        final int index1 = (int) Math.floor(position);
+
+        final Vector position1 = nodes.get(index1).getPosition();
+        final Vector position2 = nodes.get(index1 + 1).getPosition();
+
+        return position2.subtract(position1);
+    }
+
+    @Override
+    public double arcLength(double positionA, double positionB) {
+        if (nodes == null)
+            throw new IllegalStateException("Must call setNodes first.");
+
+        if (positionA > positionB)
+            return arcLength(positionB, positionA);
+
+        positionA *= nodes.size() - 1;
+        positionB *= nodes.size() - 1;
+
+        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
+     *
+     * @param indexA
+     * @param remainderA
+     * @param indexB
+     * @param remainderB
+     * @return
+     */
+    private double arcLengthRecursive(int indexA, double remainderA, int indexB, double remainderB) {
+        switch (indexB - indexA) {
+        case 0:
+            return arcLengthRecursive(indexA, remainderA, remainderB);
+
+        case 1:
+            // This case is merely a speed-up for a very common case
+            return
+                    arcLengthRecursive(indexA, remainderA, 1.0) +
+                    arcLengthRecursive(indexB, 0.0, remainderB);
+
+        default:
+            return
+                    arcLengthRecursive(indexA, remainderA, indexB - 1, 1.0) +
+                    arcLengthRecursive(indexB, 0.0, remainderB);
+        }
+    }
+
+    private double arcLengthRecursive(int index, double remainderA, double remainderB) {
+        final Vector position1 = nodes.get(index).getPosition();
+        final Vector position2 = nodes.get(index + 1).getPosition();
+
+        return position1.distance(position2) * (remainderB - remainderA);
+    }
+
+    @Override
+    public int getSegment(double position) {
+        if (nodes == null)
+            throw new IllegalStateException("Must call setNodes first.");
+
+        if (position > 1)
+            return Integer.MAX_VALUE;
+
+        position *= nodes.size() - 1;
+
+        final int index = (int) Math.floor(position);
+        return index;
+    }
+}

src/main/java/com/sk89q/worldedit/interpolation/Node.java

@@ -0,0 +1,86 @@
+// $Id$
+/*
+ * WorldEditLibrary
+ * Copyright (C) 2010 sk89q <http://www.sk89q.com> and contributors
+ *
+ * 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 <http://www.gnu.org/licenses/>.
+ */
+package com.sk89q.worldedit.interpolation;
+
+import com.sk89q.worldedit.Vector;
+
+/**
+ * Represents a node for interpolation.<br />
+ * The {@link #tension}, {@link #bias} and {@link #continuity} fields
+ * are parameters for the Kochanek-Bartels interpolation algorithm.
+ *
+ * @author TomyLobo
+ *
+ */
+public class Node {
+    private Vector position;
+
+    private double tension;
+    private double bias;
+    private double continuity;
+
+    public Node() {
+        this(new Vector(0, 0, 0));
+    }
+
+    public Node(Node other) {
+        this.position = other.position;
+
+        this.tension = other.tension;
+        this.bias = other.bias;
+        this.continuity = other.continuity;
+    }
+
+    public Node(Vector position) {
+        this.position = position;
+    }
+
+
+    public Vector getPosition() {
+        return position;
+    }
+
+    public void setPosition(Vector position) {
+        this.position = position;
+    }
+
+    public double getTension() {
+        return tension;
+    }
+
+    public void setTension(double tension) {
+        this.tension = tension;
+    }
+
+    public double getBias() {
+        return bias;
+    }
+
+    public void setBias(double bias) {
+        this.bias = bias;
+    }
+
+    public double getContinuity() {
+        return continuity;
+    }
+
+    public void setContinuity(double continuity) {
+        this.continuity = continuity;
+    }
+}

src/main/java/com/sk89q/worldedit/interpolation/ReparametrisingInterpolation.java

@@ -0,0 +1,148 @@
+// $Id$
+/*
+ * WorldEditLibrary
+ * Copyright (C) 2010 sk89q <http://www.sk89q.com> and contributors
+ *
+ * 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 <http://www.gnu.org/licenses/>.
+ */
+package com.sk89q.worldedit.interpolation;
+
+import java.util.List;
+import java.util.Map.Entry;
+import java.util.TreeMap;
+
+import com.sk89q.worldedit.Vector;
+
+/**
+ * Reparametrises another interpolation function by arc length.<br />
+ * This is done so entities travel at roughly the same speed across
+ * the whole route.
+ *
+ * @author TomyLobo
+ *
+ */
+public class ReparametrisingInterpolation implements Interpolation {
+    private final Interpolation baseInterpolation;
+    private double totalArcLength;
+    private final TreeMap<Double, Double> cache = new TreeMap<Double, Double>();
+
+    public ReparametrisingInterpolation(Interpolation baseInterpolation) {
+        this.baseInterpolation = baseInterpolation;
+    }
+
+    @Override
+    public void setNodes(List<Node> nodes) {
+        baseInterpolation.setNodes(nodes);
+        cache.clear();
+        cache.put(0.0, 0.0);
+        cache.put(totalArcLength = baseInterpolation.arcLength(0.0, 1.0), 1.0);
+    }
+
+    public Interpolation getBaseInterpolation() {
+        return baseInterpolation;
+    }
+
+    @Override
+    public Vector getPosition(double position) {
+        if (position > 1)
+            return null;
+
+        return baseInterpolation.getPosition(arcToParameter(position));
+    }
+
+    @Override
+    public Vector get1stDerivative(double position) {
+        if (position > 1)
+            return null;
+
+        return baseInterpolation.get1stDerivative(arcToParameter(position)).normalize().multiply(totalArcLength);
+    }
+
+    @Override
+    public double arcLength(double positionA, double positionB) {
+        return baseInterpolation.arcLength(arcToParameter(positionA), arcToParameter(positionB));
+    }
+
+    private double arcToParameter(double arc) {
+        if (cache.isEmpty())
+            throw new IllegalStateException("Must call setNodes first.");
+
+        if (arc > 1) arc = 1;
+        arc *= totalArcLength;
+
+        Entry<Double, Double> floorEntry = cache.floorEntry(arc);
+        final double leftArc = floorEntry.getKey();
+        final double leftParameter = floorEntry.getValue();
+
+        if (leftArc == arc) {
+            return leftParameter;
+        }
+
+        Entry<Double, Double> ceilingEntry = cache.ceilingEntry(arc);
+        if (ceilingEntry == null) {
+            System.out.println("Error in arcToParameter: no ceiling entry for "+arc+" found!");
+            return 0;
+        }
+        final double rightArc = ceilingEntry.getKey();
+        final double rightParameter = ceilingEntry.getValue();
+
+        if (rightArc == arc) {
+            return rightParameter;
+        }
+
+        return evaluate(arc, leftArc, leftParameter, rightArc, rightParameter);
+    }
+
+    private double evaluate(double arc, double leftArc, double leftParameter, double rightArc, double rightParameter) {
+        double midParameter = 0;
+        for (int i = 0; i < 10; ++i) {
+            midParameter = (leftParameter + rightParameter) * 0.5;
+            //final double midArc = leftArc + baseInterpolation.arcLength(leftParameter, midParameter);
+            final double midArc = baseInterpolation.arcLength(0, midParameter);
+            cache.put(midArc, midParameter);
+
+            if (midArc < leftArc) {
+                return leftParameter;
+            }
+
+            if (midArc > rightArc) {
+                return rightParameter;
+            }
+
+            if (Math.abs(midArc - arc) < 0.01) {
+                return midParameter;
+            }
+
+            if (arc < midArc) {
+                // search between left and mid
+                rightArc = midArc;
+                rightParameter = midParameter;
+            }
+            else {
+                // search between mid and right
+                leftArc = midArc;
+                leftParameter = midParameter;
+            }
+        }
+        return midParameter;
+    }
+
+    @Override
+    public int getSegment(double position) {
+        if (position > 1)
+            return Integer.MAX_VALUE;
+
+        return baseInterpolation.getSegment(arcToParameter(position));
+    }
+}