A simple interpolating cubic spline path that assumes that all the

points on either the x or y axis are equal and will interpolate the z 
values.


git-svn-id: svn+ssh://src.earth.threerings.net/nenya/trunk@38 ed5b42cb-e716-0410-a449-f6a68f950b19

src/java/com/threerings/jme/sprite/CubicSplinePath.java

@@ -0,0 +1,188 @@
+//
+// $Id$
+//
+// Nenya library - tools for developing networked games
+// Copyright (C) 2002-2006 Three Rings Design, Inc., All Rights Reserved
+// http://www.threerings.net/code/nenya/
+//
+// This library is free software; you can redistribute it and/or modify it
+// under the terms of the GNU Lesser General Public License as published
+// by the Free Software Foundation; either version 2.1 of the License, or
+// (at your option) any later version.
+//
+// This library 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
+// Lesser General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License along with this library; if not, write to the Free Software
+// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+
+package com.threerings.jme.sprite;
+
+import com.jme.math.Vector3f;
+
+/**
+ * Moves a sprite along an interpolated spline based on a series of control
+ * points.
+ */
+public class CubicSplinePath extends Path
+{
+    /**
+     * Creates a path for the supplied sprite traversing the supplied
+     * series of points with the specified duration between points.  The
+     * path assumes that all the control points exist on either the same
+     * x or y axis.  The non-fixed x/y axis must be in order (either ascending
+     * or descending), and the z values will be interpolated.
+     *
+     * @param points a list of points to interpolate between.  Currently
+     * all the points along one dimension must be equal.
+     * @param durations defines the elapsed time between each successive
+     * traversal.  This will as a result be shorter by one element than the
+     * points array.
+     */
+    public CubicSplinePath (
+            Sprite sprite, Vector3f[] points, float[] durations)
+    {
+        super(sprite);
+        _isX = (points[0].x != points[1].x);
+        _x = new float[points.length];
+        _y = new float[points.length];
+        _z = (_isX ? points[0].y : points[0].x);
+        for (int ii = 0; ii < points.length; ii++) {
+            _x[ii] = (_isX ? points[ii].x : points[ii].y);
+            _y[ii] = points[ii].z;
+        }
+        _end = points[points.length - 1];
+        _durations = durations;
+        calculateDerivatives();
+    }
+
+    // documentation inherited
+    public void update (float time)
+    {
+        // note the accumulated time
+        _accum += time;
+
+        // if we have surpassed the time for this segment, subtract the
+        // segment time and move on to the next segment
+        while (_current < _durations.length && _accum > _durations[_current]) {
+            _accum -= _durations[_current];
+            _current++;
+        }
+
+        // if we have completed out path, move the sprite to the final
+        // position and wrap everything up
+        if (_current >= _durations.length) {
+            _sprite.setLocalTranslation(_end);
+            _sprite.pathCompleted();
+            return;
+        }
+
+        // move the sprite to the appropriate position between points
+        _sprite.getLocalTranslation().set(interpolate(0f));
+    }
+
+    /**
+     * Calculates the second derivative values for all the control points
+     * along the path.
+     */
+    protected void calculateDerivatives ()
+    {
+        float[] u = new float[_x.length];
+        _y2 = new float[_x.length];
+        for (int ii = 1; ii < _x.length - 1; ii++) {
+            float sig = (_x[ii] - _x[ii-1])/(_x[ii+1] - _x[ii-1]);
+            float p = sig * _y2[ii-1] + 2;
+            _y2[ii] = (sig - 1f) / p;
+            u[ii] = (6f * ((_y[ii+1] - _y[ii]) / (_x[ii+1] - _x[ii]) -
+                        (_y[ii] - _y[ii-1]) / (_x[ii] - _x[ii-1])) /
+                    (_x[ii+1] - _x[ii-1]) - sig * u[ii-1]) / p;
+        }
+        for (int ii = _x.length - 2; ii >= 0; ii--) {
+            _y2[ii] = _y2[ii] * _y2[ii + 1] + u[ii];
+        }
+    }
+
+    /**
+     * Interpolates the z value based on the current time point on the path.
+     *
+     * @param delta is the difference from the current time point to
+     * interpolate the point.
+     */
+    protected Vector3f interpolate (float delta)
+    {
+        int idx = _current;
+        // no change, just use the current value
+        if (delta == 0f) {
+            delta = _accum;
+
+        // find the control point after the current one for interpolating
+        } else if (delta + _accum > _durations[idx]) {
+            delta -= _durations[idx] - _accum;
+            while (idx < _durations.length - 1) {
+                idx++;
+                if (delta < _durations[idx]) {
+                    break;
+                }
+                delta -= _durations[idx];
+            }
+            if (delta > _durations[idx] || idx == _durations.length - 1) {
+                return _end;
+            }
+
+        // find the control point before the current one for interpolating
+        } else if (_accum + delta < 0) {
+            delta += _accum;
+            while (idx > 0) {
+                idx--;
+                delta += _durations[idx];
+                if (delta > 0) {
+                    break;
+                }
+            }
+            if (delta < 0) {
+                delta = 0;
+            }
+
+        // we're using the same control point, simply adjust the time point
+        } else {
+            delta += _accum;
+        }
+
+        float h = _x[idx + 1] - _x[idx];
+        // no different between these points, just return the current value
+        if (h == 0) {
+            if (_sprite != null) {
+                return new Vector3f(_sprite.getLocalTranslation());
+            }
+            return new Vector3f();
+        }
+
+        float x = _x[idx] + h * (delta / _durations[idx]);
+        float a = (_x[idx + 1] - x) / h;
+        float b = (x - _x[idx]) / h;
+        float a3 = a * a * a, b3 = b * b * b;
+        float y = a * _y[idx] + b * _y[idx + 1] +
+            ((a3 - a) * _y2[idx] + (b3 - b) * _y2[idx + 1]) *
+            (h * h) / 6;
+        float z = y;
+        if (_isX) {
+            y = _z;
+        } else {
+            y = x;
+            x = _z;
+        }
+        return new Vector3f(x, y, z);
+    }
+
+    /** The final path point */
+    protected Vector3f _end;
+    /** The array of control points, derivatives and durations. */
+    protected float[] _x, _y, _y2, _durations;
+
+    protected float _accum, _z;
+    protected int _current;
+    protected boolean _isX;
+}