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