/*
* Copyright (c) 2009-2012 jMonkeyEngine
* All rights reserved.
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* * Redistributions in binary form must reproduce the above copyright
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* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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*/
package com.jme3.math;
import com.jme3.math.Spline.SplineType;
import java.util.List;
/**
* This class offers methods to help with curves and surfaces calculations.
* @author Marcin Roguski (Kealthas)
*/
public class CurveAndSurfaceMath {
private static final float KNOTS_MINIMUM_DELTA = 0.0001f;
/**
* A private constructor is defined to avoid instantiation of this
* class.
*/
private CurveAndSurfaceMath() {}
/**
* This method interpolates the data for the nurbs curve.
* @param u
* the u value
* @param nurbSpline
* the nurbs spline definition
* @param store
* the resulting point in 3D space
*/
public static void interpolateNurbs(float u, Spline nurbSpline, Vector3f store) {
if (nurbSpline.getType() != SplineType.Nurb) {
throw new IllegalArgumentException("Given spline is not of a NURB type!");
}
List<Vector3f> controlPoints = nurbSpline.getControlPoints();
float[] weights = nurbSpline.getWeights();
List<Float> knots = nurbSpline.getKnots();
int controlPointAmount = controlPoints.size();
store.set(Vector3f.ZERO);
float delimeter = 0;
for (int i = 0; i < controlPointAmount; ++i) {
float val = weights[i] * CurveAndSurfaceMath.computeBaseFunctionValue(i, nurbSpline.getBasisFunctionDegree(), u, knots);
store.addLocal(nurbSpline.getControlPoints().get(i)
.mult(val));
delimeter += val;
}
store.divideLocal(delimeter);
}
/**
* This method interpolates the data for the nurbs surface.
*
* @param u
* the u value
* @param v
* the v value
* @param controlPoints
* the nurbs' control points
* @param knots
* the nurbs' knots
* @param basisUFunctionDegree
* the degree of basis U function
* @param basisVFunctionDegree
* the degree of basis V function
* @param store
* the resulting point in 3D space
*/
public static void interpolate(float u, float v, List<List<Vector4f>> controlPoints, List<Float>[] knots,
int basisUFunctionDegree, int basisVFunctionDegree, Vector3f store) {
store.set(Vector3f.ZERO);
float delimeter = 0;
int vControlPointsAmount = controlPoints.size();
int uControlPointsAmount = controlPoints.get(0).size();
for (int i = 0; i < vControlPointsAmount; ++i) {
for (int j = 0; j < uControlPointsAmount; ++j) {
Vector4f controlPoint = controlPoints.get(i).get(j);
float val = controlPoint.w
* CurveAndSurfaceMath.computeBaseFunctionValue(i, basisVFunctionDegree, v, knots[1])
* CurveAndSurfaceMath.computeBaseFunctionValue(j, basisUFunctionDegree, u, knots[0]);
store.addLocal(controlPoint.x * val, controlPoint.y * val, controlPoint.z * val);
delimeter += val;
}
}
store.divideLocal(delimeter);
}
/**
* This method prepares the knots to be used. If the knots represent non-uniform B-splines (first and last knot values are being
* repeated) it leads to NaN results during calculations. This method adds a small number to each of such knots to avoid NaN's.
* @param knots
* the knots to be prepared to use
* @param basisFunctionDegree
* the degree of basis function
*/
// TODO: improve this; constant delta may lead to errors if the difference between tha last repeated
// point and the following one is lower than it
public static void prepareNurbsKnots(List<Float> knots, int basisFunctionDegree) {
float delta = KNOTS_MINIMUM_DELTA;
float prevValue = knots.get(0).floatValue();
for(int i=1;i<knots.size();++i) {
float value = knots.get(i).floatValue();
if(value<=prevValue) {
value += delta;
knots.set(i, Float.valueOf(value));
delta += KNOTS_MINIMUM_DELTA;
} else {
delta = KNOTS_MINIMUM_DELTA;//reset the delta's value
}
prevValue = value;
}
}
/**
* This method computes the base function value for the NURB curve.
* @param i
* the knot index
* @param k
* the base function degree
* @param t
* the knot value
* @param knots
* the knots' values
* @return the base function value
*/
private static float computeBaseFunctionValue(int i, int k, float t, List<Float> knots) {
if (k == 1) {
return knots.get(i) <= t && t < knots.get(i + 1) ? 1.0f : 0.0f;
} else {
return (t - knots.get(i)) / (knots.get(i + k - 1) - knots.get(i)) *
CurveAndSurfaceMath.computeBaseFunctionValue(i, k - 1, t, knots)
+ (knots.get(i + k) - t) / (knots.get(i + k) - knots.get(i + 1)) *
CurveAndSurfaceMath.computeBaseFunctionValue(i + 1, k - 1, t, knots);
}
}
}