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package com.pau101.util;
/**
* @author Paul Fulham (pau101)
*/
public final class BezierUtils
{
private BezierUtils()
{}
/**
* Compute the value of all nth degree Bernstein polynomials.
*
* @param curveDegree : degree of curve
* @param t : curve parameter on interval [0,1]
* @param scalars : curveDegree + 1 Bernstein values.
*/
public static void allBernstein(int curveDegree, float t, float scalars[])
{
int j, k;
float nt = 1 - t;
float saved;
scalars[0] = 1;
for(j = 1; j <= curveDegree; j++){
saved = 0;
for(k = 0; k < j; k++){
float temp = scalars[k];
scalars[k] = saved + nt * temp;
saved = t * temp;
}
scalars[j] = saved;
}
}
/**
* Compute point of nth degree Bezier curve.
*
* @param controlPoints : curveDegree + 1 control points
* @param curveDegree : degree of curve
* @param t : curve parameter on interval [0,1]
* @param point : resulting point
*/
public static void pointOnBezierCurve(float controlPoints[][], int curveDegree, float t, float point[])
{
float scalars[] = new float[curveDegree + 1];
int k;
allBernstein(curveDegree, t, scalars);
point[0] = point[1] = point[2] = 0;
for(k = 0; k <= curveDegree; k++){
point[0] += scalars[k] * controlPoints[k][0];
point[1] += scalars[k] * controlPoints[k][1];
point[2] += scalars[k] * controlPoints[k][2];
}
}
/**
* Compute an approximate length of a Bezier curve given the control points.
*
* @param controlPoints : control points of a Bezier curve
* @return the approximate length
*/
public static float approximateLength(float controlPoints[][])
{
float length = 0;
for(int i = 0; i < controlPoints.length - 1; i++){
float xDif = controlPoints[i + 1][0] - controlPoints[i][0];
float yDif = controlPoints[i + 1][1] - controlPoints[i][1];
float zDif = controlPoints[i + 1][2] - controlPoints[i][2];
length += Math.sqrt(xDif * xDif + yDif * yDif + zDif * zDif);
}
return length;
}
public static int tesselationSegementsForLength(float length, float scale)
{
float noLessThan = 10 * scale;
float segs = length * scale / 30F;
return (int)Math.ceil(Math.sqrt(segs * segs * 0.6 + noLessThan * noLessThan));
}
public static float[][] curve(float controlPoints[][])
{
return curve(controlPoints, 1);
}
public static float[][] curve(float controlPoints[][], float scale)
{
int count = tesselationSegementsForLength(approximateLength(controlPoints), scale);
float[][] points = new float[count][3];
for(int i = 0; i < count; i++){
float t = i / (float)(count - 1);
float[] point = new float[3];
pointOnBezierCurve(controlPoints, controlPoints.length - 1, t, point);
points[i] = point;
}
return points;
}
}
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