com.graphbuilder.curve.BezierCurve Maven / Gradle / Ivy
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/*
* Copyright (c) 2005, Graph Builder
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package com.graphbuilder.curve;
import com.graphbuilder.math.PascalsTriangle;
/**
General n-point Bezier curve implementation. The Bezier curve defines itself using all the points
from the control-path specified by the group-iterator. To compute a single point on the curve requires
O(n) multiplications where n is the group-size of the group-iterator. Thus, the Bezier curve is
considered to be expensive, but it has several mathematical properties (not discussed here) that
make it appealing. Figure 1 shows an example of a Bezier curve.
The maximum number of points that the Bezier curve can use is 1030 because the evaluation of a point
uses the nCr (n-choose-r) function. The computation uses double precision, and double precision cannot
represent the result of 1031 choose i, where i = [500, 530].
@see com.graphbuilder.curve.Curve
@see com.graphbuilder.math.PascalsTriangle
*/
public class BezierCurve extends ParametricCurve {
private static final ThreadLocal SHARED_DATA = new ThreadLocal(){
protected SharedData initialValue() {
return new SharedData();
}
};
private final SharedData sharedData = SHARED_DATA.get();
private final PascalsTriangle pascalsTriangle = new PascalsTriangle();
private static class SharedData {
// a[] is required to compute (1 - t)^n starting from the last index.
// The idea is that all Bezier curves can share the same array, which
// is more memory efficient than each Bezier curve having its own array.
private double[] a = new double[0];
}
private double t_min = 0.0;
private double t_max = 1.0;
private int sampleLimit = 1;
public BezierCurve(ControlPath cp, GroupIterator gi) {
super(cp, gi);
}
public void eval(double[] p) {
double t = p[p.length - 1];
int numPts = gi.getGroupSize();
if (numPts > sharedData.a.length)
sharedData.a = new double[2 * numPts];
sharedData.a[numPts - 1] = 1;
double b = 1.0;
double one_minus_t = 1.0 - t;
for (int i = numPts - 2; i >= 0; i--)
sharedData.a[i] = sharedData.a[i+1] * one_minus_t;
gi.set(0, 0);
int i = 0;
while (i < numPts) {
double pt = pascalsTriangle.nCr(numPts - 1, i);
if (Double.isInfinite(pt) || Double.isNaN(pt)) {
// are there any techniques that can be used
// to calculate past 1030 points?
// 1031 choose 515 == infinity
}
else {
double gravity = sharedData.a[i] * b * pt;
double[] d = cp.getPoint(gi.next()).getLocation();
for (int j = 0; j < p.length - 1; j++)
p[j] = p[j] + d[j] * gravity;
}
b = b * t;
i++;
}
}
public int getSampleLimit() {
return sampleLimit;
}
/**
Sets the sample-limit. For more information on the sample-limit, see the
BinaryCurveApproximationAlgorithm class. The default sample-limit is 1.
@throws IllegalArgumentException If sample-limit < 0.
@see com.graphbuilder.curve.BinaryCurveApproximationAlgorithm
@see #getSampleLimit()
*/
public void setSampleLimit(int limit) {
if (limit < 0)
throw new IllegalArgumentException("Sample-limit >= 0 required.");
sampleLimit = limit;
}
/**
Specifies the interval that the curve should define itself on. The default interval is [0.0, 1.0].
@throws IllegalArgumentException If t_min > t_max.
@see #t_min()
@see #t_max()
*/
public void setInterval(double t_min, double t_max) {
if (t_min > t_max)
throw new IllegalArgumentException("t_min <= t_max required.");
this.t_min = t_min;
this.t_max = t_max;
}
/**
Returns the starting interval value.
@see #setInterval(double, double)
@see #t_max()
*/
public double t_min() {
return t_min;
}
/**
Returns the finishing interval value.
@see #setInterval(double, double)
@see #t_min()
*/
public double t_max() {
return t_max;
}
/**
The only requirement for this curve is the group-iterator must be in range or this method returns quietly.
*/
public void appendTo(MultiPath mp) {
if (!gi.isInRange(0, cp.numPoints()))
throw new IllegalArgumentException("group iterator not in range");;
int n = mp.getDimension();
double[] d = new double[n + 1];
d[n] = t_min;
eval(d);
if (connect)
mp.lineTo(d);
else
mp.moveTo(d);
BinaryCurveApproximationAlgorithm.genPts(this, t_min, t_max, mp);
}
public void resetMemory() {
if (sharedData.a.length > 0)
sharedData.a = new double[0];
}
}