/*
* Copyright (c) 2005, Graph Builder
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* * Neither the name of Graph Builder nor the names of its contributors 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 "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
package com.graphbuilder.curve;
import com.graphbuilder.math.
PascalsTriangle;
/**
<p>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.
<p><center><img align="center" src="doc-files/bezier1.gif"/></center>
<p>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 {
// 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 static 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 >
a.length)
a = new double[2 *
numPts];
a[
numPts - 1] = 1;
double
b = 1.0;
double
one_minus_t = 1.0 -
t;
for (int
i =
numPts - 2;
i >= 0;
i--)
a[
i] =
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 =
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 (
a.length > 0)
a = new double[0];
}
}