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The Apache Commons Codec package contains simple encoder and decoders for
various formats such as Base64 and Hexadecimal. In addition to these
widely used encoders and decoders, the codec package also maintains a
collection of phonetic encoding utilities.
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/*
* 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;
/**
The natural-cubic-spline is constructed using piecewise third order polynomials which pass through all the
control-points specified by the group-iterator. The curve can be open or closed. Figure 1 shows an open
curve and figure 2 shows a closed curve.
SHARED_DATA = new ThreadLocal(){
protected SharedData initialValue() {
return new SharedData();
}
};
private final SharedData sharedData = SHARED_DATA.get();
private static class SharedData {
private double[][] pt = new double[0][];
private double[][] data = new double[0][];
private int ci = 0;
}
private boolean closed = false;
public NaturalCubicSpline(ControlPath cp, GroupIterator gi) {
super(cp, gi);
}
protected void eval(double[] p) {
int n = p.length - 1; // dimension
double t = p[n];
double t2 = t * t;
double t3 = t2 * t;
int j = 0;
for (int i = 0; i < n; i++)
p[i] = sharedData.data[j++][sharedData.ci] + sharedData.data[j++][sharedData.ci] * t + sharedData.data[j++][sharedData.ci] * t2 + sharedData.data[j++][sharedData.ci] * t3;
}
// n is the # of points
// dim is the dimension
private void precalc(int n, int dim, boolean closed) {
n--;
double[] a = sharedData.data[4 * dim];
double[] b = sharedData.data[4 * dim + 1];
double[] c = sharedData.data[4 * dim + 2];
int k = 0;
if (closed) {
double[] d = sharedData.data[4 * dim + 3];
double e, f, g, h;
for (int j = 0; j < dim; j++) {
d[1] = a[1] = e = 0.25;
b[0] = e * 3 * (sharedData.pt[1][j] - sharedData.pt[n][j]);
h = 4;
f = 3 * (sharedData.pt[0][j] - sharedData.pt[n-1][j]);
g = 1;
for (int i = 1; i < n; i++) {
a[i+1] = e = 1.0 / (4.0 - a[i]);
d[i+1] = -e * d[i];
b[i] = e * (3.0 * (sharedData.pt[i+1][j] - sharedData.pt[i-1][j]) - b[i-1]);
h = h - g * d[i];
f = f - g * b[i-1];
g = -a[i] * g;
}
h = h - (g + 1) * (a[n] + d[n]);
b[n] = f - (g + 1) * b[n-1];
c[n] = b[n] / h;
c[n-1] = b[n-1] - (a[n] + d[n]) * c[n];
for (int i = n-2; i >= 0; i--) {
c[i] = b[i] - a[i+1] * c[i+1] - d[i+1] * c[n];
}
double[] w = sharedData.data[k++];
double[] x = sharedData.data[k++];
double[] y = sharedData.data[k++];
double[] z = sharedData.data[k++];
for (int i = 0; i < n; i++) {
w[i] = sharedData.pt[i][j];
x[i] = c[i];
y[i] = 3 * (sharedData.pt[i+1][j] - sharedData.pt[i][j]) - 2 * c[i] - c[i+1];
z[i] = 2 * (sharedData.pt[i][j] - sharedData.pt[i+1][j]) + c[i] + c[i+1];
}
w[n] = sharedData.pt[n][j];
x[n] = c[n];
y[n] = 3 * (sharedData.pt[0][j] - sharedData.pt[n][j]) - 2 * c[n] - c[0];
z[n] = 2 * (sharedData.pt[n][j] - sharedData.pt[0][j]) + c[n] + c[0];
}
}
else {
for (int j = 0; j < dim; j++) {
a[0] = 0.5;
for (int i = 1; i < n; i++) {
a[i] = 1.0 / (4 - a[i-1]);
}
a[n] = 1.0 / (2.0 - a[n-1]);
b[0] = a[0] * (3 * (sharedData.pt[1][j] - sharedData.pt[0][j]));
for (int i = 1; i < n; i++) {
b[i] = a[i] * (3 * (sharedData.pt[i+1][j] - sharedData.pt[i-1][j]) - b[i-1]);
}
b[n] = a[n] * (3 * (sharedData.pt[n][j] - sharedData.pt[n-1][j]) - b[n-1]);
c[n] = b[n];
for (int i = n-1; i >= 0; i--) {
c[i] = b[i] - a[i] * c[i+1];
}
double[] w = sharedData.data[k++];
double[] x = sharedData.data[k++];
double[] y = sharedData.data[k++];
double[] z = sharedData.data[k++];
for (int i = 0; i < n; i++) {
w[i] = sharedData.pt[i][j];
x[i] = c[i];
y[i] = 3 * (sharedData.pt[i+1][j] - sharedData.pt[i][j]) - 2 * c[i] - c[i+1];
z[i] = 2 * (sharedData.pt[i][j] - sharedData.pt[i+1][j]) + c[i] + c[i+1];
}
w[n] = sharedData.pt[n][j];
x[n] = 0;
y[n] = 0;
z[n] = 0;
}
}
}
/**
The closed attribute determines which tri-diagonal matrix to solve.
@see #getClosed()
*/
public void setClosed(boolean b) {
closed = b;
}
/**
Returns the value of closed. The default value is false.
@see #setClosed(boolean)
*/
public boolean getClosed() {
return closed;
}
/**
Returns a value of 1.
*/
public int getSampleLimit() {
return 1;
}
/**
The requirements for this curve are the group-iterator must be in-range and have a group size of at least 2.
If these requirements are not met then this method raises IllegalArgumentException
*/
public void appendTo(MultiPath mp) {
if (!gi.isInRange(0, cp.numPoints()))
throw new IllegalArgumentException("Group iterator not in range");
final int n = gi.getGroupSize();
if (n < 2)
throw new IllegalArgumentException("Group iterator size < 2");
int dim = mp.getDimension();
// make sure there is enough room
//-------------------------------------------------------
int x = 3 + 4 * dim + 1;
if (sharedData.data.length < x) {
double[][] temp = new double[x][];
for (int i = 0; i < sharedData.data.length; i++)
temp[i] = sharedData.data[i];
sharedData.data = temp;
}
if (sharedData.pt.length < n) {
int m = 2 * n;
sharedData.pt = new double[m][];
for (int i = 0; i < sharedData.data.length; i++)
sharedData.data[i] = new double[m];
}
//-------------------------------------------------------
gi.set(0, 0);
for (int i = 0; i < n; i++)
sharedData.pt[i] = cp.getPoint(gi.next()).getLocation(); // assign the used points to pt
precalc(n, dim, closed);
sharedData.ci = 0; // do not remove
double[] p = new double[dim + 1];
eval(p);
if (connect)
mp.lineTo(p);
else
mp.moveTo(p);
// Note: performing a ci++ or ci = ci + 1 results in funny behavior
for (int i = 0; i < n; i++) {
sharedData.ci = i;
BinaryCurveApproximationAlgorithm.genPts(this, 0.0, 1.0, mp);
}
}
public void resetMemory() {
if (sharedData.pt.length > 0)
sharedData.pt = new double[0][];
if (sharedData.data.length > 0)
sharedData.data = new double[0][];
}
}