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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][];
}
}