Mega Code Archive
A spline factory instance
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/*
* This code is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, write to the Free
* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
* MA 02111-1307, USA.
*/
//package no.geosoft.cc.geometry.spline;
/**
* A spline factory instance.
*
* @author <a href="mailto:jacob.dreyer@geosoft.no">Jacob Dreyer</a>
*/
public class SplineFactory
{
/**
* Create a Bezier spline based on the given control points.
* The generated curve starts in the first control point and ends
* in the last control point.
*
* @param controlPoints Control points of spline (x0,y0,z0,x1,y1,z1,...).
* @param nParts Number of parts to divide each leg into.
* @return Spline (x0,y0,z0,x1,y1,z1,...).
*/
public static double[] createBezier (double[] controlPoints, int nParts)
{
Spline spline = new BezierSpline (controlPoints, nParts);
return spline.generate();
}
/**
* Create a cubic spline based on the given control points.
* The generated curve starts in the first control point and ends
* in the last control point.
*
* @param controlPoints Control points of spline (x0,y0,z0,x1,y1,z1,...).
* @param nParts Number of parts to divide each leg into.
* @return Spline (x0,y0,z0,x1,y1,z1,...).
*/
public static double[] createCubic (double[] controlPoints, int nParts)
{
Spline spline = new CubicSpline (controlPoints, nParts);
return spline.generate();
}
/**
* Create a Catmull-Rom spline based on the given control points.
* The generated curve starts in the first control point and ends
* in the last control point.
* Im addition, the curve intersects all the control points.
*
* @param controlPoints Control points of spline (x0,y0,z0,x1,y1,z1,...).
* @param nParts Number of parts to divide each leg into.
* @return Spline (x0,y0,z0,x1,y1,z1,...).
*/
public static double[] createCatmullRom (double[] controlPoints, int nParts)
{
Spline spline = new CatmullRomSpline (controlPoints, nParts);
return spline.generate();
}
/**
* Testing the spline package.
*
* @param args Not used.
*/
public static void main (String[] args)
{
double[] c = new double[12];
c[0] = 0.0; // x0
c[1] = 0.0; // y0
c[2] = 0.0; // z0
c[3] = 1.0; // x1
c[4] = 1.0; // y1
c[5] = 0.0; // z1
c[6] = 2.0; // x2
c[7] = -1.0; // y2
c[8] = 0.0; // z2
c[9] = 10.0; // x3
c[10] = 0.0; // y3
c[11] = 0.0; // z3
double[] spline1 = SplineFactory.createBezier (c, 20);
double[] spline2 = SplineFactory.createCubic (c, 20);
double[] spline3 = SplineFactory.createCatmullRom (c, 20);
System.out.println ("-- Bezier");
for (int i = 0; i < spline1.length; i+=3)
System.out.println (spline1[i] + "," + spline1[i+1] + "," + spline1[i+2]);
System.out.println ("-- Cubic");
for (int i = 0; i < spline2.length; i+=3)
System.out.println (spline2[i] + "," + spline2[i+1] + "," + spline2[i+2]);
System.out.println ("-- Catmull-Rom");
for (int i = 0; i < spline3.length; i+=3)
System.out.println (spline3[i] + "," + spline3[i+1] + "," + spline3[i+2]);
}
}
/*
* This code is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, write to the Free
* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
* MA 02111-1307, USA.
*/
//package no.geosoft.cc.geometry.spline;
/**
* An abstract class defining a general spline object.
*
* @author <a href="mailto:jacob.dreyer@geosoft.no">Jacob Dreyer</a>
*/
abstract class Spline
{
protected double controlPoints_[];
protected int nParts_;
abstract double[] generate();
}
/*
* (C) 2004 - Geotechnical Software Services
*
* This code is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, write to the Free
* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
* MA 02111-1307, USA.
*/
//package no.geosoft.cc.geometry.spline;
/**
* A Bezier spline object. Use the SplineFactory class to create
* splines of this type.
*
* @author <a href="mailto:jacob.dreyer@geosoft.no">Jacob Dreyer</a>
*/
class BezierSpline extends Spline
{
/**
* Construct a bezier spline. Package local; Use the SplineFactory
* to create splines of this type. The control points are used according
* to the definition of Bezier splines.
*
* @param controlPoints Control points of spline (x0,y0,z0,x1,y1,z1,...)
* @param nParts Number of parts in generated spline.
*/
BezierSpline (double controlPoints[], int nParts)
{
controlPoints_ = controlPoints;
nParts_ = nParts;
}
/**
* Generate this spline.
*
* @return Coordinates of the spline (x0,y0,z0,x1,y1,z1,...)
*/
double[] generate()
{
if (controlPoints_.length < 9) {
double[] copy = new double[controlPoints_.length];
System.arraycopy (controlPoints_, 0, copy, 0, controlPoints_.length);
return copy;
}
int n = controlPoints_.length / 3;
int length = (n - 3) * nParts_ + 1;
double spline[] = new double[length * 3];
p (0, 0, controlPoints_, spline, 0);
int index = 3;
for (int i = 0; i < n - 3; i += 3) {
for (int j = 1; j <= nParts_; j++) {
p (i, j / (double) nParts_, controlPoints_, spline, index);
index += 3;
}
}
return spline;
}
private void p (int i, double t, double cp[], double spline[], int index)
{
double x = 0.0;
double y = 0.0;
double z = 0.0;
int k = i;
for (int j = 0; j <= 3; j++) {
double b = blend (j, t);
x += b * cp[k++];
y += b * cp[k++];
z += b * cp[k++];
}
spline[index + 0] = x;
spline[index + 1] = y;
spline[index + 2] = z;
}
private double blend (int i, double t)
{
if (i == 0) return (1 - t) * (1 - t) * (1 - t);
else if (i == 1) return 3 * t * (1 - t) * (1 - t);
else if (i == 2) return 3 * t * t * (1 - t);
else return t * t * t;
}
}
/*
* This code is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, write to the Free
* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
* MA 02111-1307, USA.
*/
//package no.geosoft.cc.geometry.spline;
/**
* A cubic spline object. Use the SplineFactory class to create
* splines of this type.
*
* @author <a href="mailto:jacob.dreyer@geosoft.no">Jacob Dreyer</a>
*/
class CubicSpline extends Spline
{
/**
* Construct a cubic spline. Package local; Use the SplineFactory
* to create splines of this type. The control points are used according
* to the definition of cubic splines.
*
* @param controlPoints Control points of spline (x0,y0,z0,x1,y1,z1,...)
* @param nParts Number of parts in generated spline.
*/
CubicSpline (double controlPoints[], int nParts)
{
initialize (controlPoints, nParts);
}
protected void initialize (double controlPoints[], int nParts)
{
nParts_ = nParts;
// Endpoints are added three times to get them include in the
// generated array
controlPoints_ = new double[controlPoints.length + 12];
System.arraycopy (controlPoints, 0, controlPoints_, 6,
controlPoints.length);
controlPoints_[0] = controlPoints_[6];
controlPoints_[1] = controlPoints_[7];
controlPoints_[2] = controlPoints_[8];
controlPoints_[3] = controlPoints_[6];
controlPoints_[4] = controlPoints_[7];
controlPoints_[5] = controlPoints_[8];
controlPoints_[controlPoints_.length - 3] = controlPoints_[controlPoints_.length - 9];
controlPoints_[controlPoints_.length - 2] = controlPoints_[controlPoints_.length - 8];
controlPoints_[controlPoints_.length - 1] = controlPoints_[controlPoints_.length - 7];
controlPoints_[controlPoints_.length - 6] = controlPoints_[controlPoints_.length - 9];
controlPoints_[controlPoints_.length - 5] = controlPoints_[controlPoints_.length - 8];
controlPoints_[controlPoints_.length - 4] = controlPoints_[controlPoints_.length - 7];
}
/**
* Generate this spline.
*
* @return Coordinates of the spline (x0,y0,z0,x1,y1,z1,...)
*/
double[] generate()
{
int n = controlPoints_.length / 3;
int length = (n - 3) * nParts_ + 1;
double spline[] = new double[length * 3];
p (2, 0, controlPoints_, spline, 0);
int index = 3;
for (int i = 2; i < n - 1; i++) {
for (int j = 1; j <= nParts_; j++) {
p (i, j / (double) nParts_, controlPoints_, spline, index);
index += 3;
}
}
return spline;
}
private void p (int i, double t, double cp[], double spline[], int index)
{
double x = 0.0;
double y = 0.0;
double z = 0.0;
int k = (i - 2) * 3;
for (int j = -2; j <= 1; j++) {
// TODO: Precompute blending matrix
double b = blend (j, t);
x += b * cp[k++];
y += b * cp[k++];
z += b * cp[k++];
}
spline[index + 0] = x;
spline[index + 1] = y;
spline[index + 2] = z;
}
protected double blend (int i, double t)
{
if (i == -2) return (((-t + 3) * t - 3) * t + 1) / 6;
else if (i == -1) return (((3 * t - 6) * t) * t + 4) / 6;
else if (i == 0) return (((-3 * t + 3) * t + 3) * t + 1) / 6;
else return (t * t * t) / 6;
}
}
/*
* This code is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This code is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this program; if not, write to the Free
* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
* MA 02111-1307, USA.
*/
//package no.geosoft.cc.geometry.spline;
/**
* A Catmull-Rom spline object. Use the SplineFactory class to create
* splines of this type.
*
* @author <a href="mailto:jacob.dreyer@geosoft.no">Jacob Dreyer</a>
*/
class CatmullRomSpline extends CubicSpline
{
/**
* Construct a Catmull-Rom spline. Package local; Use the SplineFactory
* to create splines of this type. The control points are used according
* to the definition of Catmull-Rom splines.
*
* @param controlPoints Control points of spline (x0,y0,z0,x1,y1,z1,...)
* @param nParts Number of parts in generated spline.
*/
CatmullRomSpline (double controlPoints[], int nParts)
{
super (controlPoints, nParts);
}
protected void initialize (double controlPoints[], int nParts)
{
nParts_ = nParts;
// Endpoints are added twice to force in the generated array
controlPoints_ = new double[controlPoints.length + 6];
System.arraycopy (controlPoints, 0, controlPoints_, 3,
controlPoints.length);
controlPoints_[0] = controlPoints_[3];
controlPoints_[1] = controlPoints_[4];
controlPoints_[2] = controlPoints_[5];
controlPoints_[controlPoints_.length - 3] = controlPoints_[controlPoints_.length - 6];
controlPoints_[controlPoints_.length - 2] = controlPoints_[controlPoints_.length - 5];
controlPoints_[controlPoints_.length - 1] = controlPoints_[controlPoints_.length - 4];
}
protected double blend (int i, double t)
{
if (i == -2) return ((-t + 2) * t - 1) * t / 2;
else if (i == -1) return (((3 * t - 5) * t) * t + 2) / 2;
else if (i == 0) return ((-3 * t + 4) * t + 1) * t / 2;
else return ((t - 1) * t * t) / 2;
}
}
]]>