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/*
* Copyright (C) 2000, Institute for MicroTherapy
*
* This software and supporting documentation were developed by
*
* University of Witten/Herdecke
* Department of Radiology and MicroTherapy
* Institute for MicroTherapy
* Medical computer science
*
* Universitaetsstrasse 142
* 44799 Bochum, Germany
*
* http://www.microtherapy.de/go/cs
* mailto:computer.science@microtherapy.de
*
* THIS SOFTWARE IS MADE AVAILABLE, AS IS, AND THE INSTITUTE MAKES NO
* WARRANTY REGARDING THE SOFTWARE, ITS PERFORMANCE, ITS MERCHANTABILITY
* OR FITNESS FOR ANY PARTICULAR USE, FREEDOM FROM ANY COMPUTER DISEASES
* OR ITS CONFORMITY TO ANY SPECIFICATION. THE ENTIRE RISK AS TO QUALITY
* AND PERFORMANCE OF THE SOFTWARE IS WITH THE USER.
*
* $Author: kleber $
* $Date: 2001/06/06 10:32:30 $
* $Revision: 1.1.1.1 $
* $State: Exp $
*/
package viewer.paint;
import java.awt.geom.*;
/**
* The <code>GeometryTool</code> class is a collection
* of geometrical utilities. <p>
*
* @author Annacker
* @version $Id: GeometryTool.java,v 1.1.1.1 2001/06/06 10:32:30 kleber Exp $
*/
public final class GeometryTool
{
/**
* The constructor was implemented only to prevent
* the <code>GeometryTool</code> from being instantiated.
*/
private GeometryTool()
{
// intentionally left blank
}
/**
* Returns a cubic spline following the given coordinates.
* The precision is given as ratio of lines to draw between
* two coordinates to the distance between them. <p>
*
* @param coords the coordinates to follow.
* @param precision the precision/smoothness (see above).
*
* @return the path of the spline.
*/
public static GeneralPath getCubicSpline(Point2D.Double[] coords, double precision)
{
// generate resulting path
GeneralPath path = new GeneralPath();
// do we have enough points for a spline?
int n = coords.length;
if(n > 2)
{
// yes, get cubic polynomials, separately for x- and y-coordinates
double[] x = new double[n];
double[] y = new double[n];
for(int i = 0; i < n; i++)
{
x[i] = coords[i].getX();
y[i] = coords[i].getY();
}
CubicPolynomial[] xPoly = calculateCubicPolynomials(x);
CubicPolynomial[] yPoly = calculateCubicPolynomials(y);
// interpolate path point by point
path.moveTo(xPoly[0].calculate(0.0), yPoly[0].calculate(0.0));
for(int i = 0; i < xPoly.length; i++)
{
double step = 1.0 / (coords[0].distance(coords[1]) * precision);
for(double j = step; j <= 1.0; j += step)
{
path.lineTo(xPoly[i].calculate(j), yPoly[i].calculate(j));
}
}
}
else
{
// no, can we create a straight path?
if(n > 1)
{
// yes, do it
path.moveTo((float)coords[0].getX(), (float)coords[0].getY());
path.lineTo((float)coords[1].getX(), (float)coords[1].getY());
}
}
// return the spline path
return path;
}
/**
* Calculates the cubic polynomials that interpolate
* the given values. There are given as many polynomials
* as coordinates minus one. <p>
*
* @param y the values to interpolate.
*
* @return the cubic polynomials.
*/
private static CubicPolynomial[] calculateCubicPolynomials(double[] y)
{
// calculate the derivatives at the given points.
int n = y.length - 1;
double[] gamma = new double[n + 1];
double[] delta = new double[n + 1];
double[] derivative = new double[n + 1];
gamma[0] = 1.0 / 2.0;
for(int i = 1; i < n; i++)
{
gamma[i] = 1.0 / (4.0 - gamma[i - 1]);
}
gamma[n] = 1.0 / (2.0 - gamma[n - 1]);
delta[0] = 3.0 * (y[1] - y[0]) * gamma[0];
for(int i = 1; i < n; i++)
{
delta[i] = (3.0 * (y[i + 1] - y[i - 1]) - delta[i - 1]) * gamma[i];
}
delta[n] = (3.0 * (y[n] - y[n - 1]) - delta[n - 1]) * gamma[n];
derivative[n] = delta[n];
for(int i = n - 1; i >= 0; i--)
{
derivative[i] = delta[i] - gamma[i] * derivative[i + 1];
}
// calculate the coefficients of the cubic polynomials
CubicPolynomial[] poly = new CubicPolynomial[n];
for(int i = 0; i < n; i++)
{
poly[i] = new CubicPolynomial(y[i], derivative[i],
3.0 * (y[i + 1] - y[i]) - 2.0 * derivative[i] - derivative[i + 1],
2.0 * (y[i] - y[i + 1]) + derivative[i] + derivative[i + 1]);
}
// return the polynomials
return poly;
}
}
/**
* The <code>CubicPolynomial</code> class only holds and calculates
* cubic polynomials as a helper for {@link GeometryTool#getCubicSpline}. <p>
*
* @author Kai Annacker
* @version $Id: GeometryTool.java,v 1.1.1.1 2001/06/06 10:32:30 kleber Exp $
*/
class CubicPolynomial
{
/**
* The constant coefficient.
*/
private double a;
/**
* The linear coefficient.
*/
private double b;
/**
* The quadratic coefficient.
*/
private double c;
/**
* The cubic coefficient.
*/
private double d;
/**
* Creates a new cubic polynomial with the given coefficients. <p>
*
* @param a constant coefficient.
* @param b linear coefficient.
* @param c quadratic coefficient.
* @param d cubic coefficient.
*/
protected CubicPolynomial(double a,double b,double c,double d)
{
// copy the coefficients
this.a = a;
this.b = b;
this.c = c;
this.d = d;
}
/**
* Calculates the cubic polynomial for the given value. <p>
*
* @param x the value to calculate for.
*
* @return the polynomial value.
*/
protected float calculate(double x)
{
return (float)((((d * x) + c) * x + b) * x + a);
}
}
/*
* CVS Log
* $Log: GeometryTool.java,v $
* Revision 1.1.1.1 2001/06/06 10:32:30 kleber
* Init commit for DICOMscope 3.5
* Create new CVS
*
*/
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