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/* XLogo4Schools - A Logo Interpreter specialized for use in schools, based on XLogo by Lo�c Le Coq
* Copyright (C) 2013 Marko Zivkovic
*
* Contact Information: marko88zivkovic at gmail dot com
*
* This program is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License as published by the Free
* Software Foundation; either version 2 of the License, or (at your option)
* any later version. This program 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 General
* Public License for more details. You should have received a copy of the
* GNU General Public License along with this program; if not, write to the Free
* Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
* MA 02110-1301, USA.
*
*
* This Java source code belongs to XLogo4Schools, written by Marko Zivkovic
* during his Bachelor thesis at the computer science department of ETH Z�rich,
* in the year 2013 and/or during future work.
*
* It is a reengineered version of XLogo written by Lo�c Le Coq, published
* under the GPL License at http://xlogo.tuxfamily.org/
*
* Contents of this file were initially written by Lo�c Le Coq,
* modifications, extensions, refactorings might have been applied by Marko Zivkovic
*/
package xlogo.kernel.perspective;
import java.math.BigDecimal;
import xlogo.kernel.DrawPanel;
/**
* @author Marko : This is now decoupled from Application
*
*/
public class Conic
{
private DrawPanel dp;
BigDecimal a;
BigDecimal b;
BigDecimal c;
BigDecimal d;
BigDecimal e;
BigDecimal f;
BigDecimal deux = new BigDecimal(2);
private final BigDecimal un = BigDecimal.ONE;
private final BigDecimal zero = BigDecimal.ZERO;
BigDecimal[][] A = new BigDecimal[2][2];
private BigDecimal[] eigenValue = new BigDecimal[2];
private BigDecimal[][] eigenVect = new BigDecimal[2][2];
private BigDecimal[] center = new BigDecimal[2];
private double halfXAxis;
private double halfYAxis;
public Conic(DrawPanel dp, BigDecimal[] v)
{
this.dp = dp;
this.a = v[0];
this.b = v[1];
this.c = v[2];
this.d = v[3];
this.e = v[4];
this.f = v[5];
A[0][0] = a;
A[1][1] = c;
// b/2
A[0][1] = b.divide(deux);
A[1][0] = b.divide(deux);
drawConic();
}
private void drawConic()
{
calculateEigenVect();
// ellipse
BigDecimal det = det(A);
if (det.compareTo(zero) == 1)
{
// Looking for center
calculateCenter();
// The main equation becomes with the center as Origin:
// aX^2+bXY+cY^2+omega=0
// double omega=a*Math.pow(center[0],2)+c*Math.pow(center[1],2)
// +b*center[0]*center[1]+d*center[0]+e*center[1]+f;
BigDecimal omega = a.multiply(center[0].pow(2)).add(c.multiply(center[1].pow(2)))
.add(center[0].multiply(center[1]).multiply(b)).add(d.multiply(center[0]))
.add(e.multiply(center[1])).add(f);
// We apply the rotation with the Eigen Vect Matrix
// Now the equation becomes: lambda*X^2+mu*Y^2+omega=0
// with lambda and mu the eigen Values
// 1/sqrt(eigenValue[0]/-omega)
halfXAxis = 1 / Math.sqrt(eigenValue[0].divide(omega.negate(), 20, BigDecimal.ROUND_HALF_EVEN)
.doubleValue());
// 1/sqrt(eigenValue[1]/-omega)
halfYAxis = 1 / Math.sqrt(eigenValue[1].divide(omega.negate(), 20, BigDecimal.ROUND_HALF_EVEN)
.doubleValue());
double angle = Math.atan(eigenVect[1][0].divide(eigenVect[0][0], 20, BigDecimal.ROUND_HALF_EVEN)
.doubleValue());
// System.out.println(toString());
dp.drawEllipseArc(halfXAxis, halfYAxis, angle, center[0].doubleValue(),
center[1].doubleValue(), 0, 360);
}
// hyperbola
else if (det.compareTo(zero) == -1)
{
calculateCenter();
}
// parabola
else
{}
}
private void calculateEigenValue()
{
// Polynom: acX^2-(a+c)X+A[0][1]^2
// tmp=a+c
BigDecimal tmp = A[0][0].add(A[1][1]);
// Discriminant delta=(a-c)^2+4*A[0][1]^2
BigDecimal delta = A[0][0].subtract(A[1][1]).pow(2).add(new BigDecimal(4).multiply(A[0][1].pow(2)));
// calculate the eigen Values
eigenValue[0] = tmp.subtract(sqrt(delta)).divide(deux);
eigenValue[1] = tmp.add(sqrt(delta)).divide(deux);
}
private void calculateEigenVect()
{
if (A[0][1].compareTo(zero) == 0)
{
eigenValue[0] = A[0][0];
eigenValue[1] = A[1][1];
eigenVect[0][0] = un;
eigenVect[1][0] = zero;
eigenVect[0][1] = zero;
eigenVect[1][1] = un;
}
else
{
calculateEigenValue();
BigDecimal tmp = A[0][0].subtract(eigenValue[0]);
eigenVect[0][0] = un;
// System.out.println("pb: "+tmp+"\n"+A[0][1]);
eigenVect[1][0] = tmp.negate().divide(A[0][1], 20, BigDecimal.ROUND_HALF_EVEN);
// vector length and then normalize
tmp = sqrt(eigenVect[0][0].pow(2).add(eigenVect[1][0].pow(2)));
eigenVect[0][0] = eigenVect[0][0].divide(tmp, 20, BigDecimal.ROUND_HALF_EVEN);
eigenVect[1][0] = eigenVect[1][0].divide(tmp, 20, BigDecimal.ROUND_HALF_EVEN);
eigenVect[0][1] = eigenVect[1][0].negate();
eigenVect[1][1] = un;
}
}
private void calculateCenter()
{
// System determinant
// df/dx=0 and df/dy=0
// double det=4*a*c-Math.pow(b,2);
BigDecimal det = new BigDecimal(4).multiply(a).multiply(c).subtract(b.pow(2));
// xCenter=(-2*c*d+b*e)/det;
center[0] = (deux.negate().multiply(c).multiply(d).add(b.multiply(e))).divide(det, 20,
BigDecimal.ROUND_HALF_EVEN);
// yCenter=(-2*a*e+b*d)/det;
center[1] = (deux.negate().multiply(a).multiply(e).add(b.multiply(d))).divide(det, 20,
BigDecimal.ROUND_HALF_EVEN);
}
private BigDecimal det(BigDecimal[][] M)
{
return M[0][0].multiply(M[1][1]).subtract(M[0][1].multiply(M[1][0]));
}
public String toString()
{
String st = "centre: " + center[0] + " " + center[1] + "\n" + "Valeurs propres: " + eigenValue[0] + " "
+ eigenValue[1] + "\n" + "Vecteurs propres:\n" + eigenVect[0][0] + " " + eigenVect[0][1] + "\n"
+ eigenVect[1][0] + " " + eigenVect[1][1] + "\n" + "Demi Axe: X " + halfXAxis + " Y " + halfYAxis;
return st;
}
private BigDecimal sqrt(BigDecimal b)
{
BigDecimal precision = new BigDecimal(0.00000000001);
int scale = precision.scale();
if (b.scale() < scale)
{
b = b.setScale(scale);
}
// Initial guess
// G = A/2
BigDecimal g = new BigDecimal(Math.sqrt(b.doubleValue()));
// Iterate until we're done
while (true)
{
// G* = ((A/G)+G)/2
BigDecimal gStar = b.divide(g, BigDecimal.ROUND_HALF_EVEN).add(g).divide(deux, BigDecimal.ROUND_HALF_EVEN);
BigDecimal delta = gStar.subtract(g);
delta = delta.abs();
if (delta.compareTo(precision) < 0)
break;
g = gStar;
}
return g;
}
}
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