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 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
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 *      http://www.apache.org/licenses/LICENSE-2.0
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 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
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package org.apache.commons.math3.geometry.euclidean.twod;

import java.util.List;

import org.apache.commons.math3.fraction.BigFraction;
import org.apache.commons.math3.geometry.enclosing.EnclosingBall;
import org.apache.commons.math3.geometry.enclosing.SupportBallGenerator;
import org.apache.commons.math3.util.FastMath;

Class generating an enclosing ball from its support points.
Since:3.3
/** Class generating an enclosing ball from its support points. * @since 3.3 */
public class DiskGenerator implements SupportBallGenerator<Euclidean2D, Vector2D> {
{@inheritDoc}
/** {@inheritDoc} */
public EnclosingBall<Euclidean2D, Vector2D> ballOnSupport(final List<Vector2D> support) { if (support.size() < 1) { return new EnclosingBall<Euclidean2D, Vector2D>(Vector2D.ZERO, Double.NEGATIVE_INFINITY); } else { final Vector2D vA = support.get(0); if (support.size() < 2) { return new EnclosingBall<Euclidean2D, Vector2D>(vA, 0, vA); } else { final Vector2D vB = support.get(1); if (support.size() < 3) { return new EnclosingBall<Euclidean2D, Vector2D>(new Vector2D(0.5, vA, 0.5, vB), 0.5 * vA.distance(vB), vA, vB); } else { final Vector2D vC = support.get(2); // a disk is 2D can be defined as: // (1) (x - x_0)^2 + (y - y_0)^2 = r^2 // which can be written: // (2) (x^2 + y^2) - 2 x_0 x - 2 y_0 y + (x_0^2 + y_0^2 - r^2) = 0 // or simply: // (3) (x^2 + y^2) + a x + b y + c = 0 // with disk center coordinates -a/2, -b/2 // If the disk exists, a, b and c are a non-zero solution to // [ (x^2 + y^2 ) x y 1 ] [ 1 ] [ 0 ] // [ (xA^2 + yA^2) xA yA 1 ] [ a ] [ 0 ] // [ (xB^2 + yB^2) xB yB 1 ] * [ b ] = [ 0 ] // [ (xC^2 + yC^2) xC yC 1 ] [ c ] [ 0 ] // So the determinant of the matrix is zero. Computing this determinant // by expanding it using the minors m_ij of first row leads to // (4) m_11 (x^2 + y^2) - m_12 x + m_13 y - m_14 = 0 // So by identifying equations (2) and (4) we get the coordinates // of center as: // x_0 = +m_12 / (2 m_11) // y_0 = -m_13 / (2 m_11) // Note that the minors m_11, m_12 and m_13 all have the last column // filled with 1.0, hence simplifying the computation final BigFraction[] c2 = new BigFraction[] { new BigFraction(vA.getX()), new BigFraction(vB.getX()), new BigFraction(vC.getX()) }; final BigFraction[] c3 = new BigFraction[] { new BigFraction(vA.getY()), new BigFraction(vB.getY()), new BigFraction(vC.getY()) }; final BigFraction[] c1 = new BigFraction[] { c2[0].multiply(c2[0]).add(c3[0].multiply(c3[0])), c2[1].multiply(c2[1]).add(c3[1].multiply(c3[1])), c2[2].multiply(c2[2]).add(c3[2].multiply(c3[2])) }; final BigFraction twoM11 = minor(c2, c3).multiply(2); final BigFraction m12 = minor(c1, c3); final BigFraction m13 = minor(c1, c2); final BigFraction centerX = m12.divide(twoM11); final BigFraction centerY = m13.divide(twoM11).negate(); final BigFraction dx = c2[0].subtract(centerX); final BigFraction dy = c3[0].subtract(centerY); final BigFraction r2 = dx.multiply(dx).add(dy.multiply(dy)); return new EnclosingBall<Euclidean2D, Vector2D>(new Vector2D(centerX.doubleValue(), centerY.doubleValue()), FastMath.sqrt(r2.doubleValue()), vA, vB, vC); } } } }
Compute a dimension 3 minor, when 3d column is known to be filled with 1.0.
Params:
  • c1 – first column
  • c2 – second column
Returns:value of the minor computed has an exact fraction
/** Compute a dimension 3 minor, when 3<sup>d</sup> column is known to be filled with 1.0. * @param c1 first column * @param c2 second column * @return value of the minor computed has an exact fraction */
private BigFraction minor(final BigFraction[] c1, final BigFraction[] c2) { return c2[0].multiply(c1[2].subtract(c1[1])). add(c2[1].multiply(c1[0].subtract(c1[2]))). add(c2[2].multiply(c1[1].subtract(c1[0]))); } }