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/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* 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
*
* https://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/*
* This is not the original file distributed by the Apache Software Foundation
* It has been modified by the Hipparchus project
*/
package org.hipparchus.geometry.euclidean.twod;
import java.util.List;
import org.hipparchus.fraction.BigFraction;
import org.hipparchus.geometry.enclosing.EnclosingBall;
import org.hipparchus.geometry.enclosing.SupportBallGenerator;
import org.hipparchus.util.FastMath;
/** Class generating an enclosing ball from its support points.
*/
public class DiskGenerator implements SupportBallGenerator {
/** Empty constructor.
*
* This constructor is not strictly necessary, but it prevents spurious
* javadoc warnings with JDK 18 and later.
*
* @since 3.0
*/
public DiskGenerator() { // NOPMD - unnecessary constructor added intentionally to make javadoc happy
// nothing to do
}
/** {@inheritDoc} */
@Override
public EnclosingBall ballOnSupport(final List support) {
if (support.isEmpty()) {
return new EnclosingBall<>(Vector2D.ZERO, Double.NEGATIVE_INFINITY);
} else {
final Vector2D vA = support.get(0);
if (support.size() < 2) {
return new EnclosingBall<>(vA, 0, vA);
} else {
final Vector2D vB = support.get(1);
if (support.size() < 3) {
final Vector2D center = new Vector2D(0.5, vA, 0.5, vB);
// we could have computed r directly from the vA and vB
// (it was done this way up to Hipparchus 1.0), but as center
// is approximated in the computation above, it is better to
// take the final value of center and compute r from the distances
// to center of all support points, using a max to ensure all support
// points belong to the ball
// see
final double r = FastMath.max(Vector2D.distance(vA, center),
Vector2D.distance(vB, center));
return new EnclosingBall<>(center, r, 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(vA.getX()), new BigFraction(vB.getX()), new BigFraction(vC.getX())
};
final BigFraction[] c3 = {
new BigFraction(vA.getY()), new BigFraction(vB.getY()), new BigFraction(vC.getY())
};
final BigFraction[] c1 = {
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 Vector2D center = new Vector2D( m12.divide(twoM11).doubleValue(),
-m13.divide(twoM11).doubleValue());
// we could have computed r directly from the minors above
// (it was done this way up to Hipparchus 1.0), but as center
// is approximated in the computation above, it is better to
// take the final value of center and compute r from the distances
// to center of all support points, using a max to ensure all support
// points belong to the ball
// see
final double r = FastMath.max(Vector2D.distance(vA, center),
FastMath.max(Vector2D.distance(vB, center),
Vector2D.distance(vC, center)));
return new EnclosingBall<>(center, r, vA, vB, vC);
}
}
}
}
/** Compute a dimension 3 minor, when 3d 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])));
}
}
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