001/*******************************************************************************
002 * This software is provided as a supplement to the authors' textbooks on digital
003 * image processing published by Springer-Verlag in various languages and editions.
004 * Permission to use and distribute this software is granted under the BSD 2-Clause
005 * "Simplified" License (see http://opensource.org/licenses/BSD-2-Clause).
006 * Copyright (c) 2006-2023 Wilhelm Burger, Mark J. Burge. All rights reserved.
007 * Visit https://imagingbook.com for additional details.
008 ******************************************************************************/
009package imagingbook.common.geometry.fitting.circle.algebraic;
010
011
012import imagingbook.common.geometry.basic.Pnt2d;
013import imagingbook.common.math.Arithmetic;
014
015import static imagingbook.common.math.Arithmetic.sqr;
016
017/**
018 * <p>
019 * Performs an exact circle fit to 3 given (non-collinear) points. If the fit is unsuccessful, {@link #getParameters()}
020 * returns {@code null}. See the Appendix of [1] (Sec. F.2.2) for details.
021 * </p>
022 * <p>
023 * [1] W. Burger, M.J. Burge, <em>Digital Image Processing &ndash; An Algorithmic Introduction</em>, 3rd ed, Springer
024 * (2022).
025 * </p>
026 *
027 * @author WB
028 * @version 2022/11/17
029 */
030public class CircleFit3Points implements CircleFitAlgebraic {
031        
032        private final double[] p;
033        
034        @Override
035        public double[] getParameters() {
036                return this.p;
037        }
038
039        /**
040         * Constructor. Fits a circle to the specified three sample points. If the fit is unsuccessful,
041         * {@link #getParameters()} returns {@code null}.
042         *
043         * @param p0 sample point 1
044         * @param p1 sample point 2
045         * @param p2 sample point 3
046         */
047        public CircleFit3Points(Pnt2d p0, Pnt2d p1, Pnt2d p2) {
048                final double x0 = p0.getX();
049                final double y0 = p0.getY();
050                final double x1 = p1.getX();
051                final double y1 = p1.getY();
052                final double x2 = p2.getX();
053                final double y2 = p2.getY();
054                
055                final double A = x0 * (y1 - y2) - y0 * (x1 - x2) + x1 * y2 - x2 * y1;           
056                if (Arithmetic.isZero(A)) {
057                        this.p = null;
058                } 
059                else {
060                        final double R0 = sqr(x0) + sqr(y0);
061                        final double R1 = sqr(x1) + sqr(y1);
062                        final double R2 = sqr(x2) + sqr(y2);
063                        final double B = R0 * (y2 - y1) + R1 * (y0 - y2) + R2 * (y1 - y0);
064                        final double C = R0 * (x1 - x2) + R1 * (x2 - x0) + R2 * (x0 - x1);
065                        final double D = R0 * (x2 * y1 - x1 * y2) + R1 * (x0 * y2 - x2 * y0) + R2 * (x1 * y0 - x0 * y1);        
066                        this.p = new double[] {A, B, C, D};
067                }
068        }
069
070        /**
071         * Constructor. Fits a circle to the specified three sample points, passed as an array of points. Only the first
072         * three points are used, additional points are ignored. If the fit is unsuccessful, {@link #getParameters()}
073         * returns {@code null}.
074         *
075         * @param pts three or more sample points
076         */
077        public CircleFit3Points(Pnt2d[] pts) {
078                this(pts[0], pts[1], pts[2]);
079        }
080
081
082}