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.line;
010
011import imagingbook.common.geometry.basic.Pnt2d;
012import imagingbook.common.math.Arithmetic;
013import imagingbook.common.math.Matrix;
014
015import java.util.Locale;
016
017import static imagingbook.common.math.Arithmetic.sqr;
018
019/**
020 * <p>
021 * This class represents a line in parametric form: x = s + t v, where s is a start point on the line, v is a direction
022 * vector, and t is a real variable. Instances are immutable. See Sec. 10.1 and Appendix F.1 of [1] for details.
023 * </p>
024 * <p>
025 * [1] W. Burger, M.J. Burge, <em>Digital Image Processing &ndash; An Algorithmic Introduction</em>, 3rd ed, Springer
026 * (2022).
027 * </p>
028 *
029 * @author WB
030 * @version 2022/11/18
031 */
032public class ParametricLine {
033        
034        private final double[] s, v;
035        
036        public ParametricLine(double[] s, double[] v) {
037                if (s.length != 2 || v.length != 2) {
038                        throw new IllegalArgumentException("vectors s, v must be of length 2");
039                }
040                if (Arithmetic.isZero(Matrix.normL2squared(v))) {
041                        throw new IllegalArgumentException("direction vector (v) must be nonzero");
042                }
043                this.s = s.clone();
044                this.v = v.clone();
045        }
046        
047        public double[] getS() {
048                return s;
049        }
050
051        public double[] getV() {
052                return v;
053        }
054        
055        // --------------------------
056        
057        public static ParametricLine from(AlgebraicLine al) {
058                double[] p = al.getParameters();
059                // not needed, since algebraic lines are always normalized (i.e. A^2 + B^2 = 1)
060                double norm2 = sqr(p[0]) + sqr(p[1]);           // = A^2 + B^2
061                double scale = -p[2] / norm2;                           // = -C / ||(A,B)||^2
062                double[] s = {scale * p[0], scale * p[1]};      // = (-CA, -CB)
063                double[] v = {-p[1], p[0]};                                     // = (-B, A)
064                return new ParametricLine(s, v);
065        }
066        
067        @Override
068        public String toString() {
069                return String.format(Locale.US, "%s <s=[%.3f, %.3f], v=[%.3f, %.3f]>",
070                                this.getClass().getSimpleName(), s[0], s[1], v[0], v[1]);
071        }
072        
073        // --------------------------
074        
075        public static void main (String[] args) {
076                Pnt2d p1 = Pnt2d.from(1, 2);
077                Pnt2d p2 = Pnt2d.from(4, 3);
078                
079                AlgebraicLine al1 = AlgebraicLine.from(p1, p2);
080                System.out.println("al1 = " + al1);
081                
082                ParametricLine pl = ParametricLine.from(al1);
083                System.out.println("pl = " + pl);
084                
085                AlgebraicLine al2 = AlgebraicLine.from(pl);
086                System.out.println("al2 = " + al2);
087                
088                System.out.println("al1 = al2 ? " + al1.equals(al2, 1e-6));
089        }
090
091        /*
092        al1 = AlgebraicLine <a=-0.316, b=0.949, c=-1.581>
093        pl = ParametricLine <s=[-0.500, 1.500], v=[-0.949, -0.316]>
094        al2 = AlgebraicLine <a=0.316, b=-0.949, c=1.581>
095        al1 = al2 ? true
096        */
097
098}