/* circle_circle_intersection() * * Determine the points where 2 circles in a common plane intersect. * * int circle_circle_intersection( * // center and radius of 1st circle * double x0, double y0, double r0, * // center and radius of 2nd circle * double x1, double y1, double r1, * // 1st intersection point * double *xi, double *yi, * // 2nd intersection point * double *xi_prime, double *yi_prime) * * This is a public domain work. 3/26/2005 Tim Voght * Ported to lib2geom, 2006 Nathan Hurst * * Copyright 2006 Nathan Hurst <njh@mail.csse.monash.edu.au> * * This library is free software; you can redistribute it and/or * modify it either under the terms of the GNU Lesser General Public * License version 2.1 as published by the Free Software Foundation * (the "LGPL") or, at your option, under the terms of the Mozilla * Public License Version 1.1 (the "MPL"). If you do not alter this * notice, a recipient may use your version of this file under either * the MPL or the LGPL. * * You should have received a copy of the LGPL along with this library * in the file COPYING-LGPL-2.1; if not, write to the Free Software * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA * You should have received a copy of the MPL along with this library * in the file COPYING-MPL-1.1 * * The contents of this file are subject to the Mozilla Public License * Version 1.1 (the "License"); you may not use this file except in * compliance with the License. You may obtain a copy of the License at * http://www.mozilla.org/MPL/ * * This software is distributed on an "AS IS" basis, WITHOUT WARRANTY * OF ANY KIND, either express or implied. See the LGPL or the MPL for * the specific language governing rights and limitations. * */ #include <stdio.h> #include <math.h> #include "point.h" namespace Geom{ int circle_circle_intersection(Point X0, double r0, Point X1, double r1, Point & p0, Point & p1) { /* dx and dy are the vertical and horizontal distances between * the circle centers. */ Point D = X1 - X0; /* Determine the straight-line distance between the centers. */ double d = L2(D); /* Check for solvability. */ if (d > (r0 + r1)) { /* no solution. circles do not intersect. */ return 0; } if (d <= fabs(r0 - r1)) { /* no solution. one circle is contained in the other */ return 1; } /* 'point 2' is the point where the line through the circle * intersection points crosses the line between the circle * centers. */ /* Determine the distance from point 0 to point 2. */ double a = ((r0*r0) - (r1*r1) + (d*d)) / (2.0 * d) ; /* Determine the coordinates of point 2. */ Point p2 = X0 + D * (a/d); /* Determine the distance from point 2 to either of the * intersection points. */ double h = sqrt((r0*r0) - (a*a)); /* Now determine the offsets of the intersection points from * point 2. */ Point r = (h/d)*rot90(D); /* Determine the absolute intersection points. */ p0 = p2 + r; p1 = p2 - r; return 2; } }; #ifdef TEST void run_test(double x0, double y0, double r0, double x1, double y1, double r1) { double x3, y3, x3_prime, y3_prime; printf("x0=%F, y0=%F, r0=%F, x1=%F, y1=%F, r1=%F :\n", x0, y0, r0, x1, y1, r1); Geom::Point p0, p1; Geom::circle_circle_intersection(Geom::Point(x0, y0), r0, Geom::Point(x1, y1), r1, p0, p1); printf(" x3=%F, y3=%F, x3_prime=%F, y3_prime=%F\n", p0[0], p0[1], p1[0], p1[1]); } int main(void) { /* Add more! */ run_test(-1.0, -1.0, 1.5, 1.0, 1.0, 2.0); run_test(1.0, -1.0, 1.5, -1.0, 1.0, 2.0); run_test(-1.0, 1.0, 1.5, 1.0, -1.0, 2.0); run_test(1.0, 1.0, 1.5, -1.0, -1.0, 2.0); exit(0); } #endif

Generated by Doxygen 1.6.0 Back to index