Jump to content

Algorithm Implementation/Geometry/Tangents between two circles

Add links
From Wikibooks, open books for an open world

This code finds the set of common tangents between two circles.

Java

[edit | edit source]
import java.util.Arrays; public class CircleTangents {  /**  * Finds tangent segments between two given circles.  *  * Returns an empty, or 2x4, or 4x4 array of doubles representing  * the two exterior and two interior tangent segments (in that order).  * If some tangents don't exist, they aren't present in the output.  * Each segment is represent by a 4-tuple x1,y1,x2,y2.  *   * Exterior tangents exist iff one of the circles doesn't contain  * the other. Interior tangents exist iff circles don't intersect.  *  * In the limiting case when circles touch from outside/inside, there are  * no interior/exterior tangents, respectively, but just one common  * tangent line (which isn't returned at all, or returned as two very  * close or equal points by this code, depending on roundoff -- sorry!)  *  * Java 6 (1.6) required, for Arrays.copyOf()  */  public static double[][] getTangents(double x1, double y1, double r1, double x2, double y2, double r2) {  double d_sq = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);  if (d_sq <= (r1-r2)*(r1-r2)) return new double[0][4];  double d = Math.sqrt(d_sq);  double vx = (x2 - x1) / d;  double vy = (y2 - y1) / d;  double[][] res = new double[4][4];  int i = 0;  // Let A, B be the centers, and C, D be points at which the tangent  // touches first and second circle, and n be the normal vector to it.  //  // We have the system:  // n * n = 1 (n is a unit vector)   // C = A + r1 * n  // D = B +/- r2 * n  // n * CD = 0 (common orthogonality)  //  // n * CD = n * (AB +/- r2*n - r1*n) = AB*n - (r1 -/+ r2) = 0, <=>  // AB * n = (r1 -/+ r2), <=>  // v * n = (r1 -/+ r2) / d, where v = AB/|AB| = AB/d  // This is a linear equation in unknown vector n.  for (int sign1 = +1; sign1 >= -1; sign1 -= 2) {  double c = (r1 - sign1 * r2) / d;  // Now we're just intersecting a line with a circle: v*n=c, n*n=1  if (c*c > 1.0) continue;  double h = Math.sqrt(Math.max(0.0, 1.0 - c*c));  for (int sign2 = +1; sign2 >= -1; sign2 -= 2) {  double nx = vx * c - sign2 * h * vy;  double ny = vy * c + sign2 * h * vx;  double[] a = res[i++];  a[0] = x1 + r1 * nx;  a[1] = y1 + r1 * ny;  a[2] = x2 + sign1 * r2 * nx;  a[3] = y2 + sign1 * r2 * ny;  }  }    return Arrays.copyOf(res, i);  } }
[edit | edit source]
Retrieved from "https://en.wikibooks.org/w/index.php?title=Algorithm_Implementation/Geometry/Tangents_between_two_circles&oldid=3677615"