circle Line Intersection - Java java.lang

Java examples for java.lang:Math Geometry Line

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Description

circle Line Intersection

Demo Code

/**/* ww w  . ja  v a  2s .c o  m*/
 * Copyright 1998-2007, CHISEL Group, University of Victoria, Victoria, BC, Canada.
 * All rights reserved.
 */
//package com.java2s;

import java.awt.geom.Point2D;

public class Main {
    /**
     * @param theta    Angle of line from (0,0), in radians
     * @param r       Radius of the circle.
     * @param h       X coordinate of centre of circle
     * @param k       Y coordinate of centre of circle
     * @param result    An array of 2 Point2D objects. Returns the 0, 1, or 2 points of intersection.
     *                result [0] is the first point of intersection, result[1] is the sectod point of intersection
     *                Either may be null.
     */
    public static void circleLineIntersection(double theta, double r,
            double h, double k, Point2D[] result) {
        if (result.length != 2) {
            (new Exception("result must have length 2!")).printStackTrace();
            return;
        }

        /* equation of a line, y=m*x+b, since one point at 0,0 and m=dy/dx=tan(theta) this line becomes y=tan(theta)*x
           equation of a circle, (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center of the circle and r is its radius
                    
           after a bit of algebra and the quadratic equation, solving for x gives ...
                x = (-b +/- sqrt(b^2 - 4*a*c))/2*a
               where    a = 1 + tan(theta)^2,
                     b = -2*h - 2*k*tan(theta), and
                     c = h^2 + k^2 - r^2
                       
         *** Note: There is absolutely no consideration of extreme values or other checks
         * for computational errors in the following code (ex. when theta approaches PI/2, tan(theta) approaches infinity)
         * As of Aug 2003, this method is only used to find the intersection of arcs with the corners of rounded rectangles
         * so these extremes do not come into play.
         */
        double tanTheta = Math.tan(theta);
        double a = 1.0 + Math.pow(tanTheta, 2);
        double b = -2.0 * h - 2.0 * k * tanTheta;
        double c = Math.pow(h, 2) + Math.pow(k, 2) - Math.pow(r, 2);

        try {
            double x1 = (-b + Math.sqrt(Math.pow(b, 2) - 4.0 * a * c))
                    / (2.0 * a);
            double y1 = x1 * tanTheta;
            result[0] = new Point2D.Double(x1, y1);
        } catch (RuntimeException e) {
            e.printStackTrace();
            result[0] = null;
        }
        try {
            double x2 = (-b - Math.sqrt(Math.pow(b, 2) - 4.0 * a * c))
                    / (2.0 * a);
            double y2 = x2 * tanTheta;
            result[1] = new Point2D.Double(x2, y2);
        } catch (RuntimeException e1) {
            e1.printStackTrace();
            result[1] = null;
        }
    }
}

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