圆线交点

Question

public static ArrayList<IntPoint> getCircleLineIntersectionPoint(IntPoint pointA, IntPoint pointB, IntPoint center, int radius) {
    // returns a list of intersection points between a line which passes through given points,
    // pointA and pointB, and a circle described by given radius and center coordinate

    double disc, A, B, C, slope, c;
    double x1, x2, y1, y2;
    IntPoint point1, point2;
    ArrayList<IntPoint> intersections = new ArrayList<IntPoint>();  
    try{
        slope = Util.calculateSlope(pointA, pointB);
    }catch (UndefinedSlopeException e){         
        C =  Math.pow(center.y, 2) + Math.pow(pointB.x, 2) - 2 * pointB.x * center.x + Math.pow(center.x, 2) - Math.pow(radius, 2);
        B = -2 * center.y;
        A = 1;
        disc = Math.pow(B, 2) - 4 * 1 * C;
        if (disc < 0){
            return intersections;
        }
        else{
            y1 = (-B + Math.sqrt(disc)) / (2 * A);
            y2 = (-B - Math.sqrt(disc)) / (2 * A);

            x1 = pointB.x;
            x2 = pointB.x;
        }
        point1 = new IntPoint((int)x1, (int)y1);
        point2 = new IntPoint((int)x2, (int)y2);
        if (Util.euclideanDistance(pointA,  point2) > Util.euclideanDistance(pointA, point1)){
            intersections.add(point1);
        }
        else{
            intersections.add(point2);
        }
        return intersections;
    }
    if (slope == 0){
        C =  Math.pow(center.x, 2)  + Math.pow(center.y, 2) + Math.pow(pointB.y, 2) - 2 * pointB.y * center.y  - Math.pow(radius, 2);
        B = -2 * center.x;
        A = 1;
        disc = Math.pow(B, 2) - 4 * 1 * C;
        if (disc < 0){
            return intersections;
        }
        else{
            x1 = (-B + Math.sqrt(disc)) / (2*A);
            x2 = (-B - Math.sqrt(disc)) / (2*A);
            y1 = pointB.y;
            y2 = pointB.y;
        }
    }
    else{
        c = slope * pointA.x + pointA.y;
        B = (2 * center.x + 2 * center.y * slope  + 2 * c * slope);
        A = 1 + Math.pow(slope, 2);
        C = (Math.pow(center.x, 2) + Math.pow(c, 2) + 2 * center.y * c + Math.pow(center.y, 2) - Math.pow(radius, 2));
        disc = Math.pow(B, 2) - (4 * A * C);

        if (disc < 0){
            return intersections;
        }
        else{
            x1 = (-B + Math.sqrt(disc)) / (2 * A);
            x2 = (-B - Math.sqrt(disc)) / (2 * A);

            y1 = slope * x1 - c;
            y2 = slope * x2 - c;
        }
    }

    point1 = new IntPoint((int)x1, (int)y1);
    point2 = new IntPoint((int)x2, (int)y2);
    if (Util.euclideanDistance(pointA,  point2) > Util.euclideanDistance(pointA, point1)){
        //if (Util.angleBetween(pointA, pointB, point1) < Math.PI/2){
            intersections.add(point1);
        //}
    }
    else{
        //if (Util.angleBetween(pointA, pointB, point1) < Math.PI/2){
            intersections.add(point2);
        //}
    }       
    return intersections;
}

我使用上面的算法来测试圆和线之间的交集.它有时很好,但在其他时候它失败了.代码表示,其是从圆和直线的方程同时求解X衍生的方程(x-a)^+(y-b)^2=r^2和y = mx - mx1 + y1.有没有人知道我在数学或其他地方出错了？

Answer 1

你的计算似乎很长,我没有看到你测试的不同情况的使用.无论如何,因为我发现问题很有趣,我试图自己解决它并提出以下内容.随意更换double radius的int radius,并使用IntPointS,但是要知道,你每次投,如在评论中讨论的那样,一点效果都没有准确的整数交点将成为错误的.

执行计算的背景是:从A点开始,矢量AB的缩放版本指向圆上的点.该点与中心的距离半径.因此,| AC + scalingFactor*AB | = r.

import java.util.Arrays;
import java.util.Collections;
import java.util.List;

public class CircleLine {

    public static List<Point> getCircleLineIntersectionPoint(Point pointA,
            Point pointB, Point center, double radius) {
        double baX = pointB.x - pointA.x;
        double baY = pointB.y - pointA.y;
        double caX = center.x - pointA.x;
        double caY = center.y - pointA.y;

        double a = baX * baX + baY * baY;
        double bBy2 = baX * caX + baY * caY;
        double c = caX * caX + caY * caY - radius * radius;

        double pBy2 = bBy2 / a;
        double q = c / a;

        double disc = pBy2 * pBy2 - q;
        if (disc < 0) {
            return Collections.emptyList();
        }
        // if disc == 0 ... dealt with later
        double tmpSqrt = Math.sqrt(disc);
        double abScalingFactor1 = -pBy2 + tmpSqrt;
        double abScalingFactor2 = -pBy2 - tmpSqrt;

        Point p1 = new Point(pointA.x - baX * abScalingFactor1, pointA.y
                - baY * abScalingFactor1);
        if (disc == 0) { // abScalingFactor1 == abScalingFactor2
            return Collections.singletonList(p1);
        }
        Point p2 = new Point(pointA.x - baX * abScalingFactor2, pointA.y
                - baY * abScalingFactor2);
        return Arrays.asList(p1, p2);
    }

    static class Point {
        double x, y;

        public Point(double x, double y) { this.x = x; this.y = y; }

        @Override
        public String toString() {
            return "Point [x=" + x + ", y=" + y + "]";
        }
    }


    public static void main(String[] args) {
        System.out.println(getCircleLineIntersectionPoint(new Point(-3, -3),
                new Point(-3, 3), new Point(0, 0), 5));
        System.out.println(getCircleLineIntersectionPoint(new Point(0, -2),
                new Point(1, -2), new Point(1, 1), 5));
        System.out.println(getCircleLineIntersectionPoint(new Point(1, -1),
                new Point(-1, 0), new Point(-1, 1), 5));
        System.out.println(getCircleLineIntersectionPoint(new Point(-3, -3),
                new Point(-2, -2), new Point(0, 0), Math.sqrt(2)));
    }