11 
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;
}

我正在使用上述算法来测试圆和线之间的交点。它有时可以正常工作，但有时会失败。该代码表示​​从圆和线方程同时求解 x 和 得到的(x-a)^+(y-b)^2=r^2方程y = mx - mx1 + y1。有没有人知道我的数学或其他地方哪里出错了？

4

2 回答 2

30

您的计算似乎很长，我看不到您测试的不同案例的用途。无论如何，因为我发现这个问题很有趣，所以我尝试自己解决它并提出以下问题。随意替换double radius并int radius使用IntPoints，但请注意，每次转换时，如评论中所讨论的，不是精确整数交点的结果都会出错。

执行计算的背景是这样的：从点 A，矢量 AB 的缩放版本指向圆上的一个点。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)));
    }
于 2012-10-24T18:05:42.667 回答
0

这里有一个解决方案import javax.vecmath.Vector2d;

static Vector2d[] circleLineIntersection1(Vector2d a, Vector2d b, Vector2d o, double radius) {

    Vector2d p1 = new Vector2d(a);
    Vector2d p2 = new Vector2d(b);
    p1.sub(o);
    p2.sub(o);

    Vector2d d = new Vector2d();
    d.sub(p2, p1);

    double det = p1.x * p2.y - p2.x * p1.y;

    double dSq = d.lengthSquared();

    double discrimant = radius * radius * dSq - det * det;

    if (discrimant < 0) {
        return new Vector2d[0];
    }

    if (discrimant == 0) {
        Vector2d[] t = new Vector2d[1];
        t[0] = new Vector2d(det * d.y / dSq + o.x, -det * d.x / dSq + o.y);

        return t;
    }

    double discSqrt = Math.sqrt(discrimant);

    double sgn = 1;
    if (d.y < 0) {
        sgn = -1;
    }

    Vector2d[] t = new Vector2d[2];
    t[0] = new Vector2d((det * d.y + sgn * d.x * discSqrt) / dSq + o.x, (-det * d.x + Math.abs(d.y) * discSqrt) / dSq + o.y);
    t[1] = new Vector2d((det * d.y - sgn * d.x * discSqrt) / dSq + o.x, (-det * d.x - Math.abs(d.y) * discSqrt) / dSq + o.y);
    return t;

}
于 2015-03-15T22:43:59.537 回答