java 圆线交点

Circle Line Intersection points

提问by cobie

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;
}

I am using the above algorithm to test for intersection between a circle and a line. It works fine sometimes but at other times it fails. The code represents the equation which is derived from solving for x simultaneously from circle and line equations (x-a)^+(y-b)^2=r^2and y = mx - mx1 + y1. Has anyone got an idea where I am going wrong either in my maths or elsewhere?

我正在使用上述算法来测试圆和线之间的交点。有时它工作正常，但有时它会失败。该代码表示​​从圆和线方程(x-a)^+(y-b)^2=r^2和 中同时求解 x 导出的方程y = mx - mx1 + y1。有没有人知道我的数学或其他地方出了什么问题？

回答by arne.b

Your calculations seem quite long, and I do not see the use of the different cases you test. Anyway, since I found the problem interesting I attempted to solve it myself and came up with the following. Feel free to replace double radiusby int radiusand use IntPoints, but be aware that every time you cast, as discussed in the comments, results that are not exact integer intersection points will become wrong.

你的计算看起来很长，我没有看到你测试的不同情况的使用。无论如何，因为我发现这个问题很有趣，所以我试图自己解决它并提出以下建议。随意更换double radius的int radius，并使用IntPointS，但是要知道，你每次投，如评论，一点效果都没有准确的整数交点将成为讨论错误的时间。

The background of the calculations performed is this: From point A, a scaled version of vector AB points to a point on the circle. That point has distance radius from center. Hence, |AC + scalingFactor * AB|=r.

执行计算的背景是这样的：从 A 点，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)));
    }

回答by Florian Prud'homme

Here a solution with import javax.vecmath.Vector2d;

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;

}