题解 | 直线与圆交点间距

import java.util.Scanner;
// 参考：https://blog.nowcoder.net/n/034e8ed5f3a64b629e16d127fbb52400
class Point {
    double x, y;
    Point(double A, double B) {
        x = A;
        y = B;
    }
}

class Line {
    Point point_A, point_B;
    Line(Point A, Point B) {
        point_A = A;
        point_B = B;
    }
}

class Circle {
    Point O;
    int r;
    Circle(Point A, int B) {
        O = A;
        r = B;
    }
}

public class Main {

// 辅助方法：计算点到直线的距离
    public static double distPointToLine(Point p, Line l) {
        double xp = p.x, yp = p.y;
        double xA = l.point_A.x, yA = l.point_A.y;
        double xB = l.point_B.x, yB = l.point_B.y;

        /**
        1. 向量叉积
        对于两个向量 AB 和 AP：
        AB = (xB-xA, yB-yA) 是直线的方向向量
        AP = (xp-xA, yp-yA) 是从点A指向点P的向量
        |AB × AP| = |(xB-xA)(yp-yA) - (yB-yA)(xp-xA)|
         */
        // 方法用于返回两个参数的平方和的平方根，没有中间溢出或下溢。
        double lineBase = Math.hypot(xA - xB, yA - yB);
        if (lineBase == 0) { // 直线退化为一个点
            return Math.hypot(xp - xA, yp - yA);
        }
        // 这两个向量的叉积大小等于以它们为邻边构成的平行四边形的面积：
        double numerator = Math.abs((xp - xA) * (yB - yA) - (yp - yA) * (xB - xA));

        // 2.点到直线的距离实际上就是平行四边形的高：
        // 距离 = 平行四边形面积 / 底边长度
        //      = |AB × AP| / |AB|
        return numerator / lineBase;
    }

    public static double getDistance(Circle circle, Line l) {
        double d = distPointToLine(circle.O, l);
        double r = circle.r;
        // 根据勾股定理，我们有： r*r = d*d + (l/2)^2
        double halfChordSq = r * r - d * d;

        // 题目保证不相离，但为健壮性处理浮点误差
        if (halfChordSq < 0) {
            halfChordSq = 0;
        }
        // 反推出弦长  l = 2√(r^2-d^2)
        return 2.0 * Math.sqrt(halfChordSq);
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        double ox = scanner.nextDouble();
        double oy = scanner.nextDouble();
        int r = scanner.nextInt();

        double x1 = scanner.nextDouble();
        double y1 = scanner.nextDouble();
        double x2 = scanner.nextDouble();
        double y2 = scanner.nextDouble();

        Point center = new Point(ox, oy);
        Circle circle = new Circle(center, r);

        Point p1 = new Point(x1, y1);
        Point p2 = new Point(x2, y2);
        Line l = new Line(p1, p2);

        double result = getDistance(circle, l);
        System.out.printf("%.6f\n", result);

        scanner.close();
    }
}