javascript - 2个圆圈javascript之间的交集

Question

我正在尝试做一个函数来检测两个圆之间的交点。如果是，则得分为真，否则得分为假，但我想我迷路了，所以它没有显示我想要的东西。如果有人可以帮助我，请。谢谢如果有人知道我洗耳恭听的答案，那肯定是我在 javascript 中编码不正确

function AreCirclesIntersecting(c0,c1) {

    x0 = c0['center']['x'];
    y0 = c0['center']['y'];
    r0 = c0['center']['r'];
    x1 = c1['center']['x'];
    y1 = c1['center']['y'];
    r1 = c1['center']['r'];


    var a, dx, dy, d, h, rx, ry;
    var x2, y2;

    /* dx and dy are the vertical and horizontal distances between
     * the circle centers.
     */
    dx = x1 - x0;
    dy = y1 - y0;

    /* Determine the straight-line distance between the centers. */
    d = Math.sqrt((dy*dy) + (dx*dx));

    /* Check for solvability. */
    if (d > (r0 + r1)) {
        /* no solution. circles do not intersect. */
        return false;
    }
    if (d < Math.abs(r0 - r1)) {
        /* no solution. one circle is contained in the other */
        return false;
    }

    /* 'point 2' is the point where the line through the circle
     * intersection points crosses the line between the circle
     * centers.  
     */

    /* Determine the distance from point 0 to point 2. */
    a = ((r0*r0) - (r1*r1) + (d*d)) / (2.0 * d) ;

    /* Determine the coordinates of point 2. */
    x2 = x0 + (dx * a/d);
    y2 = y0 + (dy * a/d);

    /* Determine the distance from point 2 to either of the
     * intersection points.
     */
    h = Math.sqrt((r0*r0) - (a*a));

    /* Now determine the offsets of the intersection points from
     * point 2.
     */
    rx = -dy * (h/d);
    ry = dx * (h/d);

    /* Determine the absolute intersection points. */
    var xi = x2 + rx;
    var xi_prime = x2 - rx;
    var yi = y2 + ry;
    var yi_prime = y2 - ry;

    return [xi, xi_prime, yi, yi_prime];

}

const circles = [
    {center: {x: 10.0, y: 10.0}, radius: 5.0},
    {center: {x: 20.0, y: 20.0}, radius: 15.0},
    {center: {x: 20.0, y: 10.0}, radius: 5.0},
    {center: {x: 20.0, y: 25.0}, radius: 7.5},
];

const q7_result1 = AreCirclesIntersecting(circles[0], circles[1]);
console.log(q7_result1); // Expected output: true

const q7_result2 = AreCirclesIntersecting(circles[0], circles[2]);
console.log(q7_result2); // Expected output: true

const q7_result3 = AreCirclesIntersecting(circles[1], circles[3]);
console.log(q7_result3); // Expected output: false

const q7_result4 = AreCirclesIntersecting(circles[2], circles[3]);
console.log(q7_result4); // Expected output: false

Answer 1

我不会说数学，但在如何检索 r 值方面存在问题。在 circles 中，它们是 radius 直接位于对象上，但您正尝试使用 ['center']['r']。我修改了你的代码，它现在正在输出结果:

function AreCirclesIntersecting(c0,c1) {

    x0 = c0['center']['x'];
    y0 = c0['center']['y'];
    r0 = c0['radius']; // MODIFICATION HERE
    x1 = c1['center']['x'];
    y1 = c1['center']['y'];
    r1 = c1['radius']; // MODIFICATION HERE


    var a, dx, dy, d, h, rx, ry;
    var x2, y2;

    /* dx and dy are the vertical and horizontal distances between
     * the circle centers.
     */
    dx = x1 - x0;
    dy = y1 - y0;

    /* Determine the straight-line distance between the centers. */
    d = Math.sqrt((dy*dy) + (dx*dx));

    /* Check for solvability. */
    if (d > (r0 + r1)) {
        /* no solution. circles do not intersect. */
        return false;
    }
    if (d < Math.abs(r0 - r1)) {
        /* no solution. one circle is contained in the other */
        return false;
    }

    /* 'point 2' is the point where the line through the circle
     * intersection points crosses the line between the circle
     * centers.  
     */

    /* Determine the distance from point 0 to point 2. */
    a = ((r0*r0) - (r1*r1) + (d*d)) / (2.0 * d) ;

    /* Determine the coordinates of point 2. */
    x2 = x0 + (dx * a/d);
    y2 = y0 + (dy * a/d);

    /* Determine the distance from point 2 to either of the
     * intersection points.
     */
    h = Math.sqrt((r0*r0) - (a*a));

    /* Now determine the offsets of the intersection points from
     * point 2.
     */
    rx = -dy * (h/d);
    ry = dx * (h/d);

    /* Determine the absolute intersection points. */
    var xi = x2 + rx;
    var xi_prime = x2 - rx;
    var yi = y2 + ry;
    var yi_prime = y2 - ry;

    return [xi, xi_prime, yi, yi_prime];

}

const circles = [
    {center: {x: 10.0, y: 10.0}, radius: 5.0},
    {center: {x: 20.0, y: 20.0}, radius: 15.0},
    {center: {x: 20.0, y: 10.0}, radius: 5.0},
    {center: {x: 20.0, y: 25.0}, radius: 7.5},
];

const q7_result1 = AreCirclesIntersecting(circles[0], circles[1]);
console.log(q7_result1); // Expected output: true

const q7_result2 = AreCirclesIntersecting(circles[0], circles[2]);
console.log(q7_result2); // Expected output: true

const q7_result3 = AreCirclesIntersecting(circles[1], circles[3]);
console.log(q7_result3); // Expected output: false

const q7_result4 = AreCirclesIntersecting(circles[2], circles[3]);
console.log(q7_result4); // Expected output: false

// draw the circles for debugging
(() => {
  const canvas = document.createElement('canvas');
  canvas.width = canvas.height = '100';
  document.body.append(canvas);
  const context = canvas.getContext('2d');
  for (const {center: {x,y},radius :r} of circles) {
    context.beginPath();
    context.arc(x,y,r,0, 2 * Math.PI);
    context.stroke();
  }
})()