我得到了两个圆的（x，y）中心位置及其半径，但我需要使用 JavaScript 找到它们的交点（用红色标记）。
我认为就数学而言，最好的解释是在这里找到（两个圆圈的交集），但我并不真正理解数学，所以我无法实现它。
例如 d = ||P1 - P0|| , 做什么 || 代表？这是否意味着结果数字始终为正数？
还有 P2 = P0 + a ( P1 - P0 ) / d ，这里的 P 不是 (10, 50) 吗？但是在 JavaScript 中执行 (10,50)+13 会得到 63，所以它只是忽略了第一个数字，那么会发生什么？结果应该是（23,63）还是？还有 P1-P0 部分或 (40,30)-(10,60)，你如何在 JavaScript 中表达？
将网站上的 C 函数翻译成 JavaScript：
function intersection(x0, y0, r0, x1, y1, r1) {
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];
}
根据 AutoMonkey 的回答，我做了一些调整，以便在响应中提供更多信息，并在圆圈相同时进行处理。
/**
* @description Get information about the intersection points of a circle.
* Adapted from: https://stackoverflow.com/a/12221389/5553768.
* @param {Object} c1 An object describing the first circle.
* @param {float} c1.x The x coordinate of the circle.
* @param {float} c1.y The y coordinate of the circle.
* @param {float} c1.r The radius of the circle.
* @param {Object} c2 An object describing the second circle.
* @param {float} c2.x The x coordinate of the circle.
* @param {float} c2.y The y coordinate of the circle.
* @param {float} c2.r The radius of the circle.
* @returns {Object} Data about the intersections of the circles.
*/
function intersection(c1, c2) {
// Start constructing the response object.
const result = {
intersect_count: 0,
intersect_occurs: true,
one_is_in_other: false,
are_equal: false,
point_1: { x: null, y: null },
point_2: { x: null, y: null },
};
// Get vertical and horizontal distances between circles.
const dx = c2.x - c1.x;
const dy = c2.y - c1.y;
// Calculate the distance between the circle centers as a straight line.
const dist = Math.hypot(dy, dx);
// Check if circles intersect.
if (dist > c1.r + c2.r) {
result.intersect_occurs = false;
}
// Check one circle isn't inside the other.
if (dist < Math.abs(c1.r - c2.r)) {
result.intersect_occurs = false;
result.one_is_in_other = true;
}
// Check if circles are the same.
if (c1.x === c2.x && c1.y === c2.y && c1.r === c2.r) {
result.are_equal = true;
result.are_equal = true;
}
// Find the intersection points
if (result.intersect_occurs) {
// Centroid is the pt where two lines cross. A line between the circle centers
// and a line between the intersection points.
const centroid = (c1.r * c1.r - c2.r * c2.r + dist * dist) / (2.0 * dist);
// Get the coordinates of centroid.
const x2 = c1.x + (dx * centroid) / dist;
const y2 = c1.y + (dy * centroid) / dist;
// Get the distance from centroid to the intersection points.
const h = Math.sqrt(c1.r * c1.r - centroid * centroid);
// Get the x and y dist of the intersection points from centroid.
const rx = -dy * (h / dist);
const ry = dx * (h / dist);
// Get the intersection points.
result.point_1.x = Number((x2 + rx).toFixed(15));
result.point_1.y = Number((y2 + ry).toFixed(15));
result.point_2.x = Number((x2 - rx).toFixed(15));
result.point_2.y = Number((y2 - ry).toFixed(15));
// Add intersection count to results
if (result.are_equal) {
result.intersect_count = null;
} else if (result.point_1.x === result.point_2.x && result.point_1.y === result.point_2.y) {
result.intersect_count = 1;
} else {
result.intersect_count = 2;
}
}
return result;
}
用法：
intersection(
{x: 1, y: 1, r: 2},
{x: 0, y: -1, r: 1}
)
// Result
result = {
intersect_count: 2,
intersect_occurs: true,
one_is_in_other: false,
are_equal: false,
point_1: { x: 1, y: -1 },
point_2: { x: -0.6, y: -0.2 },
}
确认：
https://www.desmos.com/calculator/cj12hc9jsk
