我得到了(X,Y)中心的两个圆及其半径的位置,但我需要找到使用JavaScript的交叉点(用红色标出)。
我认为最好的解释,就数学而言被发现这里 (两个圆的交点),但我真的不明白的数学,所以我不能够实现它。
例如d = || P1 - P0 || 什么做|| 代表? 这是否意味着得到的数字始终是一个积极的?
而且还P2 = P0 + A(P1 - P0)/ d,不是在P东西在这里像(10,50)? 但这样做(10,50)在JavaScript +13给你63,所以它只是忽略了第一号,那么我们假设发生什么呢? 如果结果为(23,63),这里还是? 同时,也是P1-P0部分或(40,30) - (10,60),你如何表达在JavaScript?
翻译网站上的JavaScript C函数:
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];
}
文章来源: A JavaScript function that returns the x,y points of intersection between two circles?