A JavaScript function that returns the x,y points

问题:

I got the (x,y) center location of two circles and their radius but I need to find their intersection points (marked with red) using JavaScript.

I think the best explanation as far as the math is concerned is found here (Intersection of two circles), but I don't really understand the math so I'm not able to implement it.

For example d = ||P1 - P0|| , what do the || stand for? Does it mean that the resulting number is always a positive?

And also P2 = P0 + a ( P1 - P0 ) / d , aren't the P's here something like (10, 50)? But doing (10,50)+13 in JavaScript gives you 63, so it just ignores the first number, so what's suppose to happen? Should the outcome be (23,63) here or? And also the P1-P0 part or (40,30)-(10,60), how do you express that in JavaScript?

回答1:

Translated the C function on the site to 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];
    }