Analyzing a point along a line

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
/**
 * 
 * @param {[x,y]} a line end-point
 * @param {[x,y]} b line end-point
 * @param {[x,y]} w point to test
 * @returns {object or null} Returns null if ((a == b) and (c != a)), otherwise
 * return an object like:
 *   {
 *      t {real} : fractional distance between a and b,
 *      i {[x, y] : perpendicular point of intersection between a and b,
 *      d {real} : distance from i to the test point (w) 
 *                      d > 0 ==> d is to the right of a-b,
 *                      d < 0 ==> d is to the left of a-b
 *   }
 */
function PointAlongLine(a, b, w) {
    var ax = a[0], ay = a[1];
    var bx = b[0], by = b[1];
    var wx = w[0], wy = w[1];

    if (ax === bx && ay === by) {
        if (ax === wx && ay === wy) {
            return {t: 1, i: [ax, ay], d: 0};
        } else {
            return null;
        }
    }

    var denom = Math.pow(bx - ax, 2) + Math.pow(by - ay, 2);

    var t = ((wx - ax) * (bx - ax) + (wy - ay) * (by - ay)) / (denom);

    var ix = ax + t * (bx - ax);
    var iy = ay + t * (by - ay);

    var dist = ((by - ay) * wx - (bx - ax) * wy + bx * ay - by * ax) / (Math.sqrt(denom));

    return {
        t: t,
        i: [ix, iy],
        d: dist
    };
}