html5-canvas Navigating along a Path Length of a Quadratic Curve
Example
Given the 3 points of a quadratic curve the following function returns the length.
function quadraticBezierLength(x1,y1,x2,y2,x3,y3)
var a, e, c, d, u, a1, e1, c1, d1, u1, v1x, v1y;
v1x = x2 * 2;
v1y = y2 * 2;
d = x1 - v1x + x3;
d1 = y1 - v1y + y3;
e = v1x - 2 * x1;
e1 = v1y - 2 * y1;
c1 = (a = 4 * (d * d + d1 * d1));
c1 += (b = 4 * (d * e + d1 * e1));
c1 += (c = e * e + e1 * e1);
c1 = 2 * Math.sqrt(c1);
a1 = 2 * a * (u = Math.sqrt(a));
u1 = b / u;
a = 4 * c * a - b * b;
c = 2 * Math.sqrt(c);
return (a1 * c1 + u * b * (c1 - c) + a * Math.log((2 * u + u1 + c1) / (u1 + c))) / (4 * a1);
}
Derived from the quadratic bezier function F(t) = a * (1 - t)2 + 2 * b * (1 - t) * t + c * t2
