dd-get-medial-point-coeffs

function ddGetMedialPointCoeffs(p: number[][], v: number[][], ps: number[][]): { A: number[][]; B: number[][]; C: number[][]; D: number[][]; H: number[][]; }

Defined in get-medial-points/double-double/dd-get-medial-point-coeffs.ts:35

Returns polynomial coefficients for ray parameter values t, bezier parameter values s and medial points for points q(t) and b(s) (an order 0, 1, 2 or 3 bezier curve) that satisfy the medial condition with respect to p and ps:

Let p be a fixed point in the plane. Let v be a direction vector defining the ray q(t) = p + t⋅v. Let ps be a cubic bezier curve.

• q(t) is equidistant from p and the nearest point on ps
• that common distance is locally minimal among such candidates

In other words, this function returns candidate ray parameters for the sought medial point(s). Selecting physically valid solutions (if needed) is done by the caller or by a later stage of this routine.

Parameters:

Name	Type	Description
p	number[][]	base point
v	number[][]	ray direction from p
ps	number[][]	bezier control points, e.g. [[0,0],[1,1],[2,1],[3,0]]