get-medial-point-coeffs-bez3

function getMedialPointCoeffsBez3(p: number[], v: number[], ps: number[][]): { A: number[]; B: number[]; C: number[]; D: number[]; H: number[]; }

Defined in get-medial-points/double/get-medial-point-coeffs-bez3.ts:24

Returns the polynomial coefficients for the ray parameter t and the curve parameter s that encode the medial condition for q(t) = p + t⋅v and a cubic bezier curve ps.

The returned coefficients describe the equations whose common solutions satisfy:

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

More specifically, this function returns:

• A and B: the coefficients of E2(s,t) = A(s)⋅t + B(s)
• C and D: the coefficients of E1(s,t) = C(s)⋅t + D(s)
• H: the eliminated polynomial A(s)⋅D(s) - B(s)⋅C(s) whose roots are candidate s values for medial points

Parameters:

Name	Type	Description
p	number[]	base point
v	number[]	ray direction from p
ps	number[][]	cubic bezier control points, i.e. an order 3 bezier curve given as an array of control points, e.g. [[0,0],[1,1],[2,1],[3,0]]