get-medial-point-coeffs-bez2-same-curve

function getMedialPointCoeffsBez2_SameCurve(t: number, v: number[], ps: number[][]): { A: number[]; B: number[]; H: number[]; }

Defined in get-medial-points/double/get-medial-point-coeffs-bez2-same-curve.ts:26

Returns polynomial coefficients for the same-curve quadratic medial-point case, where p = b(t) on the same quadratic bezier ps and v is normal to the curve at that parameter t.

The returned coefficients encode:

• A, B: E2(s, τ) = (s - t)^2⋅(A(s)⋅τ + B(s)) // * * C, D: E1(s, τ) = C(s)⋅τ + D(s)
• H: the reduced eliminant in s

Here τ is the ray parameter in q(τ) = p + τ⋅v. For a candidate root s of H, recover τ from A(s)⋅τ + B(s) = 0, i.e. τ = -B(s)/A(s) when A(s) ≠ 0.

In this same-curve setup, the full eliminant has the form H_full(s) = (s - t)^4*(l1*s + l0). This function returns only the reduced factor H(s) = l1*s + l0 (the repeated (s - t)^4 factor is omitted).

Parameters:

Name	Type	Description
t	number	parameter on ps where p = b(t)
v	number[]	ray direction from p; assumed normal to ps at t
ps	number[][]	order 2 bezier control points, e.g. [[0,0],[1,1],[2,1]]