get-medial-point-coeffs-bez1

function getMedialPointCoeffsBez1(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-bez1.ts:21

Returns the polynomial coefficients used to recover ray parameter values t for a ray q(t) = p + t⋅v and an order-1 bezier curve ps.

The returned polynomials encode the medial-condition equations in s and t. For any valid solution, t is recovered by eliminating s and solving the resulting ray equation, or equivalently by using the linear form A(s)⋅t + B(s) = 0, which gives t = -B(s)/A(s).

More specifically, the returned values represent:

• 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 vector starting from p
ps	number[][]	order 1 bezier control points, i.e. a line segment given as an array of control points, e.g. [[0,0],[2,1]]