Module curve_surface 

Where a curve pierces a surface.

Elsewhere this is GeomAPI_IntCS and the line/quadric half of IntAna. Two consumers drive it: edge/face interference in the boolean’s pave filler, and the exact point-in-solid classifier, which is a ray/surface query per face, the very use docs/PLAN.md carries what remains exact.

Well-posed, for once

C(t) = S(u, v) is three equations in three unknowns; unlike the surface/surface system, nothing has to be pinned for Newton to converge to a point. The analytic cases are still answered in closed form first: a line against a plane or a quadric is a linear or quadratic equation, and solving a quadratic by iteration would be slower and less exact than writing down its roots.

A curve lying in the surface

A line in a plane crosses it nowhere and everywhere. That is an overlap (the parameter range of the curve that lies in the surface), and it is a different answer from any list of points. Detected where the analytic forms can see it; the general path reports whatever isolated piercings its sampling resolves, and says so.

Structs

CurveSurfaceIntersection

What a curve does to a surface.

CurveSurfaceOptions

How hard the general path looks.

Piercing

One piercing of a surface by a curve.

Functions

intersect_curve_surface

Where a curve pierces a surface.