Curve Families and Parameterization

Spline solving and rendering are expressed in a local frame for each segment.

Local chord frame

Each segment is normalized into a chord-aligned coordinate system:

the segment start is (0, 0)
the segment end is (1, 0)
tangent angles are represented relative to the chord direction

This makes the curve family reusable across arbitrary world-space geometry.

`TwoParamCurve`

TwoParamCurve is the abstraction for families defined by two endpoint tangent angles:

Render(th0, th1) returns local control geometry
ComputeCurvature(th0, th1) estimates endpoint curvature
EndpointTangent(th) provides the default boundary tangent model

`MyCurve`

MyCurve is the concrete family used by the package and sample. It provides:

baseline cubic rendering
curvature-aware Render4(...) output for smoother joints
the endpoint tangent rule used by the global solver

`TwoCubics` and `CurveGrid`

The tuner workflow stores samples of a curve family using TwoCubics. Those masters are arranged in CurveGrid, which:

exploits symmetry to reduce stored data
interpolates between sampled masters
supports JSON serialization and tuning-oriented experimentation