Expand description
Waypoint-based spline path construction and evaluation kernels.
§Design
All splines are odd-order (p = 2m+1, m >= 1):
- order 3 (m=1): C2 cubic, boundary specifies v at both ends
- order 5 (m=2): C4 quintic, boundary specifies v,a at both ends
- order 7 (m=3): C6 septic, boundary specifies v,a,j at both ends
The user supplies start_state and end_state matrices of shape (dim, m),
where column r-1 contains the r-th derivative value at the endpoint.
None means all-zero (the most common default).
Internally, all orders share a single solve_general_thomas solver that
implements the O(N) block-Thomas algorithm on the m×m block-tridiagonal
system arising from Hermite parametrisation + C^{m+1}..C^{2m} continuity.
Structs§
- Spline
Config - Spline
Path - Piecewise-polynomial path in normalised segment coordinates.