al math

Splines

Return Bezier, B-Spline, Catmull-Rom, and Hermite cubic basis matrices (mat4).

bezier-step
bspline-step
catmullrom-step
hermite-step

Global integer variables which specify the "stepping" factor for piecewise Bezier (3), B-Spline (1), Catmull-Rom (1), and Hermite (2) cubic basis functions.

(sample-pcs reallist m ustep u)
(sample-pcs vec3list m ustep u)

Sample a 1D or 3D piecewise cubic spline defined by a list of control points (reallist for 1D, vec3list for 3D), a basis matrix, m, and basis stepping factor, ustep, at the parametric position u.

Let n be the number of control points. n should be greater than or equal to 4. u should be in the range [0, (n - 4 + ustep) / ustep] for non-periodic splines and [0, (n - 4 + ustep) / ustep + 4 - ustep] for periodic splines.