Documentation

A B-spline, defined by a knot vector (see Knots) and a sequence of control points.

bSpline kts cps creates a B-spline with the given knot vector and control points. The degree is automatically inferred as the difference between the number of spans in the knot vector (numKnots kts - 1) and the number of control points (length cps).

Evaluate a B-spline at the given point. This uses a slightly modified version of de Boor's algorithm which is only strictly correct inside the domain of the spline. Unlike the standard algorithm, the basis functions always sum to 1, even outside the domain of the spline. This is mainly useful for "clamped" splines - the values at or outside the endpoints will always be the value of the nearest control point.

For a standard implementation of de Boor's algorithm, see evalNaturalBSpline. For a (much slower) strictly mathematically correct evaluation, see evalReferenceBSpline.

Evaluate a B-spline at the given point. This uses de Boor's algorithm, which is only strictly correct inside the domain of the spline.

For a (much slower) strictly mathematically correct evaluation, see evalReferenceBSpline.

Insert one knot into a BSpline without changing the spline's shape.

Split a B-spline at the specified point (which must be inside the spline's domain), returning two disjoint splines, the sum of which is equal to the original. The domain of the first will be below the split point and the domain of the second will be above.

The table from de Boor's algorithm, calculated for the entire spline. If that is not necessary (for example, if you are only evaluating the spline), then use slice on the spline first. splitBSpline currently uses the whole table. It is probably not necessary there, but it greatly simplifies the definition and makes the similarity to splitting Bezier curves very obvious.