Boundary conditions

BSplineKit.BoundaryConditions

Contains some boundary condition definitions.

Natural <: BoundaryCondition

Generalised natural boundary condition.

This boundary condition is convenient for spline interpolations, as it provides extra constraints enabling to equate the number of unique B-spline knots to the number of data points.

For cubic splines (order $k = 4$), this corresponds to natural cubic splines, imposing the second derivatives to be zero at the boundaries ($S''(a) = S''(b) = 0$).

For higher-order splines, this boundary condition generalises the standard natural cubic splines, by setting derivatives of order $2, 3, …, k/2$ to be zero at the boundaries. For instance, for $k = 6$ (quintic splines), this imposes $S'' = S''' = 0$. In practice, BSplineKit.jl achieves this by using basis recombination.

Note that, for symmetry reasons, only even-order splines are supported by this BC.

Periodic <: BoundaryCondition

Represents periodic boundary conditions with a given period L.

Periodic(L::Real)

Constructs periodic boundary conditions with period L.