ISplineKernel1D Interface

This interface defines the contract for 1D interpolation kernels that can be applied along each axis in N-dimensional tensor-product grid surfaces. Kernels are used to perform dimension-reduction interpolation: the N-dimensional problem is solved by recursively applying 1D interpolation along each axis.

Contract requirements:

• Implementations must be stateless (no instance fields beyond constants) and thread-safe.
• All evaluation methods must not allocate memory (no heap allocations) and should be suitable for use in tight, high-performance loops.
• The kernel must work with non-uniform grids (variable spacing between knots).
• The spans x and f passed to evaluation methods will always have length equal to Width.

Built-in kernels: The SplineKernels class provides standard implementations:

• Linear: 2-point linear interpolation (width 2).
• CubicHermite: 4-point cubic Hermite with centered finite differences (width 4). This kernel produces the same results as the original hard-coded cubic implementation.

Custom kernels: You can implement this interface to provide custom interpolation behavior such as PCHIP (monotone cubic), higher-order splines, or domain-specific kernels. The kernel width must be fixed (cannot depend on data).

Relation to CubicSpline: The cubic Hermite kernel (CubicHermite) is a local cubic interpolation method that uses only 4 neighboring points and computes slopes via centered finite differences. It is not the same as any specific CubicSplineKind (Natural, Clamped, NotAKnot, etc.), which are global methods that solve a tridiagonal system. For tensor-product surfaces that use global cubic splines, see the specialized 2D/3D cubic surface implementations created via [!:GridSurface.CreateCubic(Vector<double>, Vector<double>, Matrix<double>)].

Reference