TensorSplineGridSurface Class

public sealed class TensorSplineGridSurface : GridSurface

Public NotInheritable Class TensorSplineGridSurface
	Inherits GridSurface

public ref class TensorSplineGridSurface sealed : public GridSurface

[<SealedAttribute>]
type TensorSplineGridSurface = 
    class
        inherit GridSurface
    end

Inheritance

Object  →  Surface  →  GridSurface  →  TensorSplineGridSurface

This class implements general N-dimensional interpolation on rectilinear grids using tensor-product decomposition: interpolation is performed by recursively applying a 1D spline kernel along each axis (dimension reduction). The kernel is specified via the ISplineKernel1D interface, allowing flexible interpolation methods.

Supported kernels:

• Linear: 2-point linear interpolation.
• CubicHermite: 4-point cubic Hermite with centered finite differences (Catmull-Rom style). This is the default kernel.
• Custom kernels implementing ISplineKernel1D (e.g., PCHIP, monotone cubic).

Boundary conditions: The GridBoundaryCondition parameter controls how the kernel accesses grid values during stencil assembly when the stencil extends beyond the grid bounds. Supported modes include clamp (default), periodic, reflect, and fill with a constant value.

Performance: All evaluation methods (value, gradient, Hessian) perform zero heap allocations on the hot path by using stack-allocated buffers. The tensor-product evaluation is efficient for moderate dimensions (typically up to 4-6 dimensions in practice).

Relation to specialized 2D/3D surfaces: This class provides a general implementation that works for any dimension. For 2D and 3D grids, specialized implementations (CubicGridSurface2D, CubicGridSurface3D) may offer better performance by precomputing derivatives, but they are limited to natural cubic splines and do not support custom kernels or boundary conditions.

Reference