CubicGridSurface3D Class

public sealed class CubicGridSurface3D : GridSurface

Public NotInheritable Class CubicGridSurface3D
	Inherits GridSurface

public ref class CubicGridSurface3D sealed : public GridSurface

[<SealedAttribute>]
type CubicGridSurface3D = 
    class
        inherit GridSurface
    end

Inheritance

Object  →  Surface  →  GridSurface  →  CubicGridSurface3D

This class provides a specialized, high-performance implementation of 3D cubic interpolation on rectilinear grids. It precomputes all partial derivatives (∂f/∂x, ∂f/∂y, ∂f/∂z, ∂²f/∂x∂y, ∂²f/∂x∂z, ∂²f/∂y∂z, ∂³f/∂x∂y∂z) at all grid nodes using natural cubic splines (CubicSpline) along each axis, then evaluates tricubic Hermite patches in O(1) time per query.

Spline type: This surface uses Natural cubic splines along each axis, which enforce zero second derivative at the boundaries. The resulting surface has C² continuity in the interior and smooth (but extrapolated) behavior near edges.

Difference from tensor-product splines: Unlike TensorSplineGridSurface, which applies 1D kernels recursively and supports arbitrary boundary conditions and kernels, this class is limited to 3D, uses only natural cubic splines, and does not support custom boundary conditions. However, it offers better performance by precomputing all derivatives once during construction.

Performance: All evaluation methods (value, gradient, Hessian) perform zero heap allocations. Construction is O(N) where N is the total number of grid points, though the memory footprint is higher than 2D due to storing seven derivative arrays in addition to the function values.

Creation: Create instances using CreateCubic(IReadOnlyList<IReadOnlyList<Double>>, IReadOnlyList<Double>, ExtrapolationMode) for 3D grids. For custom boundary conditions or N-dimensional grids, use CreateCubicTensorSpline(IReadOnlyList<IReadOnlyList<Double>>, IReadOnlyList<Double>, GridBoundaryCondition, ExtrapolationMode) or CreateTensorSpline(IReadOnlyList<IReadOnlyList<Double>>, IReadOnlyList<Double>, ISplineKernel1D, GridBoundaryCondition, ExtrapolationMode) instead.

Reference