SplineKernels.CubicHermite Property

public static ISplineKernel1D CubicHermite { get; }

Public Shared ReadOnly Property CubicHermite As ISplineKernel1D
	Get

public:
static property ISplineKernel1D^ CubicHermite {
	ISplineKernel1D^ get ();
}

static member CubicHermite : ISplineKernel1D with get

Property Value

This kernel performs local cubic interpolation using a 4-point stencil. At each evaluation point, it computes slopes using centered finite differences from neighboring points, then constructs a cubic Hermite polynomial on the current segment. This is also known as Catmull-Rom interpolation.

Continuity: C¹ (continuous value and first derivative)

Width: 4 (uses 4 neighboring points for each segment)

Characteristics:

• Local method (no global solve required)
• Passes through all data points (interpolating, not approximating)
• May overshoot and oscillate near sharp features
• Not guaranteed to preserve monotonicity

Difference from CubicSpline: This kernel is not the same as any CubicSplineKind (Natural, Clamped, NotAKnot). Those are global cubic spline methods that solve tridiagonal systems to ensure C² continuity or specific boundary conditions. This kernel is purely local and achieves only C¹ continuity.

Backward compatibility: This kernel produces the same results as the original hard-coded cubic implementation in earlier versions of the tensor-product grid surface code.

Reference