RadialBasisFunctions.Cubic Property

public static RadialBasisFunction Cubic { get; }

Public Shared ReadOnly Property Cubic As RadialBasisFunction
	Get

public:
static property RadialBasisFunction^ Cubic {
	RadialBasisFunction^ get ();
}

static member Cubic : RadialBasisFunction with get

Property Value

The cubic kernel grows as the cube of the radius and produces smoother interpolants than the linear kernel. Its derivative is φ'(r) = 3 r², which vanishes at the origin and increases with r. The cubic kernel is commonly used in scattered data interpolation for problems where increased smoothness is required.

Note: This is a conditionally positive definite (CPD) kernel that requires polynomial augmentation. RBF interpolation with this kernel automatically includes an affine polynomial tail to ensure well-posedness and exact reproduction of linear functions.

Reference