RadialBasisFunctions.ThinPlate Property

public static RadialBasisFunction ThinPlate { get; }

Public Shared ReadOnly Property ThinPlate As RadialBasisFunction
	Get

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

static member ThinPlate : RadialBasisFunction with get

Property Value

The thin-plate spline kernel is a classical choice that minimizes bending energy. It does not require a shape parameter. The value at r=0 is defined as 0 by continuity. This kernel is conditionally positive definite of order 2.

The kernel is defined as φ(r) = r² log(r) for r > 0, and φ(0) = 0.

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