MultivariatePolynomial Class

public sealed class MultivariatePolynomial : Surface

Public NotInheritable Class MultivariatePolynomial
	Inherits Surface

public ref class MultivariatePolynomial sealed : public Surface

[<SealedAttribute>]
type MultivariatePolynomial = 
    class
        inherit Surface
    end

Inheritance

Object  →  Surface  →  MultivariatePolynomial

This class represents a polynomial function p: ℝᵈ → ℝ as a linear combination of monomials:

p(x) = Σᵢ cᵢ · φᵢ(x)

where φᵢ(x) are the basis monomials (x^αᵢ) from a MultivariatePolynomialBasis and cᵢ are the coefficients.

This class inherits from Surface and provides evaluation and gradient computation for polynomial surfaces. It supports both single-point and batched operations for efficient evaluation at multiple points.

Multivariate polynomials are used for polynomial augmentation in radial basis function interpolation with conditionally positive definite (CPD) kernels.

Reference