A High-Order-Integration Scheme for Global Polynomial Representations of Closed Surfaces

We provide a novel high-order integration scheme crossing the limitations of established curved triangle techniques, that can be applied to a broad class of surfaces, providing a high-order approximation of the integrand and the geometry of the surface. This approach relies on recent results of multivariate interpolation which enable a global polynomial level set to be used to implicitly represent a broad class of closed surfaces.