Hermite parametric surface interpolation based on Argyris element

TL;DR

This paper introduces a local, efficient method for Hermite interpolation of parametric spline surfaces on triangulations, capable of handling arbitrary topologies with two variations: C1 quintic and G1 octic.

Contribution

It presents a novel local construction scheme for Hermite spline surfaces that interpolates points, tangent planes, and curvature, including a higher-degree G1 octic variation for arbitrary topologies.

Findings

The G1 octic scheme can approximate surfaces of arbitrary topology.

The method is local and computationally efficient.

Numerical examples demonstrate effective surface approximation.

Abstract

In this paper, Hermite interpolation by parametric spline surfaces on triangulations is considered. The splines interpolate points, the corresponding tangent planes and normal curvature forms at domain vertices and approximate tangent planes at midpoints of domain edges. Two variations of the scheme are studied: C1 quintic and G1 octic. The latter is of higher polynomial degree but can approximate surfaces of arbitrary topology. The construction of the approximant is local and fast. Some numerical examples of surface approximation are presented.