Hermite parametric surface interpolation based on Argyris element
This work provides a local and fast interpolation scheme for surface approximation, but it is an incremental improvement over existing spline-based methods.
The paper presents a Hermite interpolation method for parametric spline surfaces on triangulations, achieving C1 quintic and G1 octic continuity with local and fast construction, demonstrated through numerical examples.
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.