Hermite parametric surface interpolation based on Argyris element

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. Hermite surface approximation scheme based on Argyris element.C1 scheme variation uses quintic and G1 variant uses octic triangular patches.Interpolation of geometric data (points, tangent planes, normal curvature forms).Local construction and linear complexity.