Interpolation to C1 boundary conditions by polynomial of degree six

Abstract

A new method for constructing triangular patches to pass the C1 interpolation conditions (boundary curves and cross-boundary slopes), on the boundary of triangles is presented. The triangular patch is constructed by a basic triangular operator and an error triangular operator. The basic operator is a polynomial of degree six, which approximates the interpolation conditions with a higher approximation precision, while the error operator is constructed by the side-vertex method, which passes the C1 error boundary conditions. The C1 error boundary conditions are formed by the C1 interpolation conditions minus the boundary curves and cross-boundary slopes taken from the basic operator. The basic operator and the error operator are put together to form the triangular patch. Comparison results of the new method with other two methods are included.