Constructing triangular patch by basic approximation operator plus additional interpolation operator

摘要

A new method for constructing triangular patches is presented. The triangular patch that interpolates the given boundary curves and cross-boundary slopes is constructed by a basic approximation operator plus an additional interpolation operator. The basic approximation operator is constructed by a polynomial surface of degree five which approximates the given interpolation conditions. The additional interpolation operator is formed by the side-vertex method. The basic and the additional operators have different roles in constructing the triangular patch: the first one makes the triangular patch approximate the given interpolation conditions with a polynomial approximation precision of degree five, while the second one makes it satisfy the given interpolation conditions. The triangular patch reproduces polynomial surfaces of degree five. Comparison results of the new method with the other two methods are included.