C¹ Polynomial Interpolation Surface of Degree 4 on a Triangle

The constructed surface patch can be regarded as comprised of a basic patch and three transition patches.The basic patch is formed by forcing the three subdivision curves to intersect at a common point inside the triangle and share a common tangent plane at the intersection point.The resultant patch satisfies the given boundary curves and keeps cross-boundary slope continuity.In comparison with Nielson’s side-vertex method,the new surface has higher interpolation precision,it constructs a triangle patch which reproduces a polynomial of degree four.