Constructing Cubic Polynomial Interpolation Surfaces on Triangular Domain

Many special projects, such as mining shape fitting and water depth render, need large amounts of data and have certain requirement on smoothness of interpolation surfaces while the surfaces can't be too convex. To satisfy these requirements, this paper presents a C¹ continue cubic polynomial interpolation surface and a target method for estimating partial derivatives. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, interpolated three piecewise cubic polynomial patches on each triangle which were C¹ continue on each edge respectively, and the weighted combination of the three patches constructed surface patch of each triangle. Lastly, all surface patches of all triangles were jointed together to form the whole surface. To make the surface be closed to advised shape as far as possible, different partial derivatives estimation methods were used according to the data point was boundary point or not. New method is simple to compute and has a good local property. The result of new surface is given in experiments.