Generating Symbolic Interpolants for Scattered Data with Normal Vectors

Algorithms to generate a triangular or a quadrilateral interpolant with G^1 -continuity are given in this paper for arbitrary scattered data with associated normal vectors over a prescribed triangular or quadrilateral decomposition. The interpolants are constructed with a general method to generate surfaces from moving B\'ezier curves under geometric constraints. With the algorithm, we may obtain interpolants in complete symbolic parametric forms, leading to a fast computation of the interpolant. A dynamic interpolation solid modelling software package DISM is implementedbased on the algorithm which can be used to generate and manipulate solid objects in an interactive way.