Modelling a three-dimensional (3D) point cloud with smooth mathematical surfaces or high-quality triangle meshes is an essential component of many applications in Computer Graphics, Visualization and Computer-Aided Design/Engineering. A vital prerequisite for that is the construction of a
for a given 3D point-set; this problem is the focus of the present paper. The proposed method employs ideas and tools from “point-based geometric modelling” in order to construct a set of continuous surfaces locally-fitted to a point set. Then parameterization is achieved by orthogonally projecting the point set onto these surfaces.