A Synthesis Process for Fair Free-Form Surfaces

This paper describes a stepwise synthesis process for surface generation which leads from a set of prefaired curves, which form a regular or irregular mesh topology, via a mesh fairing process to a free-form surface that interpolates the mesh curves with G 1 or G 2 continuity and is subsequently faired based on some choice of variational fairness criterion. After briefly reviewing earlier work on the construction of a fair curve mesh the paper concentrates on two main ideas: 1. The interpolation of the given mesh topologies for given continuity and compatibility conditions with minimal polynomial degrees by local interpolants in Bezier form. Irregular, n-sided mesh cells are decomposed into assemblies of quadrilaterals. 2. A fairing process is applied to each patch. The free interior Bezier control points and twist vectors are determined by minimizing a chosen fairness measure. The effects of different variational fairness criteria on the shape and quality of the surface are explored.