The analysis of barycentric coordinates for convex polytope and application for the method to control geometric continuity in FFD

Abstract

We have presented a free–form and parametric deformation method based on barycentric coordinates for a convex polytope to achieve effective styling or mechanical design processes. However in the method, only geometric continuity can be preserved at the boundary between deformed and non–deformed portions. So, the resulting model is not appropriate for certain application purposes. In this paper, we propose a new method of parametric deformation where user can keep geometric continuity based on an analysis of derivative of barycentric coordinates at the boundary between deformed and non–deformed portions.