Free-Form Deformation for Mesh Models based on Barycentric Coordinates for Convex Polytope

Abstract

In this paper, we present a parametric deformation method for mesh models based on barycentric coordinates for convex polytope. First, we propose a FFD (free-form deformation) based on barycentric coordinates. Arbitrary convex polytope can be used for the deformation handle of the FFD. Next, we propose an automatic handle construction method for the FFD based on definition and classification of deformation types. Deformation handles suitable for user intended deformation types can be automatically constructed by selecting the deformation type and model portions to be deformed. Finally, we propose a parametric handle deformation method driven by the affine transformation. In our method, user can deform the model by selecting deformation type, portions to be deformed, and by manipulating one or two deformation parameters. Moreover, we propose a method for preserving approximated geometric continuity at the boundary between deformed portions and non-deformed portions of the models. For this purpose, we impose geometric constrains derived from analysis of derivatives of barycentric coordinates on the deformation handle for each deformation type.