Adaptive implicit modeling using subdivision curves and surfaces as skeletons

Recent work has shown that implicit modeling using levels of details (LODs) is possible thanks to the use of subdivision-curves as skeletons. However, the geometric skeleton of a 3D shape is, in the general case, a graph of interconnected curve segments and surface patches, the exclusive use of curve skeletons is therefore not sufficient. We present a model that uses a graph of interconnected subdivision curves and surfaces as a skeleton, on which a varying radius can be specified in order to control surface thickness. The subdivision levels of the skeleton provide levels of detail for the field function that defines the implicit surface. Its visualization is achieved by generating a coarse mesh that surrounds the skeleton. At high valence skeleton vertices, triangulation topology issues are managed by locally overlapping the iso-surface triangulations. The mesh is then adaptively refined in order to sample the current LOD of the implicit surface within an error tolerance. The last contribution is a new solution to the unwanted blending problem. It avoids blending between parts of the surface that do not correspond to neighboring skeletal elements, and ensures C¹ continuity everywhere. All these methods are integrated into an interactive modeling system, where the user can create, view and edit complex shapes at different levels of detail.