A feature-based approach for smooth surfaces
Shigeo Takahashi, Yoshihisa Shinagawa, Tosiyasu L. Kunii · 1997
Feature-based representation has become a topic of interest in shape modeling techniques.Such featurebased techniques are, however, still restricted to polyhedral shapes, and none has been done on smooth surfaces.This paper presents a new feature-based approach for smooth surfaces.Here, the smooth surfaces are assumed to be 2-dimensional @differentiable manifolds within a theoretical framework.As the shape features, crit,ical points such as peaks, pits, and passes are used.We also use a critical point graph called the R.eeb graph to represent the topological skelet,ons of a smooth object.Since the critical points have close relations with the entities of B-reps, the framework of thtx B-reps can easily be applied to our approach.In our method, the shape design process begins with specifying the topological skeletons using the Reeb graph.The Reeb graph is edited by pasting the entities called cells that have one-to-one correspondences with the critical points.In addition to the topological skeletons, users also design the geometry of the objects with smooth surfaces by specifying the flow curves that run on the object surface.From these flow curves, the system automatically creates a control network that encloses the object shape.The surfaces are interpolated from t#he cont,rol network by minimizing t,he cllergy function subject to the deform&ion of the surfaces using variat,ional optimization.1