Feature-based approach for smooth surfaces

Abstract

Feature-based representation has become a topic of interest in shape modeling techniques. Such feature-based techniques are, however, still restricted to polyhedra 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 C2-differentiable manifolds within a theoretical framework. As the shape features, critical points such as peaks, pits, and passes are used. We also use a critical point graph called the Reeb graph to represent the topological skeletons of a smooth object. Since the critical points have lose relations with the entities of B-reps, the framework of the 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 the control network by minimizing the energy function subject to the deformation of the surfaces using variational optimization.