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authors Takahashi, S., Shinagawa, Y. and Kunii, T.L.
year 1997
title A Feature-Based Approach for Smooth Surfaces
source Proceedings of Fourth Symposium on Solid Modeling, pp. 97-110
summary Feature-based representation has become a topic of interest in shape modeling techniques. Such feature- based techniques are, however, still restricted to polyhedral shapes, and none has been done on smooth sur- faces. This paper presents a new feature-based ap- proach for smooth surfaces. Here, the smooth surfaces are assumed to be 2-dimensional @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 R.eeb graph to represent the topological skeletons 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 enti- ties 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 allergy function subject to the deformation of the surfaces using variational optimization.
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