| As polyhedral subdivision process provides a simple and efficient way to generate surfaces over polyhedral networks, it has become one of the basic tools in Computer Aided Geometric Design(CAGD) for modeling complex surfaces. In Chapter 2, we introduce some famous subdivision surfaces. Surfaces can be generated easily by subdividing polyhedral networks recursively, however, over simple or rough polyhedral network, it is difficult to get the surfaces which designers want to model(For example, in the Sketch system being researched in Japan, the networks generated by hand are much simple and rough). So, to the designers who use subdivision surfaces to model surfaces, there is a difficult question that how to efficiently control the final shape generated by subdivision surfaces.In order to solve this question, we provide a simple and efficient way: fillet operations as well as the fillet rules and algorithm. The main idea of fillet operation is to create a complex or precise polyhedral network by fillet operation and algorithm. By implementing subdivision over the precise networks, we can get the shape which the designers want to model. Generally, the number of edges that meet at one vertex is no restriction and the sharpness of every edge can be different.In the rules of fillet operation, the corner fitting algorithm ensures that the geometric feature of the edges can be maintained after implementing fillet operation, and ensures that the network generated by fillet operation is a standard polygon model. We will discuss the fillet concept, rules and corner fitting algorithm in Chapter 3 clearly. In order to make it easy for the designers to implement fillet operation, we also provide an adaptive algorithm and an interactive operation of implementing fillet operations in Chapter 4.The fillet operations proposed here will strengthen the functions of Computer Graphics system that use subdivision surfaces to model surfaces. (For example, it works well in the Sketch system in Japan)... |
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