Polygon Model上的Fillet操作及算法

【作者】 刘伟中；

【导师】 施锡泉； 钱晓元；

【作者基本信息】 大连理工大学 ， 计算数学， 2002， 硕士

【摘要】 由于多面体细分算法提供了一个简单而有效的曲面生成方法，它已经成为在计算机辅助几何设计(CAGD)中进行复杂曲面造型的一个基本工具。在第二章中，我们介绍了几个常见的细分曲面。利用细分方法，曲面可以很容易的通过递归地细分多面体网格得到，但是，在简单而粗糙的多面体网格上(如日本正在研究的Sketch平台中，用手画经识别而生成的网格既简单又粗糙)，很难得到设计者想要的形状。如何有效的控制最终由细分方法生成的曲面成为摆在用细分方法进行曲面造型者前面的一个难题。 为了解决这一问题，我们提出了一种行之有效的方法：Fillet操作，并且给出了相应的Fillet规则及算法。Fillet操作及算法主要思想是：首先运用Fillet操作及规则生成一个复杂而精细的多面体网格，然后再对这个精细的网格进行细分，就可以得到设计者想要的形状。一般地，对初始网格来说，相交于一个顶点的边数并没有限制，而且，每条边的Fillet值可以不同。 在我们提出的Fillet规则中，角点协调算法保证了曲面在执行Fillet操作的边上的几何特征，并且保证了最终生成的网格是一个标准的Polygon Model。Fillet的概念、规则及角点协调算法在第三章中详细讲解。为了方便设计者执行Fillet操作，我们还在第四章中给出了细分曲面上的自适应和交互Fillet操作的思想及算法。 我们提出的Fillet操作及算法将有助于加强用细分方法进行曲面造型的计算机图形系统(如在日本的Sketch系统上得到了很好的运用)。更多还原

【Abstract】 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)更多还原