( 1 ) presents a grid - based intersection algorithm of parametric surface and plane , which is characterized by effectiveness and conciseness , and has been successfully implemented in the rp data processing software 所作的主要工作如下: ( 1 )提出一种基于网格划分的参数曲面与平面求交算法。这种算法简单、实用,已成功地应用于基于cad模型直接分层的rp数据处理软件中。
According to topological structure of control mesh , we generate generalized rational parametric surfaces in two manners . for a control mesh with consistent parameterization , the surface can be easily constructed because it can be mapped to differential manifold directly 对于具有简单拓扑结构,存在着一致的全局参数化的控制网格,我们将把控制网格直接映射到微分流形上,因此可以很容易地对曲面进行构造和控制。
Its properties and design method is discussed in chapter 4 . for control meshes with arbitrary topology , we present a universal method in chapter 5 to construct parametric curves and surfaces . generalized rational parametric surface can be controlled precisely and flexible , and it is easy to model local features and 3d primitives 然后,在第五章中,我们将控制网格进一步推广到任意可定向二维拓扑流形,提出了一个通用的方法将控制网格映射到与之拓扑同胚的微分流形上,统一了广义有理参数曲线曲面的构造过程。