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。
In chapter 3 , we discuss a novel parametric curve representation scheme on 1d manifold in - depth . all construction and design techniques for parametric curves , such as basis function design , parameterization , and local features control etc . are discussed in detail . a new construction method for conic curve is also presented 对于广义有理参数曲线,我们在第三章中对它的基函数设计、参数化方法、浙江大学博士学位论文局部控制和局部特征设计等各个构造和设计环节进行了详细的讨论,并提出了新的二次曲线的精确构造方法。
Grpcs provides a unified framework for parametric curve and surface . it does not only inherit a lot of good properties from nurbs such as locality , convex hull , affine and perspective invariance etc . , but also has the ability to directly represent trimmed surfaces and closed surfaces 广义有理参数曲线曲面在表示形式和计算方法上具有高度的统一性,它不仅继承了nurbs的很多优良性质,比如局部控制性、凸包性、仿射和投影不变性等,而且可以直接表示裁剪曲面和闭合的曲线曲面。