A STUDY ON NC-CUTTER PATH GENERATION FOR SUBDIVISION SURFACES

最近，细分曲面越来越受到关注。然而，与参数曲面相比，细分曲面没有足够的建模工具。在本文中，我们提出了一种用常用的蒙皮和插值方法直接构造细分曲面的方法。蒙皮方法包括两种不同的方法。一种侧重于结果表面的平滑度，另一种侧重于给定曲线的特征。利用该方法，可以根据给定的截面曲线和路径曲线直观地构造剖分曲面。我们的插值方法是取一组设计曲线，这些曲线不假设具有精确的连通性，以便于设计人员输入曲线。该方法首先从曲线的空间关系推导出曲面的连通性，然后确定曲面的拓扑结构。然后采用组合细分方案生成插值曲面。生成的曲面保证经过设计者给出的曲线。在此基础上，开发了原型软件，通过实例对这些方法进行了评价。结果表明，这些方法对表面设计是有效的，但在某些情况下，它们不能生成公平的表面。提出了我们今后的工作，以扩大该方法和细分方案。

Recently, subdivision surfaces are getting more attention. However in contrast to the case of parametric surfaces, there are not enough modeling tools for subdivision surfaces. In this paper, we propose a method for direct construction of subdivision surfaces with popular skinning and interpolation methods. The skinning methods consists of two different approaches. One focuses on smoothness of the resulting surface and the other on features of the give curves. With this method, intuitive construction of subdivision surface from given sectional curves and path curve can be made.Our interpolation method is designed to take a set of design curves which are not assumed to have accurate connectivity so as to facilitate the designer to input curves. First our method deduces the connectivity from the spatial relationship of the curves and then decides the topology of the surface. Then it applies combined subdivision scheme to generate an interpolating surface. The generated surface is guaranteed to go through the curves given by the designer.Based on those methods, prototype software was developed to evaluate them using several examples. The results show that those methods are effective for surface design, but for some cases they fail to generate fair surfaces. It suggests our future work to extend the method and subdivision schemes.