Cyclides in Solid Modelling

将进行循环在实体建模中的应用研究。环是一类具有圆形曲率线的四阶曲面，由杜宾在19世纪早期发现。它们具有有趣的特性，可以通过算法来提高当前实体建模器的能力。循环在计算机辅助几何设计领域的影响被设想为包括以下应用：(1)复杂固体的偏移量的生成和(2)固体的可变半径混合。这两个问题在不同的应用中都很重要。初步调查表明，这种自行车可以成功地解决这两个问题。这项工作涉及到在实体模型的补偿和混合中使用循环的具体研究问题。

Research on applications of cyclides in solid modelling will be conducted. Cyclides are a class of fourth-order surfaces with circular lines of curvature, discovered by Dupin in the early 19th century. They possess interesting properties that can be algorithmically exploited to enhance the capability of the current solid modelers. The impact of cyclides in the realm of computer aided geometric design is envisioned to include application in: (1) the generation of offsets of complex solids and (2) variable radii blends of solids. Both are important problems with varied applications. Initial investigations indicate the cyclides can be successfully used to solve both problems. This work deals with specific research issues that pertain to the use of cyclides in offsets and blends of solid models.