论文标题
Dupin Cyclides作为Darboux Cyclides的子空间
Dupin Cyclides as a Subspace of Darboux Cyclides
论文作者
论文摘要
Dupin Cyclides是几何设计和体系结构中使用的有趣代数表面，可平稳地连接运河表面并构建模型表面。 Dupin Cyclides是Darboux Cyclides的特殊案例，这又是$ \ Mathbb r^3 $ 3或4的一般表面。本文得出了识别Dupin Cyclides的代数条件。我们的目标是在隐式方程的系数上实现可行的代数方程，每个组合都定义了本地（编辑4）的完整相交的组合。此外，本文对所有真实表面进行了分类和较低的尺寸退化，这是Dupin Cyclides的隐式方程定义的。
Dupin cyclides are interesting algebraic surfaces used in geometric design and architecture to join canal surfaces smoothly and to construct model surfaces. Dupin cyclides are special cases of Darboux cyclides, which in turn are rather general surfaces in $\mathbb R^3$ of degree 3 or 4. This article derives the algebraic conditions for recognition of Dupin cyclides among the general implicit form of Darboux cyclides. We aim at practicable sets of algebraic equations on the coefficients of the implicit equation, each such set defining a complete intersection (of codimension 4) locally. Additionally, the article classifies all real surfaces and lower dimensional degenerations defined by the implicit equation for Dupin cyclides.
