论文标题
基于棋盘图案的离散等温网
Discrete Isothermic Nets Based on Checkerboard Patterns
论文作者
论文摘要
本文通过连接边缘中点，研究了在四边形网中刻有核心板图案的离散微分几何形状。事实证明，它是一种多功能工具，它使我们能够始终定义主网，koenigs网和最终等温网作为两者的组合。 主要网基于正交性和共轭的概念，可以通过球体的一致性确定为Moebius几何的实体。离散的koenigs网是通过所谓的koenigs圆锥的存在来定义的。我们发现了Koenigs网的几个有趣的属性，包括它们可偶性和具有相同的拉普拉斯不变性。 也是本金的Koenigs网被定义为等温网。我们证明，在双重化和Moebius变换下，等温网类都是不变的。除其他外，这允许自然构造离散的最小表面及其goursat变换。
This paper studies the discrete differential geometry of the checkerboard pattern inscribed in a quadrilateral net by connecting edge midpoints. It turns out to be a versatile tool which allows us to consistently define principal nets, Koenigs nets and eventually isothermic nets as a combination of both. Principal nets are based on the notions of orthogonality and conjugacy and can be identified with sphere congruences that are entities of Moebius geometry. Discrete Koenigs nets are defined via the existence of the so called conic of Koenigs. We find several interesting properties of Koenigs nets, including their being dualizable and having equal Laplace invariants. Koenigs nets that are also principal are defined as isothermic nets. We prove that the class of isothermic nets is invariant under both dualization and Moebius transformations. Among other things, this allows a natural construction of discrete minimal surfaces and their Goursat transformations.
