标题： 主宾语 显示英文标题

标题： Principal binets

摘要： 共轭线参数化表面最早在近一个世纪前被离散化为具有平面面的四边形网格。 随着离散微分几何的最近发展，发现了主曲率线参数化的两种离散化方法：圆网和锥网，它们都是离散共轭网的特例。 随后，圆网和锥网被统一描述为李二次曲面中的各向同性线配对。 我们通过考虑李二次曲面环境空间中线配对的极对来提出一种推广。 这些对应于具有正交边的离散共轭网对，我们称之为主双网，这是主曲率线参数化的新的更一般的离散化方法。 我们还引入了正交和高斯正交参数化的两种新离散化方法。 我们所有的离散化都遵循变换群原理，这意味着它们分别满足相应的李、莫比乌斯或朗格勒不变性，类似于光滑理论。 最后，我们证明它们满足一致性原理，这意味着我们的定义可以推广到更高维的正方形格子。 我们的工作扩展了Dellinger关于棋盘图案的最新工作。 显示英文摘要

摘要： Conjugate line parametrizations of surfaces were first discretized almost a century ago as quad meshes with planar faces. With the recent development of discrete differential geometry, two discretizations of principal curvature line parametrizations were discovered: circular nets and conical nets, both of which are special cases of discrete conjugate nets. Subsequently, circular and conical nets were given a unified description as isotropic line congruences in the Lie quadric. We propose a generalization by considering polar pairs of line congruences in the ambient space of the Lie quadric. These correspond to pairs of discrete conjugate nets with orthogonal edges, which we call principal binets, a new and more general discretization of principal curvature line parametrizations. We also introduce two new discretizations of orthogonal and Gauss-orthogonal parametrizations. All our discretizations are subject to the transformation group principle, which means that they satisfy the corresponding Lie, M\"obius, or Laguerre invariance respectively, in analogy to the smooth theory. Finally, we show that they satisfy the consistency principle, which means that our definitions generalize to higher dimensional square lattices. Our work expands on recent work by Dellinger on checkerboard patterns.