We study analogs of planar-quadrilateral meshes in Laguerre sphere geometry and the approximation of smooth surfaces by them. These new Laguerre meshes can be viewed as watertight surfaces formed by planar quadrilaterals (corresponding to the vertices of a mesh), strips of right circular cones (representing the edges), and spherical faces. In the smooth limit, we get an analog of conjugate nets in Laguerre geometry, which we call Laguerre conjugate nets with respect to an attached sphere congruence. We introduce the notion of Laguerre conjugate directions, provide a method for computing them, and apply them to approximate surfaces by L-meshes with prescribed radii of spherical faces.

翻译：我们研究了拉盖尔球面几何中平面四边形网格的类似物以及光滑曲面通过它们的逼近问题。这些新型拉盖尔网格可视为由平面四边形（对应于网格顶点）、正圆锥面环带（代表边）以及球面构成的密闭曲面。在光滑极限下，我们得到了拉盖尔几何中共轭网的类似物，称之为关于附球丛的拉盖尔共轭网。引入拉盖尔共轭方向的概念，给出其计算方法，并将该方法应用于通过具有指定球面半径的L-网格逼近曲面。