Edge offset meshes in Laguerre geometry

被引:10
作者
Pottmann, Helmut [1 ]
Grohs, Philipp [1 ]
Blaschitz, Bernhard [1 ]
机构
[1] Vienna Univ Technol, Inst Diskrete Math & Geometrie, A-1040 Vienna, Austria
基金
奥地利科学基金会;
关键词
Discrete differential geometry; Laguerre geometry; Edge offset mesh; Koebe polyhedron; Minimal surface; Laguerre minimal surface; CIRCLE PATTERNS; SURFACES; PRINCIPLES;
D O I
10.1007/s10444-009-9119-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A mesh M with planar faces is called an edge offset (EO) mesh if there exists a combinatorially equivalent mesh M-d such that corresponding edges of M and M-d lie on parallel lines of constant distance d. The edges emanating from a vertex of M lie on a right circular cone. Viewing M as set of these vertex cones, we show that the image of M under any Laguerre transformation is again an EO mesh. As a generalization of this result, it is proved that the cyclographic mapping transforms any EO mesh in a hyperplane of Minkowksi 4-space into a pair of Euclidean EO meshes. This result leads to a derivation of EO meshes which are discrete versions of Laguerre minimal surfaces. Laguerre minimal EO meshes can also be constructed directly from certain pairs of Koebe meshes with help of a discrete Laguerre geometric counterpart of the classical Christoffel duality.
引用
收藏
页码:45 / 73
页数:29
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