@inproceedings{8a72346d55644b03a95c812152d8655d,
title = "Discrete surfaces in isotropic geometry",
abstract = "Meshes with planar quadrilateral faces are desirable discrete surface representations for architecture. The present paper introduces new classes of planar quad meshes, which discretize principal curvature lines of surfaces in so-called isotropic 3-space. Like their Euclidean counterparts, these isotropic principal meshes meshes are visually expressing fundamental shape characteristics and they can satisfy the aesthetical requirements in architecture. The close relation between isotropic geometry and Euclidean Laguerre geometry provides a link between the new types of meshes and the known classes of conical meshes and edge offset meshes. The latter discretize Euclidean principal curvature lines and have recently been realized as particularly suited for freeform structures in architecture, since they allow for a supporting beam layout with optimal node properties. We also present a discrete isotropic curvature theory which applies to all types of meshes including triangle meshes. The results are illustrated by discrete isotropic minimal surfaces and meshes computed by a combination of optimization and subdivision.",
keywords = "Conical mesh, Discrete differential geometry, Edge offset mesh, Isotropic geometry, Isotropic minimal surface, Surfaces in architecture",
author = "Helmut Pottmann and Yang Liu",
year = "2007",
doi = "10.1007/978-3-540-73843-5_21",
language = "English (US)",
isbn = "9783540738428",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "341--363",
booktitle = "Mathematics of Surfaces XII - 12th IMA International Conference, Proceedings",
address = "Germany",
note = "12th IMA International Conference on the Mathematics of Surfaces ; Conference date: 04-09-2007 Through 06-09-2007",
}