Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.17865 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917351829536768 |
|---|---|
| author | Ramos-Cisneros, A. Skopenkov, M. Pottmann, H. |
| author_facet | Ramos-Cisneros, A. Skopenkov, M. Pottmann, H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17865 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Approximation by Quad Meshes in Laguerre Geometry Ramos-Cisneros, A. Skopenkov, M. Pottmann, H. Computational Geometry Differential Geometry 53A70, 51B15, 68U05 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. |
| title | Approximation by Quad Meshes in Laguerre Geometry |
| topic | Computational Geometry Differential Geometry 53A70, 51B15, 68U05 |
| url | https://arxiv.org/abs/2603.17865 |