Abstract
We present a framework for designing shapes from diverse combinatorial patterns, where the vertex 1-rings and the faces are as rotationally symmetric as possible, and define such meshes as regular. Our algorithm computes the geometry that brings out the symmetries encoded in the combinatorics. We then allow designers and artists to envision and realize original meshes with great aesthetic qualities. Our method is general and applicable to meshes of arbitrary topology and connectivity, from triangle meshes to general polygonal meshes. The designer controls the result by manipulating and constraining vertex positions. We offer a novel characterization of regularity, using quaternionic ratios of mesh edges, and optimize meshes to be as regular as possible according to this characterization. Finally, we provide a mathematical analysis of these regular meshes, and show how they relate to concepts like the discrete Willmore energy and connectivity shapes.
| Original language | English |
|---|---|
| Article number | 113 |
| Journal | ACM Transactions on Graphics |
| Volume | 36 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2017 |
| Event | ACM SIGGRAPH 2017 - Los Angeles, United States Duration: 30 Jul 2017 → 3 Aug 2017 |
Bibliographical note
Publisher Copyright:© 2017 Copyright held by the owner/author(s).
Funding
This work is supported by the Israel Science Foundation, under grants 1869/15 and 2102/15, and by the Austrian Science Fund (FWF): P 29981-N35 and I 706-N26. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]. © 2017 Copyright held by the owner/author(s). Publication rights licensed to Association for Computing Machinery. 0730-0301/2017/7-ART113 $15.00 https://doi.org/10.1145/3072959.3073593
| Funders | Funder number |
|---|---|
| Austrian Science Fund | I 706-N26, P 29981-N35 |
| Israel Science Foundation | 2102/15, 1869/15 |
Keywords
- Architectural geometry
- Möbius transformations
- Polygonal patterns
- Regular meshes