Title: Compact Procedural Models for Wallpaper Group Face-Meshes

Date: Friday, April 19th, 2024

Time: 10:00 - 11:30 AM EST

Location: Klaus 1202

Virtual Link: https://gatech.zoom.us/j/98328884284

Sarang Joshi

Computer Graphics Ph.D. Student

School of Interactive Computing

Georgia Institute of Technology

Committee:

Dr. Jarek Rossignac (Advisor) - Professor Emeritus, School of Interactive Computing, Georgia Institute of Technology

Dr. Greg Turk (Co-advisor) - Professor, School of Interactive Computing, Georgia Institute of Technology

Dr. Thanos Economou - Professor, School of Architecture, College of Design, Georgia Institute of Technology

Dr. Bo Zhu - Assistant Professor, School of Interactive Computing, Georgia Institute of Technology

Abstract:

A planar mesh is a partition of the plane into a set of vertices, edges, and faces. These meshes are widely used in computer aided design, architecture, finite element analysis, and geographical information systems. A variety of these applications involve the creation and processing of computer models of meshes. As a result, it is important to have mesh representations that facilitate easy design, fast processing, and efficient storage of polygon meshes. Existing mesh representation models are unable to simultaneously satisfy all of the above criteria.

The first part of this proposal presents a computer representation for periodic planar meshes and associated algorithms that: (i) make it easy to design and edit such meshes, (ii) support fast access, traversal, and membership queries on meshes, and (iii) allow compact representations for a high degree of scalability. Our mesh representation consists of up to 4 isometry transformations acting on the mesh elements in a template region of space. We implement and validate our results for a wide range of meshes with symmetries belonging to all 17 of the planar wallpaper groups. We accomplish our goals while allowing for arbitrary mesh complexity (i.e. infinitely many vertices and edges).

In the second part of this proposal, we describe research opportunities to generalize our solution to a broader class of problems. These include: (i) supporting non-regularized faces and dangling edges, (ii) extending the design space by allowing for the creation of shared vertices and edges, (iii) creating multi-layer 3D lattices by supporting a subclass of 3D space groups, and (iv) supporting transformations that allow for non-periodic meshes. Our preliminary work demonstrates the feasibility of extending our mesh traversal data structure to a subset of the 3D space groups.