Title:  Compact Procedural Models for Creating and Processing Wallpaper Meshes

Date: Thursday, 16th  April 2026

Time: 11:00 AM - 1:00 PM (Eastern Time)

Location: CODA C1108 Brookhaven

Zoom Link: https://gatech.zoom.us/j/96426864403

Sarang Joshi

Ph.D. Candidate

School of Interactive Computing

Georgia Institute of Technology

Committee members:

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

Dr. Gregory Turk (advisor): Professor, School of Interactive Computing, Georgia Institute of Technology

Dr. Bo Zhu: Associate Professor, School of Interactive Computing, Georgia Institute of Technology

Dr. Sehoon Ha: Associate Professor, School of Interactive Computing, Georgia Institute of Technology

Dr. Jeff Wilson: Senior Research Scientist, Georgia Institute of Technology

Dr. Thanos Economou - Professor, School of Architecture, 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 their applications involve the creation and processing of computer models of polygonal planar 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 thesis 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 is based on 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.

In the second part of the thesis, we present techniques to assign unique IDs to each vertex, edge, or face of a periodic mesh with arbitrary complexity (i.e. any number of vertices and edges). We provide recipes for procedural generation of each mesh element, including those that lie on the boundary of the template region, while ensuring that it is generated exactly once. Finally, we describe some extensions and generalizations of our solution for periodic meshes to a broader class of problems. These include the creation of multi-layer 3D lattices, shape grammar representations, and bent and warped structures.