Bilkent University
Department of Computer Engineering


Computer Aided Sculpting with Graph Rotation Systems


Prof. Dr. Ergun Akleman
Visualization Department
Texas A&M University

In this presentation, I will present extended graph rotation systems that can represent orientable and non-orientable meshes, knots and links. Extended graph rotation systems can be considered a physical data structure that can be created using paper strips. With paper strip sculptures it is also possible to convincingly illustrate a variety of mathematical concepts such as curvature, vertex defect and Gaussian-Bonnet theorem with hands-on experiments. As a specific example, I will show how to create plain-weaving over an arbitrary surface using extended graph rotation systems. To create a plain-weaving on a surface, we need to create cycles that cross other cycles (or themselves) By alternatingly going over and under. We use the fact that it is possible to create such cycles, starting from any given manifold-mesh surface by simply twisting every edge of the manifold mesh. We have developed a new method that converts plain-weaving cycles to 3D thread structures. Using this method, it is possible to cover a surface without large gaps between threads by controlling the sizes of the gaps. We have developed a system that converts any manifold mesh to a plain-woven object, by interactively controlling the shapes of the threads with a set of parameters. We have demonstrated that by using this system, we can create a wide variety of plain-weaving patterns, some of which may not have been seen before.

Bio: Prof. Dr. Ergun Akleman is a professional cartoonist, illustrator and caricaturist who has published more than 500 cartoons, illustrations and caricatures. He is also a computer graphics researcher who has a background in Electronic and Computer Engineering. He received his PhD in Electrical and Computer Engineering from Georgia Institute of Technology. In the Visualization Department, he mainly teaches a wide variety of topics in covering both artistic and scientific aspects of computer graphics. The topics he usually teaches include computer animation, 3D modeling, rendering, visual storytelling, image based lighting and compositing. Dr Akleman's research work is interdisciplinary, usually motivated by aesthetic concerns. He has published extensively in the areas of shape modeling, image synthesis, artistic depiction, image based lighting, texture and tiles, computer aided caricature, electrical engineering and computer aided architecture. His most significant and influential contributions as a researcher have been in shape modeling and computer aided sculpting. His work on topological mesh modeling resulted a powerful manifold mesh modeling system, called TopMod. By using TopMod, high genus manifold shapes can easily be constructed. He also has a significant body of work in subdivision modeling and implicit modeling.


DATE: 1 June 2009,Monday@ 13:30