To Be Presented in the 11th Asian Technology Conference in Mathematics
December 12-16, 2006, Hong Kong SAR, China

Visualizing Polygonal Objects in 3D with Computer Algebra Systems: A Waterman Polyhedra Case Study

Miroslaw Majewski
College of Information Systems
Zayed University
United Arab Emirates


Polygonal objects are objects build out of multiple polygons. Examples of polygonal objects in 3D are convex and non-convex polyhedra and other various one- or two-sided shapes in 3D. In many cases modeling polygonal objects in 3D requires special algorithms, for example algorithms to calculate vertices and create polygons out of these vertices, algorithms to build a convex hull in case of convex objects, etc. Some of these tasks are very time consuming, especially while dealing with objects built out of hundreds of polygons. Therefore, algorithms to perform these tasks should be highly efficient.

In this paper I will describe construction of Waterman polyhedra and show how Waterman polyhedra can be created using Computer Algebra System MuPAD. I will briefly describe the algorithm that I developed to calculate Waterman polyhedra vertices. I will show also how OpenGL structure known as SurfaceSet can be used to create polygonal faces of polyhedra. I will discuss polyhedra coloring issues. Finally, I will show a gallery of selected Waterman polyhedra.

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