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N. Ketterl:
"Weighted Mesh Simplification of 3D Triangular Surfaces";
Supervisor: W. Purgathofer, R.F. Tobler; Institut für Computergraphik und Algorithmen, 2011.

Representing huge triangular datasets in a real-time rendering environment is a challenge receiving continuous attention. There is a growing complexity of geometric meshes on the one hand and increasing computational power of graphics hardware on the other hand. Although hardware acceleration is very powerful, simplification using software is much cheaper and more flexible. Additionally, for a large class of geometric models, simplification can be performed as a preprocessing step that does not need to run in real-time. The underlying theory of this diploma thesis is based on mesh simplification using quadric error metrics. This algorithm was first published by Michael Garland. It was implemented into Aardvark, a sophisticated rendering framework. It contains a comprehensive set of libraries dealing with data structures in general and polygonal mesh data structures in particular. The application takes a triangulated mesh as input and iteratively creates a more and more simplified approximation by weighting and collapsing suitable mesh areas. Some surface details will be lost, but the overall shape of the model will be preserved. The presented code can handle models by preprocessing static, closed triangular meshes. The iterative computation stops if an user specified percentage of the original mesh size is reached. A further improvement in a later research project will try to add vertex colors and texture coordinates to the simplification procedure.

http://publik.tuwien.ac.at/files/PubDat_227635.pdf