Mesh Processing



In computer graphics applications, three-dimensional models are almost always represented using polygonal meshes. A mesh in its simplest form consists of a set of vertices, polygons, and optionally a number of additional vertex and polygonal attributes. The complexity of a mesh can vary from low to very high depending on requirements such as rendering quality, speed and resolution. A wide spectrum of mesh processing algorithms is used by graphics and game developers for a variety of applications such as generating, simplifying, smoothing, remapping and transforming meshes. Several types of data structures and file formats are also used to store mesh data.

This chapter discusses the geometrical and topological aspects related to three-dimensional meshes and their processing. It also presents important data structures and algorithms used for operations such as mesh simplification, mesh subdivision, planar embedding, and polygon triangulation.


Convex Polygon Triangular Mesh Subdivision Scheme Simple Polygon Boundary Vertex 
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  1. Baumgart, B. (1972). Winged edge polyhedron representation (C. S. D. Stanford Artificial Intelligence Project, Trans.): Stanford University.Google Scholar
  2. Bennis, C., Vezien, J.-M., & Inglesias, G. (1991). Piecewise surface flattening for non-distorted texture mapping. SIGGRAPH Computer Graphics, 25(4), 237–246.CrossRefGoogle Scholar
  3. Botsch, M. (2010). Polygon mesh processing. Natick: A K Peters.Google Scholar
  4. Catmull, E., & Clark, J. (1978, September). Recursively generated B-spline surfaces on arbitrary topological meshes. Computer Aided Design, 10, 350–355.CrossRefGoogle Scholar
  5. De Loera, J. A., Rambau, J., & Santos, F. (2010). Triangulations: Structures for algorithms and applications. Heidelberg: Springer.MATHGoogle Scholar
  6. Edelsbrunner, H. (2001). Geometry and topology for mesh generation. Cambridge: Cambridge University Press.MATHCrossRefGoogle Scholar
  7. Floater, M., & Hormann, K. (2005). Surface parameterization: A tutorial and survey. In Advances in multiresolution for geometric modelling (pp. 157–186). Heidelberg: Springer.CrossRefGoogle Scholar
  8. Foley, J. D. (1996). Computer graphics: Principles and practice (2nd ed. in C.). Reading/Wokingham: Addison-Wesley.Google Scholar
  9. Garland, M. (1999). Quadric-based polynomial surface simplification. Ph.D., Carnegie Mellon, Pittsburgh (CMU-CS-99-105).Google Scholar
  10. Kettner, L. (1998). Designing a data structure for polyhedral surfaces. In: Proceedings of the fourteenth annual symposium on Computational geometry, Minneapolis, Minnesota, United States.Google Scholar
  11. Kobbelt, L. (2000). Root3-subdivision. In: Proceedings of the 27th annual conference on Computer graphics and interactive techniques.Google Scholar
  12. Loop, C. (1987). Smooth subdivision surfaces based on triangles. M.Sc., The University of Utah, Utah.Google Scholar
  13. Melax, S. (1998, November). A simple, fast and effective polygon reduction algorithm. Game Developer, 44–49.Google Scholar
  14. Nielsen, F. (2005). Visual computing: Geometry, graphics, and vision. Hingham/London: Charles River Media/Transatlantic, (distributor).Google Scholar
  15. Saba, S., Yavneh, I., Gotsman, C., & Sheffer, A. (2005). Practical spherical embedding of manifold triangle meshes. In: Proceedings of the international conference on shape modeling and applications 2005, BostonGoogle Scholar
  16. Schroeder, W. J., Zarge, J. A., & Lorensen, W. E. (1992). Decimation of triangle meshes. SIGGRAPH Computer Graphics, 26(2), 65–70.CrossRefGoogle Scholar
  17. Sheffer, A., Praun, E., & Rose, K. (2006). Mesh parameterization methods and their applications. Foundations and Trends in Computer Graphics and Vision, 2(2), 105–171.CrossRefGoogle Scholar
  18. Shirley, P., & Ashikhmin, M. (2007). Fundamentals of computer graphics (2nd ed.). Wellesley/London: AK Peters.Google Scholar
  19. Zorin, D. (2006). Subdivision of arbitrary meshes: Algorithms and theory (Institute of Mathematical Sciences lecture notes series). Singapore: World Scientific.Google Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Department of Computer Science and Software EngineeringUniversity of CanterburyChristchurchNew Zealand

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