____________________________________________________________________

Prerequisites:

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

- Some background notions from
- point-set topology (mathematical models of objects)
- algebraic topology (cell and simplicial complexes (meshes))

- Representations for cell and simplicial complexes
- Topological relations in cellular and simplicial complexes (meshes)
- Data structures for two-dimensional cellular complexes
- Data structures for triangle and tetrahedral meshes
- Data structures for meshes in higher dimensions

- Representation schemes for solid objects
- Representations for solid objects: properties and issues
- A taxonomy of representations schemes
- Boundary Representations (Breps)
- Space-based and object-based decompositions
- Constructive Solid Geometry (CSG)

- Building triangle and tetrahedral meshes
- Delaunay triangulation in two and three dimensions: definitions and properties
- Algorithms for building and updating a Delaunay mesh
- Surface reconstruction algorithms

- Mesh simplification
- Approximation of surfaces and scalar fields through triangle and meshes
- Taxonomy of simplification techniques for triangle meshes
- Techniques for meshes describing two-dimensional scalar fields
- Algorithms for incremental decimation and refinement of triangle and tetrahedral meshes
- Non-incremental techniques

- Geometric compression: compression techniques for triangle and tetrahedral meshes
- Compression of geometric information
- Compression of connectivity information
- Triangle strips
- Techniques based on graph traversal
- Progressive techniques

- Level-Of-Detail (LOD) modeling
- The Multi-Tessellation (MT): a dimension-independent framework for LOD modeling
- Nested hierarchical representations for regular meshes
- LOD representations based on irregular meshes
- Applications: virtual reality, terrain modeling and visualization, scientific visualization

Course work will
consist of a reading project in which the students would be required to summarize
and compare papers related to the material
taught in class or a programming project, if requested by the
students.

There will be two
exams: a midterm and a final exam.

*Weights: *Project 1/3, Midterm 1/3, Final 1/3

________________________________________________________________________
__________________

**Course Material**

*Recommended
Books:*

- H.Edelsbrunner, Geometry and Topology for Mesh Generation, Cambridge University Press, 2001(available in CS library).
- D.
Luebke, M. Reddy, J.Cohen, A. Varshney, B. Watson, R. Huebner,
Level Of Detail for 3D Graphics, Morgan Kaufmann, 2002 (available in CS library).

- C. Hoffmann, Geometric and Solid Modeling, Morgan Kaufmann, San Mateo, California, 1989 (Chapters 1-3). (available on line and a copy in CS library )
- M. Mantyla, An Introduction to Solid Modeling, Computer Science Press, 1988. (available in CS library)
- A. Paoluzzi, Geometric Programming for Computer-Aided Geometric Design, John Wiley and Sons, 2003(available in CS library).
- M. de
Berg, M.van Kreveld, M.Overmars, O. Schwarzkopf, Computational
Geometry, Springer Verlag, 1998 (available in CS library)

- A. A.G. Requicha, Geometric Modeling: A First Course, University of Southern California, 1999 (available on line )

- L. De Floriani, P. Magillo, Multiresolution mesh representation: Models and data structures, In Multiresolution in Geometric Modeling, M.Floater and A.Iske and E.Quak (Editors), Springer-Verlag, 2002, pp. 363-418
- E. Danovaro, L. De Floriani, P. Magillo, E. Puppo, Data structures for 3D Multi-Tessellations: an Overview, in: F.H.Post G.P.Bonneau, and G.M.Nielson (Editors), Proceedings of the Dagstuhl Scientific Visualization Seminar, Kluwer Academic Publishers, 2003.

- E.Danovaro, L. De Floriani, P. Magillo, Compression Methods for Triangle Meshes (preliminary version), Tech. Report University of Genova, Genova (Italy), 2002.

- M. Garland, Multiresolution modeling: Survey and Future Opportunities,
Eurographics'99, State-Of-The-ART Report.

- P.Heckbert and M.Garland, Survey of Polygonal Surface Simplification Algorithms, CMU- Technical Report 1997, Course Notes SIGGRAPH1997.
- P. Lindstrom , G.Turk, Evaluation of Memoryless Simplification, IEEE Transactions on Visualization and Computer Graphics, 5(2), pp. 98-115, April-June 1999.
- D.Luebke, Developer's Survey of Polygonal Simplification Algorithms, IEEE Computer Graphics & Applications, 21(3), pp. 24-35, May 2001.

- L. De Floriani, P. Magillo, E. Puppo, D.Sobrero, A Multi-Resolution Topological Representation for Non-manifold Meshes, Proceedings Solid Modeling 2002, Saarbruecken, Germany, June 2002.