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Methods
for Analyzing Discrete Surfaces and Their Applications
Authors: Silvia Biasotti, Giuseppe Patane'. Contact: {silvia,patane}@ge.imati.cnr.it
Level: Advanced.
Prerequisites: Basic notions of geometry and topology.
This tutorial is about geometric and topological analysis of 3D shapes. We will survey:
- definition of mathematical tools for the analysis and synthesis of 3D shapes (i.e., Morse theory, Reeb graph);
- basic notions on geometric modelling (i.e, implicit and parametric surfaces);
- data structures for discrete surfaces and volumes (i.e., triangle meshes, volumes);
- study of local properties of surfaces and scalar fields along with their discretization
(i.e, geodesic and harmonic scalar fields, critical points);
- analysis of scalar fields on discrete surfaces (computational geometry);
- point cloud approximation with implicit functions (i.e., Principal Component Analysis,
clustering techniques, Radial Basis Functions, centre selection and sparse approximations);
- computer graphics applications (i.e., Geographic Information Systems (GIS), biomedical analysis (MRI), virtual reality).
Literature:
Useful links:
- IMATI-GE/CNR (http://www.ge.imati.cnr.it);
- SHAPE MODELLING GROUP (http://www.ima.ge.cnr.it/ima/smg/home.html);
Format: Slides in pdf-format.
Course material:
- Introduction;
- local properties of surfaces;
- data structures for representing discrete data;
- analysis of scalar fields on discrete surfaces;
- local and global parameterization of discrete surfaces;
- implicit surfaces and sparse representations.
Authors: Silvia Biasotti, Giuseppe Patane'. Contact: {silvia,patane}@ge.imati.cnr.it
Level: Advanced.
Prerequisites: Basic notions of geometry and topology.
This tutorial is about geometric and topological analysis of 3D shapes. We will survey:
- definition of mathematical tools for the analysis and synthesis of 3D shapes (i.e., Morse theory, Reeb graph);
- basic notions on geometric modelling (i.e, implicit and parametric surfaces);
- data structures for discrete surfaces and volumes (i.e., triangle meshes, volumes);
- study of local properties of surfaces and scalar fields along with their discretization
(i.e, geodesic and harmonic scalar fields, critical points);
- analysis of scalar fields on discrete surfaces (computational geometry);
- point cloud approximation with implicit functions (i.e., Principal Component Analysis,
clustering techniques, Radial Basis Functions, centre selection and sparse approximations);
- computer graphics applications (i.e., Geographic Information Systems (GIS), biomedical analysis (MRI), virtual reality).
Literature:
- Milnor, J. W. Morse Theory, Princeton, NJ: Princeton University Press, 1963.
- A. T. Fomenko, T. L. Kunii, Topological Methods for Visualization. Springer-Verlag, Tokyo, Japan, 1997.
- A. Requicha, Geometric Modeling: a first course, University of Southern California, 1999.
- S. Biasotti, Computational topology methods for shape
modelling applications, Univ. of Genova, Italy, 2004
- G. Patane', Analysis and Parameterization of Triangulated
Surfaces, Univ. of Genova, Italy, 2005.
Useful links:
- IMATI-GE/CNR (http://www.ge.imati.cnr.it);
- SHAPE MODELLING GROUP (http://www.ima.ge.cnr.it/ima/smg/home.html);
Format: Slides in pdf-format.
Course material:
- Introduction;
- local properties of surfaces;
- data structures for representing discrete data;
- analysis of scalar fields on discrete surfaces;
- local and global parameterization of discrete surfaces;
- implicit surfaces and sparse representations.
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