The course requires some background in linear algebra, elementar discrete algorithms. Programming skills in C/C++.
Theoretical classes with detailed presentation, using audiovisual means, of the concepts, principles and fundamental theories.
Student presentations where the students will present the subjects they are researching to the colleagues.
Finally tutorial orientation classes, where the projects under development will be analysed and new solutions can be researched.
This course is a graduate-level introduction to the mathematical methods used in modeling geometric shapes for use in CAD/CAM, computer graphics, Augmented and Virtual Reality , and so on.
Topics to be covered include:
Homogeneous Coordinates and Geometric Transformations
Quaternions and their use in Modeling 3-D Rotations and Rigid Motions
Parametric and Implicit Representations for Curves
Splines and Continuity Constraints
B-Splines and the de Boor Algorithm
Parametric Polynomial Surfaces and NURBS
Subdivision Curves and Surfaces
Polygon Meshes for Surface Representation and Reconstruction
Constructive Solid Geometry, Binary Space Partitions, and Conversion Algorithms
Surface Reconstruction from Scattered Data Points
Mesh Simplification and Compression, as well as other Geometry Processing Algorithms
The OpenGL pipeline.
Introduction to GPU programming.
Paulo Jorge Carvalho Menezes
Project or laboratory work : 50.0%
Synthesis work: 50.0%
 3D Computer Graphics (3rd Edition), Alan H. Watt, Addison-Wesley, 2000.
 Computer Graphics: Principles and Practice, James D. Foley, Andries van Dam, Steven K. Feiner, John F. Hugues, 2nd Edition in C, Addison-Wesley, 1995.
 Computer Graphics, C Version, Donald Hearn, M. Pauline Baker, 2nd Edition, Prentice Hall,1997.
 Computational Geometry in C, O'Rourke.
 The OpenGL Programming Guide, Dave Shreiner, Mason Woo, Jackie Neider, and Tom Davis, Fifth Edition, Addison-Wesley, 2005.
 Geometric Modeling, Michael Mortenson, John Wiley & Sons, 1985.
 Spatial Augmented Reality: Merging Real and Virtual Worlds, Oliver Bimber, Ramesh Raskar, A K Peters, 2005.
 Real-Time Rendering, 2nd Edition, Tomas Moller, AK Peters , 2002.