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
The course requires some background in linear algebra, elementar discrete algorithms. Programming skills in C/C++.
Generic skills to reach
. Competence in analysis and synthesis; . Competence to solve problems; . Critical thinking; . Creativity; . Research skills; . Knowledge of a foreign language; . Computer Skills for the scope of the study; . Using the internet as a communication medium and information source; . Competence for working in group; . Competence in autonomous learning; (by decreasing order of importance)
Teaching hours per semester
total of teaching hours
assessment implementation in 20142015 Assessment Synthesis work: 50.0% Project or laboratory work : 50.0%
Bibliography of reference
 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.
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.
Laboratório com computadores adequados a computação gráfica, equipamento de realidade virtual, realidade aumentada e respectivo software.