Graphic Computation and Three-dimensional Modeling - EB3

Ano letivo: 2015-2016
Specification sheet

Specific details
course codecycle os studiesacademic semestercredits ECTSteaching language

Learning goals

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
tutorial guidance15
total of teaching hours25

Problem solving20 %
Project80 %
assessment implementation in 20152016
Assessment Synthesis work: 50.0%
Project or laboratory work : 50.0%

Bibliography of reference

[1] 3D Computer Graphics (3rd Edition), Alan H. Watt, Addison-Wesley, 2000.

[2] Computer Graphics: Principles and Practice, James D. Foley, Andries van Dam, Steven K. Feiner, John F. Hugues, 2nd Edition in C, Addison-Wesley, 1995.

[3] Computer Graphics, C Version, Donald Hearn, M. Pauline Baker, 2nd Edition, Prentice Hall,1997.

[4] Computational Geometry in C, O'Rourke.

[5] The OpenGL Programming Guide, Dave Shreiner, Mason Woo, Jackie Neider, and Tom
Davis, Fifth Edition, Addison-Wesley, 2005.

[6] Geometric Modeling, Michael Mortenson, John Wiley & Sons, 1985.

[7] Spatial Augmented Reality: Merging Real and Virtual Worlds, Oliver Bimber, Ramesh Raskar,
A K Peters, 2005.

[8] Real-Time Rendering, 2nd Edition, Tomas Moller, AK Peters , 2002.

Teaching method

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.

Resources used
Laboratório com computadores adequados a computação gráfica, equipamento de realidade virtual, realidade aumentada e respectivo software.