# Graphic Computation and Three-dimensional Modeling

**Year**

1

**Academic year**

2023-2024

**Code**

03000098

**Subject Area**

Electrical and Computer Engineering

**Language of Instruction**

Portuguese

**Mode of Delivery**

Face-to-face

**ECTS Credits**

6.0

**Type**

Elective

**Level**

3rd Cycle Studies

## Recommended Prerequisites

The course requires some background in linear algebra, elementar discrete algorithms. Programming skills in C/C++.

## Teaching Methods

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.

## Learning Outcomes

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.

## Work Placement(s)

No## Syllabus

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.

## Assessment Methods

Assessment

*Project or laboratory work : 50.0%*

*Synthesis work: 50.0%*

## Bibliography

[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.