Computer Graphics (2006/2007)

Learning outcomes

This course aims at providing the student with the tools needed
to master the algorithms and computational methods upon which
many interactive computer graphics applications are based. The
focus is on understanding the theory (geometry, radiometry) and
the computational issues (algorithms, programming) that lie
behind computer generated images.

1. Introduction to Computer Graphics.
- CG paradigms.
- Outline of a CG application.

2. Mathematical background.
- Vector and affine spaces.
- Matrices and transforms.

3. Elements of Computational Geometry.
- Elementary test operations.
- Convex hull: Graham's scan, Quickhull, Jarvi's march.
- Line segment intersection: plane sweep.
- Triangulations: generic and Delaunay's (GKS).
- Proximity problems: Shamos' algorithm and Voronoi diagrams.
- Geometric search: point location, range search (kd tree).
- Geometric data structures: Quadtree, Octree and BSP tree.

4. 3D Modeling
- Polygonal meshes.
- Parametric surfaces (hints).
- Constructive Solid Geometry (hints).
- Spatial subdivision (hints).

5. Illumination and rendering.
- Introduction: ray casting.
- Radiometry, BRDF, Rendering equation.

6. Illumination models
- Phong model
- Cook-Torrance model (hints)
- Light sources.
- Radiosity.
- Ray tracing.

7. Rasterization.
- Geometric transformations.
- Clipping.
- Hidden surfaces removal: object-space, image-space.
- Scan conversion
- Shading: Flat, Phong e Gouraud
- The OpenGL rendering pipeline.

8. Mapping techniques
- Texture mapping.
- Bump mapping.

9. Photorealism
- Reflection maps.
- Light maps.
- Geometric shadows
- Transparency

10. Techniques for interactive applications
- Visibility culling.
- Level of detail (LoD).

11. Image-based modeling and rendering
- Overview

12. Computer laboratory (12)
- Introduction to OpenGL programming

Written essay (50%) and programming project (50%).