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Advanced Graphics

*Lecturers: Dr N.A. Dodgson and Dr P.A. Benton*

*No. of lectures:* 12

*Prerequisite course: Computer Graphics and Image Processing*

**Aims**

This course provides students with a solid grounding in a variety of three-dimensional modelling mechanisms. It also provides an introduction to radiosity, animation, hardware technologies, and current commercial uses of computer graphics.

**Lectures**

Dr Dodgson and Dr Benton's lectures will be interleaved. A detailed timetable will be handed out in the first lecture.

**Revision, polygons, hardware.**Revision of the ray tracing and polygon scan conversion methods of making images from 3D models; the pros and cons of each approach. Current uses of computer graphics in animation, special effects, Computer-Aided Design and marketing. Drawing polygons. Graphics cards. [NAD, 1 lecture]**Splines for modelling arbitrary 3D geometry.**(splines are the standard 3D modelling mechanism for Computer-Aided Design). Features required of surface models in a Computer-Aided Design package. Bezier curves and surfaces. B-splines, from uniform, non-rational B-splines through to non-uniform, rational B-splines (NURBS). [NAD, 3 lectures]**Subdivision surfaces.**(an alternative mechanism for representing arbitrary 3D geometry, now widely used in the animation industry). Introduction to subdivision. Pros and cons when compared to NURBS. [NAD, 2 lectures]**Geometric methods for ray tracing.**The fundamentals of raycasting and constructive solid geometry (CSG). [PAB, 1 lecture]**Illumination: Ray tracing effects and global lighting.**Visual effects, radiosity and photon mapping. [PAB, 1 lecture]**Computational geometry.**The mathematics of discrete geometry: what can you know, and how well can you know it? [PAB, 1 lecture]**Implicit surfaces, voxels and particle systems.**A sampler of special effects techniques. [PAB, 1 lecture]**OpenGL and shaders.**Tools and technologies available today; previews of what's coming tomorrow. [PAB, 2 lectures]

**Objectives**

On completing the course, students should be able to

- compare and contrast ray tracing with polygon scan conversion;
- define NURBS basis functions, and explain how NURBS curves
and surfaces are used in 2D and 3D modelling;
- describe the underlying theory of subdivision and
define the Catmull-Clark and Doo-Sabin subdivision methods;
- understand the core technologies of ray tracing, constructive
solid geometry, computational geometry, implicit surfaces, voxel
rendering and particle systems;
- understand several global illumination technologies such as
radiosity and photon mapping, and be able to discuss each in detail;
- be able to describe current graphics technology and discuss
future possibilities.

**Recommended reading**

Students should expect to refer to one or more of these books, but should not find it necessary to purchase any of them.

* Slater, M., Steed, A. & Chrysanthou, Y. (2002). *Computer graphics and virtual environments: from realism to real-time*. Addison-Wesley.

Watt, A. (1999). *3D Computer graphics*. Addison-Wesley (3rd ed).

de Berg, M., Cheong, O., van Kreveld, M. & Overmars, M. (2008). *Computational geometry: algorithms and applications*. Springer (3rd ed.).

Rogers, D.F. & Adams, J.A. (1990). *Mathematical elements for computer graphics*. McGraw-Hill (2nd ed.).

Warren, J. & Weimer, H. (2002). *Subdivision methods for geometric design*. Morgan Kaufmann.

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