Computer Laboratory

Course pages 2014–15

Advanced Graphics

Principal lecturer: Dr Alex Benton
Taken by: Part II
Past exam questions
Information for supervisors (contact lecturer for access permission)

No. of lectures: 8
Suggested hours of supervisions: 2
Prerequisite course: Computer Graphics and Image Processing


This course provides students with a solid grounding in the main three-dimensional modelling and rendering mechanisms. It also introduces supporting topics, including graphics cards, mobile graphics, and animation.


The order of delivery of lectures is provisional and subject to change.

  • Computational geometry. The mathematics of discrete geometry: what can you know, and how well can you know it?

  • Ray tracing. The fundamentals of raycasting, constructive solid geometry (CSG), and bounding volumes.

  • Implicit surfaces, voronoi diagrams. Useful graphical and geometric techniques.

  • Splines and subdivision surfaces. Bézier curves and B-splines, from uniform, non-rational B-splines through to non-uniform, rational B-splines (NURBS). Introduction to subdivision. The key methods. Pros and cons when compared with NURBS.

  • Advanced illumination techniques. Radiosity and photon mapping.

  • OpenGL, graphics cards, and shaders. Tools and technologies available today; previews of what’s coming tomorrow.


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, 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.
* Shirley, P. & Marschner, S. (2009). Fundamentals of Computer Graphics. CRC Press (3rd ed.).
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.