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Advanced Graphics

*Lecturer: Dr P.A. Benton*

*No. of lectures:* 8

*Prerequisite course: Computer Graphics and Image Processing*

**Aims**

This course provides students with a solid grounding in a variety of three-dimensional rendering and modeling mechanisms. Topics addressed will range from low-level implementation to advanced rendering concepts and current research in computational geometry.

As there will be only eight lectures this term, interested students are expected to pursue further reading and research independently; some references and resources will also be provided during lectures.

**Lectures**

**Fundamentals.**OpenGL and JOGL. Scene graphs and bounding boxes. Polygon data structures. Simple hierarchical modeling. [1 lecture]**Computational geometry.**Geometric methods for ray tracing and Computational Solid Geometry. Surface interrogations, convexity, centroids, curvature, etc. NURBS. [3 lectures]**Rendering.**Ray tracing revisited; reflection, refraction, ray-traced effects, etc. Radiosity. [1 lecture]**Subdivision surfaces.**Univariate and bivariate subdivision schemes. [1 lecture]**Implicit surfaces.**Octrees and marching cubes. [1 lecture]**Shaders.**Current trends in hardware-accelerated 3D rendering. [1 lecture]

**Objectives**

On completing the course, students should be able to

- produce equations for each geometric primitive, derive a ray/primitive intersection algorithm for each, describe how each can be approximated by polygons
- be able to explain the basic radiosity algorithm
- define NURBS basis functions, understand the use of NURBS curves and surfaces in 2D and 3D modelling
- understand and describe a number of methods of surface modeling and generation, including computational solid geometry, subdivision surfaces and implicit surfaces
- understand algorithms for common operations on geometry, such as finding discrete curvature, convexity operations and others

**Recommended reading**

Students should expect to refer to one or more of these books. You will also be expected to draw on online resources. Other books may be added to this list as the course evolves.

You may find that it is not necessary to purchase these books, as virtually all of key facts are available on the interweb; however, if you are interested in advanced computer graphics, these texts are generally considered essential for any well-stocked reference shelf. And always remember that wikipedia is not a citable source and is only as correct as its latest update.

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

Foley, J.D., van Dam, A., Feiner, S.K. & Hughes, J.F. (1990). *Computer graphics: principles and practice*. Addison-Wesley (2nd ed.).

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

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