Computer Laboratory – Course material 2007

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Advanced Graphics

Lecturer: Dr N.A. Dodgson

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, graphics cards, and current commercial uses of computer graphics.

Lectures

Introduction. 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. [0.75 lecture]
The polygon. Drawing polygons. Graphics cards. Polygon mesh management: data structures. [0.75 lecture]
Ray tracing. The primitive geometric shapes used in ray tracing: plane, polygon, sphere, cylinder, cone, box, disc, torus. Ray intersection calculations and normal calculations for these. Converting the primitives into polygons for use in polygon scan conversion. [1.5 lectures]
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). [2.5 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. [2 lectures]
Implicit surfaces and voxels. 3D pixels and the marching cubes algorithm; medical applications of this. [1 lecture]
Other ways to create complex geometry. Generative models: extrusion, revolution, sweeping, generalised cylinders. Constructive solid geometry (CSG): set theory applied to solid objects; different implementations of this using ray tracing and polygons. [1 lecture]
Radiosity. Accurate calculation of the diffuse inter-reflections in a scene. [1.5 lectures]
Computer animation. A brief introduction to some techniques in animation. [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
define NURBS basis functions, understand the use of NURBS curves and surfaces in 2D and 3D modelling
describe and explain how to use generative models, constructive solid geometry, implicit surfaces, voxel rendering and subdivision surfaces; describe how each representation can be converted to polygons
be able to compare and contrast ray tracing with polygon scan conversion
be able to explain the basic radiosity algorithm

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.
Rogers, D.F. & Adams, J.A. (1990). Mathematical elements for computer graphics. McGraw-Hill (2nd ed.).
Foley, J.D., van Dam, A., Feiner, S.K. & Hughes, J.F. (1990). Computer graphics: principles and practice. Addison-Wesley (2nd ed.).
Warren, J. & Weimer, H. (2002). Subdivision methods for geometric design. Morgan Kaufmann.

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