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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