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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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