Prerequisite course: Computer Graphics and Image Processing
Aims
This course provides students with a solid grounding in a variety of
three-dimensional modelling mechanisms. The course also imparts a
deeper understanding of rendering techniques and knowledge of current
commercial use 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.
[0.4 lecture]
The polygon. Drawing polygons. Graphics cards. Polygon
mesh management: data structures. [0.6 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. [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. Implicit surfaces and voxels: 3D pixels and the marching
cubes algorithm; medical applications of this. [2 lectures]
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
Recommended books
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.
