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2023/24 Taught Postgraduate Module Catalogue

COMP5812M Foundations of Modelling and Rendering

15 creditsClass Size: 40

Module manager: Dr Rafael Kuffner dos Anjos

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2023/24

Pre-requisite qualifications

We will assume a good standard of C++ programming, including use of classes, basic templates, and overloading. Knowledge of computer architecture, in particular the memory hierarchy. Knowledge of data structure and algorithms. Knowledge of mathematics including linear algebra, calculus, statistics, numerical analysis, etc. Knowledge of introductory physics. Knowledge of basic Computer Graphics and hands-on experience with a rasterization-oriented 3D graphics library such as OpenGL.

This module is not approved as an Elective

Module summary

This module builds a solid foundation of understanding for the physics, mathematics and computation underlying all computer graphics. Delving deeper than a first undergraduate module in 3D graphics, one goal is to understand high-quality rendering through software raytracing as a preliminary to hardware accelerated approximation of high-quality visual effects. This will be complemented by solid coverage of the mathematics necessary for full comprehension and exploitation of accelerated graphics hardware.


Students will develop from users of existing graphics packages to understanding the fundamentals of how rendering is actually done. Starting with mathematical and physical principles, they will understand how real-time and film-quality rendering is are performed in software, and how hardware accelerated rendering relates to this high-quality model.

Learning outcomes
1. understand optical physics relevant to computer graphics, including reflections, refractions, diffraction and scattering

2. understand and implement fundamental techniques in projective and ray-traced image rasterisation

3. be able to build and/or modify software ray-tracers using light transport equations and Monte Carlo integration

4. understand material acquisition, modelling and representation, including textures, BRDFs and BSDF’s

5. understand the mathematical foundations of transformations, including rotation, scaling, shearing, translation and projection in Cartesian and homogeneous coordinates

6. understand the use of quaternions for representing and interpolating rotations

7. understand and implement barycentric, bilinear and trilinear interpolation for rasterization and texture lookups

8. understand how to represent and store geometric models of surfaces

9. develop geometric intersection tests used for object modelling, ray-tracing, collision detection and geometric acceleration structures

10. understand how modern graphics pipelines implement projective rendering


* The syllabus will broadly follow the second half of the industry standard Hughes & van Dam text, which layers details on top of an early-stage understanding of simple rendering.
* Standard approximations & models fundamental to graphics
* Graphics hardware & devices
* Basics of 2D & 3D calculus, where needed
* Material representations: textures, BRDFs’, BSDF’s
* Optical physics, including spectral representations, material properties, scattering and volumetric effects.
* Monte Carlo probability and integration
* The rendering equation, with theoretical and practical solutions.
* Geometric intersection testing in 1D, 2D and 3D;

Teaching methods

Delivery typeNumberLength hoursStudent hours
Class tests, exams and assessment240.0080.00
Private study hours40.00
Total Contact hours110.00
Total hours (100hr per 10 credits)150.00

Private study

The foundations of computer graphics involve a significant amount of mathematics and practical programming, involving a cycle of formal instruction, separate review and practical consolidation. Thus, the student is expected to spend about 2 hours per lecture reviewing the lecture material for full comprehension before building the relevant practical programming skill, with private review and coursework based assessments being approximately equal in weight, and building towards the full understanding of the material necessary to demonstrate competence at the final exam.

Opportunities for Formative Feedback

Assignments will be bi-weekly, providing monitoring of student progress on an ongoing basis.

Methods of assessment

Assessment typeNotes% of formal assessment
In-course AssessmentProgramming task20.00
In-course AssessmentProgramming task40.00
In-course AssessmentProgramming task40.00
Total percentage (Assessment Coursework)100.00

This module will be reassessed by coursework only.

Reading list

The reading list is available from the Library website

Last updated: 28/04/2023 14:54:00


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