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Programme & Unit Catalogues

## CM20219: Fundamentals of computer graphics

Credits: 6
Level: Intermediate (FHEQ level 5)
Period: Semester 1
Assessment: CW 25%, EX 75%
Supplementary Assessment: CM20219A - Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must take CM10197 and while taking this unit you must take CM20214 or take CM20221
Description: Aims:
To provide mathematical foundations underpinning the fields of Computer Graphics and Computer Vision. To illustrate the connection between mathematical foundations and fundamental operations on 2D & 3D geometry. To provide fundamental skills for visualizing graphics objects.

Learning Outcomes:
On completion of this unit students will be able to:
1. model graphical objects using lines and curves and visualize those objects
2. perform simple transformations on images, and on graphical models in 2D and 3D space.
3. represent and render graphical objects using common data structures and software libraries.

Skills:
Problem Solving (T/F, A), Application of Number (T/F, A).

Content:
GEOMETRIC TRANSFORMATIONS AND LINEAR ALGEBRA
* Vector spaces and reference frames
- 2D and 3D linear and affine transformations
- Rotation in 3D - Euler angles
- Compound geometric transformations and hierarchical animation
- Projective spaces, homogenous coordinates, perspective and cameras.
* Linear Algebra
- EVD, SVD
- Inertial axes, moments, Eigenmodels - basics of classification.
MODELLING AND DIFFERENTIALGEOMETRY
* Curves and lines
- Representations of space curves
- Piecewise curves and continuity
- Splines; Bezier and Hermite cubic curves
* Surfaces
- Modelling surfaces with planar and bicubic representations
* Differential Geometry
- Curve parameterisation, Frenet frame
- Principal axes of a surface, Jacobian, Hessian.
REPRESENTATION AND RENDERING OF OBJECTS
- Colour and colour perception
- Data structures for 3D objects
- Descriptive languages: OpenGL
Programme availability:

#### CM20219 is Compulsory on the following programmes:

Department of Computer Science
• USCM-AFB06 : BSc (hons) Computer Science (Full-time) - Year 2
• USCM-AKB07 : BSc (hons) Computer Science (Full-time with Thick Sandwich Placement) - Year 2
• USCM-AFB13 : BSc (hons) Computer Science with Mathematics (Full-time) - Year 2
• USCM-AKB14 : BSc (hons) Computer Science with Mathematics (Full-time with Thick Sandwich Placement) - Year 2
• USCM-AAB14 : BSc (hons) Computer Science with Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USCM-AAB07 : BSc (hons) Computer Science with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
• USCM-AFM01 : MComp (hons) Computer Science (Full-time) - Year 2
• USCM-AKM02 : MComp (hons) Computer Science (Full-time with Thick Sandwich Placement) - Year 2
• USCM-AAM02 : MComp (hons) Computer Science with Study Year Abroad (Full-time with Study Year Abroad) - Year 2
Department of Electronic & Electrical Engineering
• UEEE-AFB07 : BEng (hons) Computers Electronics and Communications (Full-time) - Year 3
• UEEE-AKB07 : BEng (hons) Computers Electronics and Communications (Full-time with Thick Sandwich Placement) - Year 4
• UEEE-AFM07 : MEng (hons) Computers Electronics and Communications (Full-time) - Year 3
• UEEE-AKM07 : MEng (hons) Computers Electronics and Communications (Full-time with Thick Sandwich Placement) - Year 4

#### CM20219 is Optional on the following programmes:

Department of Electronic & Electrical Engineering
• UEEE-AFB01 : BEng (hons) Electrical and Electronic Engineering (Full-time) - Year 3
• UEEE-AKB01 : BEng (hons) Electrical and Electronic Engineering (Full-time with Thick Sandwich Placement) - Year 4
• UEEE-AFM01 : MEng (hons) Electrical and Electronic Engineering (Full-time) - Year 3
• UEEE-AKM01 : MEng (hons) Electrical and Electronic Engineering (Full-time with Thick Sandwich Placement) - Year 4

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.