
Academic Year:  2015/6 
Owning Department/School:  Department of Computer Science 
Credits:  6 
Level:  Intermediate (FHEQ level 5) 
Period: 
Semester 1 
Assessment Summary:  CW 25%, EX 75% 
Assessment Detail: 

Supplementary Assessment: 
CM20219A  Mandatory Extra Work (where allowed by programme regulations) 
Requisites: 
Before taking this module you must take CM10197
While taking this module 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
CM20219 is Optional on the following programmes:Department of Electronic & Electrical Engineering
