Teaching Responsibility
LJMU Schools involved in Delivery:
Computer Science and Mathematics
Learning Methods
Lecture
Practical
Workshop
Module Offerings
4109COMP-JAN-CTY
Aims
To provide mathematical principles in computer graphics.
To explain the underpinning concepts within computer graphics.
To teach 2D computer graphics operations using a modern graphical API.
To develop programming skills in computer graphics.
Learning Outcomes
1.
Describe the primary stages of the programmable graphics pipeline in 2D context.
2.
Apply relevant mathematical principles to solve problems in real-time computer graphics.
3.
Implement logical expressions and arithmetic models to represent the decisions and actions that form the mechanics an interactive 2D graphical application.
4.
Construct mathematical models and apply them programmatically to control graphical primitives.
5.
Use a modern graphics 2D API in conjunction with a high-level programming language to develop an interactive graphical 2D application
Module Content
Outline Syllabus:Elementary numerical and algebraic processes: fractions, indices, algebraic manipulation
Two-dimensional Cartesian co-ordinates, equation of a straight line and quadratic curve, solution of linear equations containing one and two variables.
Elementary trigonometry and trigonometric functions.
Multi-dimensional vectors, vector algebra including scalar product.
Matrix multiplication for vector transformations.
Parametric equations.
Set theory and discrete maths.
Logic: simple propositional and predicate logic.
Introduction to 2D graphics via the programmable pipeline.
Applied Mathematics for 2D Computer Graphics: Affine Transformations in 2D
Introduction to the rendering pipeline: Coordinates and Model, World and Screen Spaces
Vector and Raster representation of 2D primitives within the Programmable Pipeline
Vertex and graphics primitives in a 2D environment – Buffers and Resources
Mapping Sprites via Buffers and Resources – Basic Texture Mapping and Quadrilateral Formation.
Quadrilateral-based Text Rendering.
Handling Transparency on 2D Texture mapped surfaces.
Homogeneous coordinates.
Cameras and Orthographic Projections
Applying Orthographic Representation to a 2D graphics application.
The Interactive Loop, Timing and Measuring Time.
Event Driven Input Handling and Spatial and Temporal Predicates applied to Input.
Representations of graphical data and logical state using Object-Oriented Programming techniques.
Basic Collision Detection: Broad phase.
Module Overview:
This module teaches the fundamental of, and specifically 2D, computer graphics and its underlying mathematical principles. Students will recap on a number of elementary mathematics concepts before being introduced to more complex ones and how to utilise them to solve computer graphics problems. The module teaches the practical aspects of computer graphics through a series of programming workshop using modern graphics API.
This module teaches the fundamental of, and specifically 2D, computer graphics and its underlying mathematical principles. Students will recap on a number of elementary mathematics concepts before being introduced to more complex ones and how to utilise them to solve computer graphics problems. The module teaches the practical aspects of computer graphics through a series of programming workshop using modern graphics API.
Additional Information:This module teaches the fundamental of, and specifically 2D, computer graphics and its underlying mathematical principles. Students will recap on a number of elementary mathematics concepts before being introduced to more complex ones and how to utilise them to solve computer graphics problems. The module teaches the practical aspects of computer graphics through a series of programming workshop using modern graphics API.