Module details for Mathematics for Application Development 2

Description

This module builds on Mathematics for Application Development 1 to give CGAD students the mathematical building blocks required for 3-D graphics programming.

Aims

The aim of this module is to provide the student with: the necessary mathematical tools for programming 3-D object characterisations in computer graphics.

Learning Outcomes

By the end of this module the student should be able to:

1.  Formulate and use transformation matrices (2-D & 3-D) for standard transformations and projections.

2.  Determine equations for lines and planes in 3-D, using them to compute distances, projections and intersections.

3.  Perform collision detection calculations of rays with boxes and spheres.

4.  Apply Newtonian concepts involving momentum, impulse and energy to formulate and solve resulting models.

Indicative Content

1 Viewing Transformations:

2-D viewing transformation matrices, scaling factors, aspect ratios, windows, normalised device screen, viewports.

2 Lines and Planes:

Vector (using parameters) and Cartesian equations of 3-D lines and planes. Distances from points to lines and planes. Projection of line onto a plane, intersection of lines and planes.

3 Matrix Transformations:

3-D matrix transformations of scaling, rotation, reflection and translation (homogeneous coordinates). Composite transformation by matrix multiplication.

4 Projection Matrices:

Standard orthogonal and perspective matrix transformations.

5 Ray Tracing:

Collision detection methods of rays with boxes and spheres.

6 Newtonian Concepts:

Newton’s laws of motion. Momentum and impulse, collision of bodies (1-dimensional, elastic and inelastic). Kinetic and potential energy, elastic strings. Work and Power.

7

Teaching and Learning Work Loads