Description

This is a course in geometric topics useful for the two-dimensional display of three-dimensional figures and animation of such figures.

Prerequisites

1 course with a minimum grade of C- from (MATH461, MATH240, MATH341).

 

Level of Rigor

Standard

 

Sample Textbooks

Geometric Algebra: An Algebraic System for Computer Games and Animation, by John A. Vince. 

Applied Geometry for Computer Graphics and CAD, by D. Marsh

 

Applications

Computer science (vision and image processing), chemistry (visualisation of spatial molecular structure)

 

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Additional Notes

Topics

Homogenous coordinates

The projective plane and three-dimensional projective space

Lines, planes and general flats in projective space

The join operation on flats

Plucker coordinates for lines and planes

Projections to planes in space

Projections from three-dimensional space to two-dimensional space

Projection matrices

Intersections and the meet operation on flats

Duality and orthogonality

Two and three dimensional coordinate systems

Orientation, two sided projective space

Transformations: translations, rotations, reflections, scalings, and shears

Generating figures with geometric transformations

Animations