Principles of 2D and 3D Computational Geometry

Overview
The purpose of this course is to provide a sound foundation in the techniques and theory underlying 2D and 3D computational geometry. In addition to covering the course also overviews

• applying structured programming techniques
• applying computational geometry principles in OpenGL
• applied interactive graphics programming using event models and widget sets
• Note: this course can be tailored to use other programming languages such as Java or C# ( please inquire )

Course Contents
Overview of 2D and 3D Computational Geometry

• Points in Euclidean Space
• Vectors and Directions
• Vector Orthogonality, Linear Dependence and Basis Sets
• Planes and Lines
• Sidedness Predicates

Mappings and Transformations

• Affine transformations - basic definition
• Properties and composition of affine transformations
• Viewport mapping
• Representation of Affine transformations using matrices
• Orthogonal transformations
• Rotations in space and Euler angles
• Line and Segment intersections
• Clipping and splitting of segments and polygons

Structured and Object Oriented Programming Principles and Techniques

• Classes, objects, data structures, modules, components and interfaces
• Overview of UML2 diagrams
• Devising suitable classes and class hierarchies for computational geometry applications
• Collections, containers, iteration and iterators

Non-Euclidean Computational Geometry - theory, data structures and algorithms

• Spherical geometry
• Rotations and quaternions
• Projective geometry
• Intersections, clipping and splitting

Raster Graphics and Computational Geometry

• pixels, raster images and segment rasterisation
• rays and polygon point containment
• illuminations and shading
• ray tracing

Principles of Geometric and Solid Modeling

• boundary representation
• indexed face sets
• Platonic solids
• graphs of solids
• halfedge data structures and Euler operators
• Binary Space Partitioning (BSP) trees
• basics of Constructive Solid Geometry (CSG)

Interactive Graphics Programming

• Event driven software programming
• Widgets and widget sets
• working with OpenGL
• working with the GLOW toolkit