An Introduction to Analytic Projective Geometry and Its Applications (UMAP)

This module presents an intoduction to classical projective geometry via a mostly coordinate-free analysis approach based on linear algebra. It also indicates how the theory and techniques developed may be applied to computer graphics

Table of Contents:

INTRODUCTION

HOMOGENEOUS COORDINATES AND THE PROJECTIVE PLANE
The Duality Principle
Desargues' Theorem
Pappus' Theorem

COLLINEATIONS
Matrices Induce Collineations
... And Vice Versa
Classification of Collineations

CONICS
Correlations and Polarities
Tangents and Conics
Conics and Collineations
Pascal's Theorem and Its Dual
Classification of Conics
Constructing Collineations

PROJECTIVE THREE-SPACE
The Duality Principle
Collinearity and Incidence
Collineations
Projections

SOLUTIONS TO THE EXERCISES

REFERENCES

ABOUT THE AUTHOR