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

### Author: Kit Hanes

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:INTRODUCTIONHOMOGENEOUS 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

REFERENCES

ABOUT THE AUTHOR

#### Mathematics Topics:

#### Application Areas:

#### Prerequisites:

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