I learned about projective geometry through computer vision, mostly the Hartley and Zisserman 2004 book (Multiple View Geometry in Computer Vision, ISBN 9780521540513,
R. I. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, Second. Cambridge University Press, 2004.
@book{MVG2004,
author = {Hartley, Richard ~I. and Zisserman, Andrew.},
title = {Multiple View Geometry in Computer Vision},
edition = {Second},
year = {2004},
publisher = {Cambridge University Press},
isbn = {0521540518}
}
In late 2022, I started reading Jürgen Richter-Gebert's Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry 2011, ISBN 9783642172854,
J. Richter-Gebert, Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry, 1st ed. Springer Publishing Company, Incorporated, 2011.
@book{RG_perspectives_2011,
author = {Richter-Gebert, Jürgen},
title = {Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry},
year = {2011},
isbn = {3642172857},
publisher = {Springer Publishing Company, Incorporated},
edition = {1st}
}
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry.It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications.In particular, itexplains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplaybetweengeometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the authors experience in implementing geometric software and includes hundreds ofhigh-qualityillustrations.
and I've started thinking about projective geometry in new ways. This page contains my collection of notes.
I am reading Richter-Gebert’s book (1, Richter-Gebert, 2011) and I’m in the section on Involutions and Quadrilateral Sets (chapter 8).
The involution ...
I found the Graßmann-Plücker Relations / Grassmann-Plücker Relations / Grassmann-Pluecker Relations surprising when I read about them in Jürgen Richter...
Oriented triangle area: you’re in \(\mathbb{R}^2\), and you have the coordinates of the points of the triangle \(A\), \(B\), \(C\). The oriented area ...