3
votes
3answers
314 views

On duality on finite projective planes

Hey Everyone! In nearly all (if not all) projective geometry texts I have bumped into the following theorem: "Principle of duality: If in a theorem in $\mathfrak{P}$ one switches the word point for ...
-1
votes
2answers
415 views

projective camera: back-projecting a point on the image plane into 3-space

suppose I got a projective camera model. for this model I would like to back-project a ray through a point in the image plane. I know that the equation for this is the following: $$ y(\lambda) = P^+_0 ...
6
votes
3answers
851 views

Original proof of Pappus' Hexagon Theorem

Does anyone know where I can find an english translation, preferrably online or in a book the library of a small liberal arts college would be likely to have, of the original proof of Pappus' hexagon ...
0
votes
0answers
920 views

How to get homography matrix in such case? (from one still image)

In my case as input I have such data structures: original image (RGB pixels), objects (squares) with lines crossing points in pixels (x,y) on Image Plane. I have image like this In my particular ...
2
votes
2answers
601 views

Projective transformation between polygons.

Extending my earlier question about linear transformations, what's the easiest way to test if there exists a projective linear transformation that takes one polygon to another (in ...
4
votes
1answer
173 views

Rectifying texture from image

I have a camera matrix $P$ which defines a projective transformation $\mathbb{P}^3 \rightarrow \mathbb{P}^2$. In the former space there is a plane $[ x|\pi^Tx=0 ]$. The image of the plane under $P$ ...
5
votes
4answers
765 views

Is the theory of incidence geometry complete?

Consider the basic axioms of planar incidence geometry, which allow us to speak of in-betweeness, collinearity and concurrency. These axioms per se are not complete, since for example, Desargues ...