1. ### cristina89

29
Hello people!
I'm studying about collineation. It seems to be simple, but I can't understand so much and I can't find so many things about this subject...
Can someone explain to me what exactly is a Collineation? Is this the same thing as Affine Transformation?
Is there examples that functions that are transformations but not collineation? I've found about F(x,y)=(x^3,y) but is there another one? Every book that I study just tells about this example, I wanted to see more...

Thank you so much!!

2. ### Simon Bridge

14,429
Colinear points are points on the same line.
Colineation is a projection that preserves the colinearity of the points.
i.e. if you start out with a line, the projection should also be a line.

i.e. a line in 3D space may be perpendicularly projected onto a plane and the projection is also a line.
But a projection onto the surface of a sphere turns the line into a curve.