We are all familiar with Euclidean geometry and with the fact that it describes our three-dimensional world so well. In Euclidean geometry, the sides of objects have lengths, intersecting lines determine angles between them, and two lines are said to be parallel if they lie in the same plane and never meet. Since Euclidean geometry describes our world so well, it is at first tempting to think that it is the only type of geometry.
Euclidean geometry is actually a subset of what is known as projective geometry .
To see the relationships between these different geometries, consult Figure 1. Projective geometry models well the imaging process of a camera because it allows a much larger class of transformations than just translations and rotations, a class which includes perspective projections. The four different geometries, the transformations allowed in each, and the measures that remain invariant under those transformations. Projective geometry exists in any number of dimensions, just like Euclidean geometry. That section presents many concepts which are useful in understanding the image plane and which have analogous concepts in .