This page looks at a one dimensional case of stereographic projection for a more general discussion of stereographic projection see page here.
|Here we look at a one dimensional euclidean space embedded in a two dimensional projective space, we are using the stereographic model to do this projection.
In one dimensional projective space using stereographic model:
- A straight lines is mapped to a circle in projective space.
- The point at infinity is given by θ=180 degrees.
Derivation for translation between projective (stereographic) and euclidean spaces
|The line is (1):
||y' = 1
|The circle is (2):
||x² = (1-(2y-1)²)/4
= (1-4y² +4y -1)/4
= -y² +y