Elliptic curve representation According to this page, Edward's curve point doubling can be represented in a different way by assuming $c=1$ and $d = r^2$.

It then says we can represent $x y$ as $Y Z$ satisfying $r\cdot y = \frac Y Z$

I am a bit confused. How would I then calculate the $x$ coordinate? For example, they have provided the following explicit formula:

YY = Y12
ZZ = r*Z12
V = s*(ZZ-YY)2
W = (ZZ+YY)2
Y3 = W-V
Z3 = W+V


So after obtaining $Y_3$ and $Z_3$, how would I revert back to affine coordinates and calculate $x$ and $y$?
When $c=1$ and $d = r^2$, an Edwards curve $x^2+y^2=c^2(1+dx^2y^2)$ becomes $$x^2+y^2=1+r^2x^2y^2 \iff x^2(1-r^2 y^2) = 1 - y^2$$
With the $(Y,Z)$ notation, a point $P = (x,y)$ is represented as a pair $(Y:Z)$ satisfying  $ry = Y/Z$.  Note that this representation does not allow to distinguish $P = (x,y)$ from $-P = (-x,y)$.  

Given a pair $(Y:Z)$, one can recover $\pm P = (\pm x, y)$ where $y = Y/(rZ)$ and $\pm x$ is the square root of $(1-y^2)/(1-r^2y^2)$.