According to the EdDSA specification from the IETF:
For point addition, the following method is recommended. A point (x,y) is represented in extended homogeneous coordinates (X, Y, Z, T), with x = X/Z, y = Y/Z, x * y = T/Z
I'm unfamilar with extended homogeneous coordinates, and I'm used to seeing points as simply (x, y). Can anyone explain where the T and Z variables come from in the specification document?
I found this answer on Stack Overflow that has some great detail: