So I was thinking about WAAS and how, being a type of precision navigation, it provides vertical guidance. My question is what is the actual method for determining altitude and thus relative position to the glide path?

Does the GPS receiver in the aircraft actually compute altitude (Based on GPS and WAAS signals) and then compare it to an altitude the aircraft should be on (based on the approach and lateral position)? Or is the altitude information derived from the actual altimeter on the aircraft and then a glide slope readout is provided based on altitude and lateral position?