How Does Pokémon GO Make Pokémon Appear Right In Front Of Me?

I have walked miles trying to catch Pokémon on my iPhone screen. As a seasoned Pokémon GO trainer, I think I have an idea as to how the game gets the Pokémon to appear right in front of me.

Pokémon GO uses augmented reality (AR) technology in which computer generated graphics of Pokémon are superimposed or placed in the user’s view of the real world, such as on a street corner. The game uses the phone’s GPS to track the user’s location, the phone’s compass to determine the angle, and the phone’s camera to superimpose the Pokémon image near the user. 

The earth is three dimensional. The phone’s GPS provides the user’s location coordinates, which is an intersection of latitude and longitude (e.g. 40.5187 N, 74.4121 W). The game software applies a series of virtual circles, aka the Poke-Radar, around the user’s coordinates. The phone’s camera is then used to superimpose the Pokémon image near him (e.g. 40.5154 N, 74.4134 W).  The software then creates a virtual right triangle between the two coordinates. 

The phone’s compass allows the software to determine the angle of the target in relation to the user’s location, which helps to avoid placing Pokémon in awkward places. That is why Pokémon are not placed in the sky, when the phone is pointed at a tree.