A system and method for determining positions in three-dimensional space are described. The system includes a controller, a phase image module, a presentation module and a phase determination module. The controller receives projector geometry parameters. A phase image module determines a plurality of sinusoidal images where a constant phase represents a flat plane in a three-dimensional space based on the projector geometry parameters. A presentation module projects the plurality of sinusoidal images to be captured by a camera. The phase determination module determines a phase value at a camera pixel. The phase determination module determines an intersection between the flat plane of the phase value and the camera pixel to identify a ray-plane intersection.