My Sketchup of a brushless DC motor.

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Hmm. Nobody commented this, so I guess I'll have to.
What is the thing between the pot and Q1? A current mirror??
Also, maybe I'm not following you properly, but I guess you don't need a LED for the motor to work, but it's nice to watch of course. But wth do you need an IR LED for? What am I missing out?
Disregard that, I see now, it's a feedback loop for the rotation, and the thing between the pot and Q1 is an LDR. Well done, it'll probably work, at least in theory.

Brushless Motor Commutation
Controlling brushless motors is more complicated than controlling brush motors. Brush motors rely on mechanical commutation, while brushless motors require electronic commutation. The drive determines how to channel current into the windings based on motor position, speed, and other factors. There are two main commutation methods used in industry today:
sine-wave
six-step

Brushless Motors and Sine-wave Commutation
Brushless motors are commutated electronically. The drive must measure the motor position and determine how to channel the current so the requested torque is produced with the minimal current. Most brushless motors have three windings. Sine-wave commutation channels some current in all three windings simultaneously to produce the smoothest and most efficient torque possible. Sine wave drives also allow angle-advance and other advanced commutation algorithms to extend the speed range and increase torque output of brushless motors.

Brushless Motors and Six-step Commutation
Six-step commutation is an alternative to sine-wave commutation. Six-step drives channel current into only two windings at any one time. This simplifies the design and construction of the drive. However, the torque produced by six-step drives has more ripple and is produced less efficiently, compared to sine-wave drives.