Diminished reality is as important as augmented reality, and both are possible with a device called the Reality Mediator. Over the past two decades, we have designed, built, worn, and tested many different embodiments of this device in the context of wearable computing. Incorporated into the Reality Mediator is an "EyeTap" system, which is a device that quanti es and resynthesizes light that would otherwise pass through one or both lenses of the eye(s) of a wearer. The functional principles of EyeTap devices are discussed, in detail. The EyeTap diverts into a spatial measurement system at least a portion of light that would otherwise pass through the center of projection of at least one lens of an eye of a wearer. The Reality Mediator has at least one mode of operation in which it reconstructs these rays of light, under the control of a wearable computer system. The computer system then uses new results in algebraic projective geometry and comparametric equations to perform ...