Methods and apparatus for projecting a tangible image of data characterizing an object onto a surface of the object itself. Three-dimensional measurements of the object are obtained, the measurements are processed for projection, and a tangible image is projected onto the object, the image conveying information based on the three-dimensional measurements. The image may be projected concurrently with performance of measurements. In an exemplary dental context, information derived in part from three-dimensional measurements of a tooth or replica may be projected onto the actual tooth or replica. In interactive application, a work piece is be measured during the course of fabrication, and three-dimensional information, derived from contemporaneous non-contact measurement, is projected onto the work piece in order to direct the user with the formation of the work piece.