Interactive Reconstruction via Geometric Probing

Geometric probing considers problems of determining a geometric structure or some aspect of that structure from the results of a mathematical or physical measuring device, a probe. A variety of problems from robotics, medical instrumentation, mathematical optimization, integral and computational geometry, graph theory and other areas fit into this paradigm. This paper surveys the field of geometric probing, with results ordered by probing model. The emphasis is on interactive reconstruction, where the results of all previous measurements are used to determine the orientation of the next probe so it provides the maximum amount of information about the structure. Through interactive reconstruction, finite determination strategies exist for such diverse models as finger, x-ray, and half-plane probes.