Reconstruction of polygonal sets by constrained and unconstrained double probing

The problem of recovering the shape of planar objects arises in robotics. This work deals with this problem under the assumption that composite double probings are made. Two kinds of double probes are considered and their use for reconstructing convex planar polygons is investigated. For both kinds of probes, lower bounds on the number of probings required for reconstruction under any strategy are obtained and specific strategies which are proven to be almost optimal are provided.

[1]  Steven Skiena,et al.  Problems in geometric probing , 1989, Algorithmica.

[2]  R. L. Shuo-Yen.  Reconstruction of polygons from projections , 1988 .

[3]  Mariette Yvinec,et al.  On the order induced by a set of rays: application to the probing of nonconvex polygons , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[4]  Steven Skiena,et al.  Geometric probing , 1988 .

[5]  Steven Skiena,et al.  Probing Convex Polygons with X-Rays , 1988, SIAM J. Comput..

[6]  John Paul Greschak,et al.  Reconstructing convex sets , 1985 .

[7]  Herbert J. Bernstein.  Determining the Shape of a Convex n-Sided Polygon by Using 2n+k Tactile Probes , 1986, Inf. Process. Lett..

[8]  David P. Dobkin,et al.  Probing Convex Polytopes , 1990, Autonomous Robot Vehicles.

[9]  Richard Cole,et al.  Shape from Probing , 1987, J. Algorithms.