Problem Definition :: 
Our discussion of the shape from probing problem is limited to a special class of compact planar bodies. The planarity requirement limits our investigation to the 2dimentional case. The compactness requirement is in agreement with our intuition and essentially means that the body is bounded and closed. In other words the body is a bounded 2dimentional surface without holes. Additional assumptions are made to simplify the problem:
From now on our discussion will refer to the body under investigation as a polygon. Discovering the nature of the bounding polygon is equivalent to discovering the shape of the body. The following three shapes are valid. The interior of the shapes is gray and their boundary (polygon) is black.






The following figures show three shapes that are not handled in our definition of the problem. The first shape is a nonconvex polygon and thus not covered by our discussion. The second shape is a line and cannot be accepted because the number of vertices is less than 3. The third shape is a circle and as such cannot be represented faithfully as a polygon. Note however than a polygon approximating a circle would be acceptable.



nonconvex polygon (invalid!) 
line (invalid!) 
perfect circle (invalid!) 

Problem Definition 
Probe 
