1. An apparatus for determining a shape of a medical tool in a region of interest in a patient's body, comprising: a medical positioning system configured to produce location readings with respect to points within said region of interest in accordance with an output of a location sensor connected to said tool moving within said region of interest, each location reading being associated with a three-dimensional reference coordinate system; and a control unit including a main processor and an associated memory wherein said control unit is coupled to said medical positioning system, said control unit being configured to execute pre-programmed instructions stored in said associated memory to determine a reconstruction representing the shape of said tool as a function of (1) a positional constraint that includes a first location corresponding to a first location reading produced by the medical positioning system, said first location reading indicating a constricting point along a tool path where said patient's body anatomically constrains movement of said tool in at least one degree of freedom, and (2) a shape constraint corresponding to a relaxation shape of said tool, wherein said control unit is configured through a user interface to receive an input from a user to record said first location reading produced by said medical positioning system, and wherein said signal to record said first location reading is received at a time when the medical tool is constrained by said patient's body.