Abstract: A fiber optic shape determination system having at least one optical fiber for placement within or along an elongated structure. The optical fiber defines an optical path for conveying an optical signal. The optical path manifests an interaction with the optical signal wherein the interaction occurs in a continuous fashion during the propagation of the optical signal along the optical path and produces a measurable response, the response conveying information about strain imparted to the optical fiber and a location along the optical fiber at which the strain occurs. The shape determination system also has a measurement component coupled to the optical fiber to sense the response and for determining the strain applied at different locations along the fiber and for deriving a shape of optic fiber, accordingly.