1. A method for 3D reconstruction of the positions of a catheter as it is moved within a region of a human body, comprising: (a) determining the initial 3D position of a point on a catheter at the start of insertion from outside the body for movement through a vein into the body region; (b) acquiring fixed angle, single-plane fluoroscopic 2D image data of the body region and of the catheter; (c) transferring the image data and catheter-point position to a computer; (d) determining the 2D image coordinates of the point on the catheter using the image data and the catheter-point position of step c; (e) changing the length of catheter insertion by a measured amount; (f) thereafter acquiring additional single-plane fluoroscopic image data of the body region and the catheter from the same angle, transferring the measured length change and the additional image data to the computer, and determining the 2D image coordinates of the point on the catheter; (g) computing the 3D position of the catheter point using only the 2D image coordinates, the measured length change, and smooth-curve assumptions about the catheter; (h) repeating steps e-g plural times; and (i) assembling the plural 3D positions of the point within the body region into a 3D model of the region, whereby the assembled 3D positions of the point on the catheter are determined from the start of insertion and thereafter.