A method for 3D reconstruction of the positions of a catheter as it is moved within a human body, comprising: (a) ascertaining the 3D position of a point on a catheter for insertion into the body (b) acquiring fixed-angle, single-plane fluoroscopic image data of the body and catheter (c) transferring the image data and catheter-point position to a computer (d) determining 2D image coordinates of the point on the catheter (e) changing the insertion length of catheter by a measured amount (f) acquiring additional single-plane fluoroscopic image data of the body and catheter from the same angle, transferring the length change and image data to the computer, and determining image coordinates of the point on the catheter (g) computing the 3D position of the catheter point and (h) repeating steps e-g. A 3D model is constructed by assembling the plural 3D positions of the catheter point.