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The recovery of the 3D path of the transducer used during an intravascular ultrasound (IVUS) examination is of primary importance to assess the exact 3D shape of the vessel under study. Traditionally, the reconstruction is done using biplane angiography. In this paper we explain, with three projection models, how single-plane angiography can be used to perform this task. Three types of projection geometry are analyzed: orthographic, weak perspective and full perspective. In orthographic and weak perspective projection geometries, the catheter path can be reconstructed without prior transducer depth informations. With full perspective projection geometry, precise depth location of reference points are needed in order to minimize the error of the recovered transducer's angle of incidence. We present the mathematical foundation and some simulations of the catheter path reconstruction. While reconstructing the 3D catheter path from a single-view projection is shown to be feasible, some heuristics are needed in order to obtain a path simulating the curvature of the heart pericardium vessels.