This paper is concerned with the calibration of the intrinsic and extrinsic parameters of a X-ray angiographic system for 3D reconstruction of coronary vessel centerlines. We discuss whether the isocentric model is an accurate model for the movement of the C-arm, and analyse the assumptions made by this model. We propose a methodology which takes into account these facts and we propose for each model a calibration method. The calibration only needs a phantom that is commonly available by the physicians, since it is used to calibrate geometrical distortion. Then, we test the models with the calibration grid, as well as with a phantom imaged three months later. Experimental results show that by using the proposed models, it is not necessary neither a calibration nor a refinement at each acquisition.