Vasculature geometry reconstruction from volumetric medical data is a crucial task in the development of computer guided minimally invasive vascular surgery systems. In this paper, a technique for reconstructing the geometry of vasculatures using bivariate implicit splines is developed. With the proposed technique, an implicit geometry representation of the vascular tree can be accurately constructed based on the voxels extracted directly from the surface of a certain vascular structure in a given volumetric medical dataset. Experimental results show that the geometric representation built using our method can faithfully represent the morphology and topology of vascular structures. In addition, both the qualitative and the quantitative validations have been performed to show that the reconstructed vessel geometry is of high accuracy and smoothness. An virtual angioscopy system has been implemented to indicate one of the strengths of our proposed method.