Accurate modeling of the human vascular tree from 3D computed tomography (CTA) or magnetic resonance (MRA) angiograms is required for visualization, diagnosis of vascular diseases, and computational fluid dynamic (CFD) blood flow simulations. This work describes an automated algorithm for constructing the polygonal mesh of blood vessels from such images. Each vascular segment is modeled as a tubular object, and a thin plate spline transform is used to generate the corresponding surface from its centerline-radius representation. A novel approach for generating the polygonal mesh of bifurcating vessels based on conformal mapping is presented. A mathematical description of the methodology is also provided. The model is improved by computing local intensity features with subvoxel accuracy, to slightly deform the mesh of the vascular tree for fine-tuning. The proposed algorithm was successfully tested on a 3D synthetic image containing randomly generated vascular branches. Experiment results, confirmed by real-world Time of Flight MRA, demonstrate that our methodology is consistent and capable of generating high quality triangulated meshes of vascular trees, suitable for further CFD simulations. Compared to common techniques, conformal mapping proved to be a simple and effective mathematical approach for polygonal mesh modeling of bifurcating vessels.