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There is well-documented evidence that vascular geometry has a major impact in blood flow dynamics and consequently in the development of vascular diseases, like atherosclerosis and cerebral aneurysmal disease. The study of vascular geometry and the identification of geometric features associated with a specific pathological condition can therefore shed light into the mechanisms involved in the pathogenesis and progression of the disease. Although the development of medical imaging technologies is providing increasing amounts of data on the three-dimensional morphology of the in vivo vasculature, robust and objective tools for quantitative analysis of vascular geometry are still lacking. In this paper, we present a framework for the geometric analysis of vascular structures, in particular for the quantification of the geometric relationships between the elements of a vascular network based on the definition of centerlines. The framework is founded upon solid computational geometry criteria, which confer robustness of the analysis with respect to the high variability of in vivo vascular geometry. The techniques presented are readily available as part of the VMTK, an open source framework for image segmentation, geometric characterization, mesh generation and computational hemodynamics specifically developed for the analysis of vascular structures. As part of the Aneurisk project, we present the application of the present framework to the characterization of the geometric relationships between cerebral aneurysms and their parent vasculature.