Sketching is an intuitive way to explain spatial relationships between complex objects. The French community of Anatomists are used to teaching didactic lectures on a blackboard with their colored chalks. The increasing complexity of the sketches affords to the students an opportunity to work out a mental representation of anatomical structures in 3D. To help students perform this labored step, we present a new interactive blackboard which constructs plausible 3D models of branching vessels from a single sketch. We exploit the sketching conventions used in anatomical drawings to infer depth and curvature. We then model the set of branching vessels as a convolution surface generated by a graph of skeleton curves. Classic situations, focused on arteries, have been analyzed to manage vessels' curvatures, subdivisions and overlaps. Original sketches and 3D models are presented for each case. No specific training is required to use the interface. The anatomists have begun to embrace a new generation of 3D digital modeling applications as tools for anatomical teaching. We discuss the future use of this system as a step towards the interactive teaching of anatomy.