CTA angiography brings potentially useful information for guidance in an interventional procedure. It comes with the challenge of registering this 3D modality to the projection of the coronary arteries which are deforming with the cardiac motion. A tree-spline i.e. a tree with a spline attached to each edge and shared control points between these points describes a 3D coronary tree and is able to represent its deformation along the time. We combine this description with a registration algorithm operating between the tree-spline and the angiographic projection of the coronary tree. It starts by the estimation of a rigid transformation for the iso cardiac phase time followed by a non-rigid deformation of the tree driven by the pairings formed between the projection of the edges of the tree-spline and the observed x-ray projection of the coronary arteries. The pairings are built taking into account the tree topology consistency. Anatomical constraints of length preservation is enforced when deforming the arteries. The proposed approach has been evaluated with clinical data issued from ten different clinical cases which enabling to form twenty three different experimental conditions. Encouraging results have been obtained.