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Coronary artery diseases are usually revealed using angiographies. Such images are complex to analyze because they provide a 2D (two-dimensional) projection of a 3D (three-dimensional) object. Medical diagnosis suffers from inter- and intra-clinician variability. Therefore, reliable software for the 3D modeling of the coronary tree is strongly desired. In this paper, we propose a method for automatic generation of 3D vessels model using vessels image matching based on adaptive control points to help accurately locate a disease such as arteriosclerosis. The proposed method consists of two steps: matching of corresponding control points between standard and individual vessels model, and transformation of standard vessels model. In the first step, control points are adaptively interpolated in the corresponding standard vessels image in proportion to the distance ratio if there were control points between two corner points in an individual vessels model. And then, the control points of corresponding individual vessels model matches with those of standard vessels model. In the second step, the TPS (Thin Plate Spline) interpolation function is used to modify the standard into the individual vessels model. In the experiments, we used patient angiograms from the coronary angiography in Sanggye Paik Hospital.