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This paper presents an algorithm for generating the medial axis transform (MAT) of 3D objects with free-form boundaries. The algorithm proposed uses the exact representation of the part and generates an approximate rational spline description (to within a defined tolerance) of the MAT. The algorithm generates the MAT by a tracing technique that marches along the object boundary. The level of approximation is controlled by the choice of the step size in the tracing procedure. Criteria based on distance and local curvature of boundary entities are used to identify the junction points and the search for these junction points is done in an efficient way. The algorithm works for multiply-connected objects as well. Results of implementation are provided.