Abstract: We propose a method to cut and map a closed triangular mesh onto a 2D planar domain automatically.The initial cut is optimized iteratively controlled by a cost function related to the distortion and validity of conformal mapping of the mesh.During parametrization, Rather than fixing the boundary of the parametric domain a priori as most current methods did, we allow the boundary to be generated naturally.Experimental results show that our algorithm reduces the geometric distortion effectively and ensures the validity of the conformal mapping.