A new procedure for reconstructing a smooth parametric surfaces using T-Splines from a triangulation mesh was present in this paper.In our solution

a key ingredient is that the scheme for automatically extract a quad-dominant control mesh(T-mesh)and a parameterization of the data points over the T-mesh.We use the discrete conformal parameterization as the solution of choice for mapping the 3D triangular mesh to a 2D domain

and we partition this two dimensional space by recursively subdividing it into four quadrants

then automatically constructing the T-mesh that we need for the reconstructing.By using least square approximation we can get the control point of the surface and finish our algorithm until the approximation error below a specified threshold.We use adaptive refinement of the T-mesh in order to satisfy user-specified error tolerances and demonstrate our method on real data.