Adaptive reconstruction of T-Spline surfaces of arbitrary topological type

In this paper, we present an automatic procedure for reconstructing a smooth parametric surfaces using T-Splines from a triangulation mesh .A key ingredient in our solution is a scheme for automatically constructing both T-mesh and a parameterization of the data points over T-mesh. We use the discrete conformal parameterization presented in as the solution of choice for mapping the 3D surface to a 2D domain, then using quad-tree subdivision in 2D domain to 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 result is satisfactory. We use adaptive refinement of the T-mesh in order to satisfy user-specified error tolerances and demonstrate our method on real data.