Closed Surface Reconstruction Based on Implicit T-Splines

To simplify the normal deviation constraint and optimize the smooth energy parameter of objective function, an implicit T-splines surface reconstruction algorithm is proposed.First, three dimensional T-meshes are constructed from the sample point set by using the octrees and subdivision process.And the corresponding blending function of each control coefficient is determined from the topology of three dimensional T-meshes.Then the objective function is established based on the implicit T-spline surfaces.The normal direction of the surface is controlled by adding off-surface points.The generalized cross validation (GCV) method is adopted to estimate the optimal smoothing parameter.By using least square approximation the surface reconstruction problem is transformed into solving a system of quations to get control coefficients.With the local refinement of T-splines, the approximation error can achieve the prescribed error tolerance, thus a triangular mesh model is automaticlly converted into a smooth T-spline surface.When compared with the existing algorithm, the algorithm can solve the surface reconstruction problem well, for the C¹ continuous condition is relaxed and the optimal smoothing parameter is chosen.Some examples show that it has the high accuracy approximation, fast operation speed, realistic simulation results as well.