Closed Surface Reconstruction Based On T-Spline Surfaces

In this paper, the reconstruction of smooth surfaces from such mesh models with T-spline as an approximate representation is studied. The main achievements are as follows:(1) Smooth surfaces using T-spline as a approximate representation are reconstructed from triangular mesh surfaces. After mapping the 3D triangular mesh to a 2D domain with LSCM, we use a quadtree to subdivide the 2D domain into four quadrants recursively. Then the corresponding T-mesh is constructed. By using least square approximation we can get the control points of the T-spline surface and finish our algorithm . With the local refinement of T-spline, we can make the approximation error within the prescribed error tolerance.(2) The properties of implicit T-spline blending functions are studied. By means of the properties of the 3D T-mesh and the corresponding control grid of implicit B-spline surface, we prove that all those implicit T-spline blending functions are always linearly independent.(3) An algorithm for reconstructing smooth surfaces from complicated triangular mesh surfaces was present by using implicit T-spline representation in this paper. The shapes of the surfaces are controlled by adding off-surface points. In our solution, we first construct 3D T-mesh from sampling points. Then an objective function is introduced based on implicit T-spline. After using the GCV method to choose the optimal fairness parameter, we can get the implicit T-spline surface by using least square approximation. After performing local knot insertion, we can make the approximation error within the prescribed error tolerance.(4) The programs for all of the algorithms in this paper is written in C++ language on the Visual Studio platform and mesh surfaces such as animals are reconstructed .