Adaptive Surface Reconstruction Based on Tensor Product Algebraic Splines

Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling.In this paper,we extend the mathematical model proposed by Jüttler and Felis(Adv.Comput.Math.,17(2002), pp.135-152)based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes.We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach.By measuring the fitting errors over each cell of the mesh,we recursively insert new knots in cells over which the errors are larger than some given threshold,and construct a new algebraic spline surface to better fit the given data locally.The algorithm terminates when the error over each cell is less than the threshold.We provide some examples to demonstrate our algorithm and compare it with Jüttler's method.Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.

Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis （Adv. Comput. Math., 17 （2002）, pp. 135-152） based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler＇s method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.