A Study Of Reconstruction Of Sampling Points Based On Implicit Function

The surface reconstruction of sampling points is one of the pivotal problems on reverse engineering. Many scholars at home and abroad are focus on it and implemented it by different methods. To implement the reconstruction of sampling points adopt the form of the implicit function in this thesis. The main contents are as follows:Firstly, a detailed study about the current related technologies of sampling points'reconstruction has been done. Discussing the implicit function such as the signed distance function, radial basis function and T spline, describe the processing, applying range and the flaw.With the development of survey devices and technologies, the sampling points should be preprocessed. According to the tangent plane the normal constrains were adjusted. Furthermore, for using of measurement data efficiently, the geometric topology of the data should be considered. In order to improve the geometric modeling speed, spatial data structures such as Binary Space Partition tree (BSP tree), KD-tree (multi-dimensional two -tree) and the octree can store the data. The hierarchical octree structure can significantly speed up the searching speed, so octree space partition structure indicated the data.Secondly, the reconstruction of sampling points based on the Poisson equation. According to the Gauss's theorem, the Poisson equation implemented the reconstruction. Using the iteration, Poisson equation solved the process in the case of low memory usage. Poisson's equation is zero in the boundary of the value, so the spurious surface sheets were avoided and generated the smooth surface using the examples to verify the algorithm.Finally, discussing the fast Fourier transform implemented the reconstruction. Fast Fourier methods applied the FFTW library function, with Fourier transform to obtain Fourier coefficients, and then solved the characteristic function through the inverse Fourier transform. The method of large-scale non-uniform points cloud can be reconstructed orbicular surface.