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On Sampling for Surfaces Reconstruction

注意:本论文已在Ebad Banissi, Abd. Rahni Mt. Piah and Muhammad Sarfraz(eds), IEEE Computer Society, International Conference on Computer Graphics(CGIV’04), Imaging and Visualization[C], Penang, Malaysia, 2004:120-125上发表
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Yong-chun Zhang(张永春), Fei-peng Da, Wen-zhong Song
(Research Institute of Automation, Southeast University, Nanjing, China, 210096)

Abstract: In CAD and reverse engineering, triangulation, i.e. C0 interpolation, of scattered sampled points should has the property of shape-preserving for precisely reconstruction of original surface. This depends much more on sampling. It is well known that over-sampling or under-sampling either increases computing consumption in triangulation or cannot get the correct reconstruction. In this paper, the local structure of 3D curve is firstly analyzed in frequent domain with Fourier transformation. And then the sampling frequency based on Shannon theorem is discussed. Subsequently, generalizing it to the surface case, we present in particularly a sampling method for 3D surfaces. The results indicate that , with the method, dense enough triangulations can be obtained so as to avoid over- and under-sampling. Oseenlet;Lighthill' s two-stage scheme; asymptotic solution.

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