On sampling for surfaces reconstruction

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.