Surface Reconstruction of 3D Scattered Data with Radial Basis Functions (Communications in Mathematical Research, 2021)
We use Radial Basis Functions (RBFs) to reconstruct smooth surfacesfrom 3D scattered data. An object's surface is defined implicitly as the zero set ofan RBF fitted to the given surface data. We propose improvements on the methodsof surface reconstruction with radial basis functions. A sparse approximation set ofscattered data is constructed by reducing the number of interpolating points on thesurface. We present an adaptive method for finding the off-surface normal points. Theorder of the equation decreases greatly as the number of the off-surface constraintsreduces gradually. Experimental results are provided to illustrate that the proposedmethod is robust and may draw beautiful graphics.
Keywords: radial basis function; scattered data; implicit surface; surface reconstruction.