Abstract: This paper presents a new method for the extraction of a rational Bezier surface from a set of data points. The algorithm is divided into four parts. First, a least median square fitting algorithm is used to extract a Bezier surface from the data set. Second, from this initial surface model an analysis of the data set is performed to eliminate outliers. Third, the algorithm then improves the fit over the residual points by modifying the weights of a rational Bezier surface using a non-linear optimization method. A further improvement of the fit is achieved using a new intrinsic parameterization technique. Fourth, an approximation of the region boundary is performed using a NURB with knots. Experimental results show that the current algorithm is robust and can precisely approximate complex surfaces. !19
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