Geometric modelling using rational Gaussian curves and surfaces
type: Item
instance of: scholarly article
title: Geometric modelling using rational Gaussian curves and surfaces
zbMATH Open document ID: 0836.65015
DOI: 10.1016/0010-4485(95)96800-2
author: Ardeshir Goshtasby
published in: CAD. Computer-Aided Design
publication date: 1995-11-20T00:00:00Z
review text: The author describes his rational Gaussian curves and surface approximations which are modelled on \(B\)-spline techniques. For curve approximations, he uses \({\mathbf P}(u) = \Sigma {\mathbf V}_i g_i (u)\) where the \({\mathbf V}_i\) are control points and \(g_i(u) = W_i G_i(u)/ [\Sigma W_j G_j (u)]\), \(G_i(u) = \text{exp} \{-(u - u_i)^2/2 \sigma_i ^2\}\), \(W_i \geq 0\), and for surfaces the corresponding bivariate formula. For approximation of closed curves, the formula has to be slightly changed. He gives some examples of graphics approximation and also of approximation of curves displaying empirical data, where the oscillations connected with rational approximations do not appear.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 818570
zbMATH Keywords: geometric modelling
zbMATH Keywords: rational Gaussian curves and surface approximations
zbMATH Keywords: \(B\)-spline
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
full work available at URL: 0010-4485(95)96800-2
OpenAlex ID: W2069840935
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description: scientific article; zbMATH DE number 818570