Curvature computations for degenerate surface patches
type: Item
instance of: scholarly article
title: Curvature computations for degenerate surface patches
zbMATH Open document ID: 0757.65014
DOI: 10.1016/0167-8396(92)90033-L
author: Séamus T. Tuohy
author: Franz-Erich Wolter
published in: Computer Aided Geometric Design
publication date: 1993-01-17T00:00:00Z
review text: In modeling surfaces with rational \(B\)-spline patches one encounters frequently situations where the parametric representation is singular at a boundary point. The authors develop formulas for the computation of principal curvatures at such a point if the surface admits a representation \((x,y,g(x,y))\) near the point in question and \(g\) has a regular 2-jet. \{Many problems in computer graphics arise from the use of modern texts on differential geometry that are not adapted to computational problems. There is no problem in computer graphics that cannot be treated by methods presented, e.g., by \textit{G. Salmon} and \textit{W. Fiedler} [Analytische Geometrie des Raumes (2nd ed., Leipzig 1874)]\}.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 97030
zbMATH Keywords: curvature computations
zbMATH Keywords: degenerate surface patches
zbMATH Keywords: generalized surface curvatures
zbMATH Keywords: quadratic surface
zbMATH Keywords: geometric modeling
zbMATH Keywords: rational \(B\)-spline patches
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
cites work: Q3940102
cites work: A practical guide to splines
cites work: Q4091004
cites work: Q4041056
cites work: Q4178157
cites work: Q3936665
full work available at URL: 0167-8396(92)90033-l
OpenAlex ID: W1968305082
description: scientific article; zbMATH DE number 97030