Expressing Coons-Gordon surfaces as NURBS
type: Item
instance of: scholarly article
title: Expressing Coons-Gordon surfaces as NURBS
zbMATH Open document ID: 0792.65005
DOI: 10.1016/0010-4485(94)90035-3
author: V. Pereyra
published in: CAD. Computer-Aided Design
publication date: 1994-04-26T00:00:00Z
review text: The authors combine the techniques of the well-known Boolean-sum approach to Gordon/Coons surfaces with that of the \(B\)-spline representation of curves and surfaces; what comes out is a quite nice method for the \(B\)- spline-representation (linear and to some extend rational) of Gordon/Coons surfaces. To be more precise, here are the three main steps of the method: 1) Apply a \(B\)-spline interpolation scheme to the given boundary curves in order to construct three \(B\)-spline surfaces whose Boolean sum form represents the corresponding Gordon/Coons surface. 2) Make these three surfaces compatible (by using degree elevation and knot insertion methods) so that they have the same degree, control net and knot vector. 3) Turn the Boolean sum of these three surfaces into a (unique) \(B\)- spline surface which is the exact representation of its corresponding Gordon/Coons surface by simply forming the Boolean sum of their control nets. A total of 18 figures illustrates the authors' considerations.
reviewed by: Guido Walz
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 530098
zbMATH Keywords: NURBS
zbMATH Keywords: surface representation
zbMATH Keywords: \(B\)-spline
zbMATH Keywords: \(B\)-spline surface
zbMATH Keywords: Boolean sum
zbMATH Keywords: Gordon/Coons surfaces
zbMATH Keywords: curves
zbMATH Keywords: control nets
MaRDI profile type: Publication
full work available at URL: 0010-4485(94)90035-3
OpenAlex ID: W2089127931
description: scientific article; zbMATH DE number 530098