Developable \((1, n)\)-Bézier surfaces
type: Item
instance of: scholarly article
title: Developable \((1, n)\)-Bézier surfaces
zbMATH Open document ID: 0756.65015
DOI: 10.1016/0167-8396(92)90036-O
author: Johann Lang
author: Otto Röschel
published in: Computer Aided Geometric Design
publication date: 1993-01-17T00:00:00Z
review text: The authors show that a rational Béziers patch of degree \((1,n)\) and control points \(p^{ij}\) (\(i=0,1\); \(j=0,\ldots,n\)) is a developable surface iff \[ \sum^{n-1}_{i,j,k,l=0}{n-1\choose i}{n-1\choose j}{n- 1\choose k}{n-1\choose l}\text{det}(p^{0i},p^{0j+1},p^{1k},p^{1l+1})=0 \] for all \(i+j+k+l=s\), \(0\leq s\leq 4n-4\). They give explicit formulas for \((1,2)\) and \((1,3)\) surfaces and a number of graphic examples.
Mathematics Subject Classification ID: 65D17
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D07
zbMATH DE Number: 97033
zbMATH Keywords: spline
zbMATH Keywords: piecewise polynomial interpolations
zbMATH Keywords: curve
zbMATH Keywords: surface
zbMATH Keywords: solid
zbMATH Keywords: object representations
zbMATH Keywords: Bézier surfaces
zbMATH Keywords: developable surfaces
zbMATH Keywords: spline surfaces
zbMATH Keywords: graphic examples
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
cites work: Interpolation with developable Bézier patches
cites work: Q4026368
cites work: Q5680715
cites work: Q3918679
cites work: Q3702889
cites work: Q3993269
cites work: Q3241626
full work available at URL: 0167-8396(92)90036-o
OpenAlex ID: W1996701644
description: scientific article; zbMATH DE number 97033