The geometry of projective blending surfaces
type: Item
instance of: scholarly article
title: The geometry of projective blending surfaces
zbMATH Open document ID: 0672.51015
DOI: 10.1016/0004-3702(88)90060-4
author: Christoph M. Hoffmann
author: John Hopcroft
published in: Artificial Intelligence
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://hdl.handle.net/1813/6598
review text: The main point of the article is the completeness theorem: Let G and H be irreducible quadrics. Let \(G'\) and \(H'\) be two quadrics such that \(G\cap H'=g\) and \(H\cap G'=h\) are irreducible, and assume that \(G\cap H\) is irreducible and coincides neither with g nor with h. Then every degree-4 surface F tangent to G in the curve g and tangent to H in the curve h has the equation \(K^ 2-\mu GH=0,\) where \(\mu\) is a constant and K is a quadric containing both g and h. The authors summarize foregoing investigations (affine version), explore new aspects (projective version), and discuss other methods and the prospects for deriving blending surfaces automatically.
Mathematics Subject Classification ID: 51N35
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 68U99
zbMATH DE Number: 4100057
zbMATH Keywords: classical algebraic geometry
zbMATH Keywords: blending surfaces
MaRDI profile type: Publication
OpenAlex ID: W2034903995
cites work: Q5830135
cites work: Q5571530
cites work: Automatic surface generation in computer aided design
cites work: Piecewise quadric blending of implicitly defined surfaces
Recommended article: The projective geometry of ambiguous surfaces
Recommended article: On blending of several quadratic algebraic surfaces
Recommended article: Blending algebraic surfaces
Recommended article: Mixing Surfaces, Algebra, and Geometry
Recommended article: Computer Algebra and Geometric Algebra with Applications
Recommended article: Q4856409
Recommended article: Q4035843
Recommended article: Q5489462
Recommended article: Q3592469
Recommended article: Q3592445
description: scientific article; zbMATH DE number 4100057