Cyclides in computer aided geometric design
type: Item
instance of: scholarly article
title: Cyclides in computer aided geometric design
zbMATH Open document ID: 0712.65008
DOI: 10.1016/0167-8396(90)90033-N
published in: Computer Aided Geometric Design
publication date: 1990-01-01T00:00:00Z
review text: After noting the unsatisfactory state of solid modeling using planes, circular cylinders, cones and spheres, the author points out that most blending problems can be solved using cyclides, i.e., envelopes of one- parameter families of spheres tangent to three fixed spheres. (A good description of Dupin cyclides is in \textit{D. Hilbert} and \textit{S. Cohn- Vossen} [Geometry and the imagination (1952; Zbl 0047.388), pp. 217-219]. Since all curvature lines of cyclides are circles, patches are easily defined; the formulas are given by \textit{A. W. Nutbourne} and \textit{R. R. Martin} [Differential geometry applied to curve and surface design (1988; Zbl 0635.53002)]. The author gives some impressive examples of the ease with which Dupin cyclides solve blending problems.
Mathematics Subject Classification ID: 65D17
zbMATH DE Number: 4172235
zbMATH Keywords: rational Bézier surfaces
zbMATH Keywords: offsetting
zbMATH Keywords: filleting
zbMATH Keywords: solid modeling
zbMATH Keywords: Dupin cyclides
author: Michael J. Pratt
reviewed by: Heinrich Guggenheimer
MaRDI profile type: Publication
cites work: On cyclides in geometric modeling
cites work: The approximation of non-degenerate offset surfaces
cites work: Q4178157
cites work: Spatial Planning: A Configuration Space Approach
cites work: Offsetting operations in solid modelling
cites work: Q3204082
full work available at URL: 0167-8396(90)90033-n
OpenAlex ID: W1965982184
description: scientific article; zbMATH DE number 4172235