Darboux cyclides and webs from circles

Handle URI:
http://hdl.handle.net/10754/562040
Title:
Darboux cyclides and webs from circles
Authors:
Pottmann, Helmut ( 0000-0002-3195-9316 ) ; Shi, Ling; Skopenkov, Mikhail
Abstract:
Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order ≤4 are a superset of Dupin cyclides and quadrics, and they carry up to six real families of circles. Revisiting the classical approach to these surfaces based on the spherical model of 3D Möbius geometry, we provide computational tools for the identification of circle families on a given cyclide and for the direct design of those. In particular, we show that certain triples of circle families may be arranged as so-called hexagonal webs, and we provide a complete classification of all possible hexagonal webs of circles on Darboux cyclides. © 2011 Elsevier B.V. All rights reserved.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC); Computer Science Program
Publisher:
Elsevier BV
Journal:
Computer Aided Geometric Design
Issue Date:
Jan-2012
DOI:
10.1016/j.cagd.2011.10.002
ARXIV:
arXiv:1106.1354
Type:
Article
ISSN:
01678396
Additional Links:
http://arxiv.org/abs/arXiv:1106.1354v1
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorPottmann, Helmuten
dc.contributor.authorShi, Lingen
dc.contributor.authorSkopenkov, Mikhailen
dc.date.accessioned2015-08-03T09:43:23Zen
dc.date.available2015-08-03T09:43:23Zen
dc.date.issued2012-01en
dc.identifier.issn01678396en
dc.identifier.doi10.1016/j.cagd.2011.10.002en
dc.identifier.urihttp://hdl.handle.net/10754/562040en
dc.description.abstractMotivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order ≤4 are a superset of Dupin cyclides and quadrics, and they carry up to six real families of circles. Revisiting the classical approach to these surfaces based on the spherical model of 3D Möbius geometry, we provide computational tools for the identification of circle families on a given cyclide and for the direct design of those. In particular, we show that certain triples of circle families may be arranged as so-called hexagonal webs, and we provide a complete classification of all possible hexagonal webs of circles on Darboux cyclides. © 2011 Elsevier B.V. All rights reserved.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1106.1354v1en
dc.subjectArchitectural geometryen
dc.subjectDarboux cyclideen
dc.subjectGeometry of websen
dc.subjectMöbius geometryen
dc.subjectWeb from circlesen
dc.titleDarboux cyclides and webs from circlesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.contributor.departmentComputer Science Programen
dc.identifier.journalComputer Aided Geometric Designen
dc.contributor.institutionInstitute for Information Transmission Problems, Moscow, Russian Federationen
dc.identifier.arxividarXiv:1106.1354en
kaust.authorPottmann, Helmuten
kaust.authorShi, Lingen
kaust.authorSkopenkov, Mikhailen
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