Circular arc snakes and kinematic surface generation

Handle URI:
http://hdl.handle.net/10754/562747
Title:
Circular arc snakes and kinematic surface generation
Authors:
Barton, Michael ( 0000-0002-1843-251X ) ; Shi, Ling; Kilian, Martin; Wallner, Johannes; Pottmann, Helmut ( 0000-0002-3195-9316 )
Abstract:
We discuss the theory, discretization, and numerics of curves which are evolving such that part of their shape, or at least their curvature as a function of arc length, remains unchanged. The discretization of a curve as a smooth sequence of circular arcs is well suited for such purposes, and allows us to reduce evolution of curves to the evolution of a control point collection in a certain finite-dimensional shape space. We approach this evolution by a 2-step process: linearized evolution via optimized velocity fields, followed by optimization in order to exactly fulfill all geometric side conditions. We give applications to freeform architecture, including "rationalization" of a surface by congruent arcs, form finding and, most interestingly, non-static architecture. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd.
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:
Wiley
Journal:
Computer Graphics Forum
Issue Date:
May-2013
DOI:
10.1111/cgf.12020
Type:
Article
ISSN:
01677055
Sponsors:
This research has in part been supported by the Austrian Science Fund (FWF, grant P23735). We also want to thank Florin Isvoranu for help with architectural realization.
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.authorBarton, Michaelen
dc.contributor.authorShi, Lingen
dc.contributor.authorKilian, Martinen
dc.contributor.authorWallner, Johannesen
dc.contributor.authorPottmann, Helmuten
dc.date.accessioned2015-08-03T11:04:12Zen
dc.date.available2015-08-03T11:04:12Zen
dc.date.issued2013-05en
dc.identifier.issn01677055en
dc.identifier.doi10.1111/cgf.12020en
dc.identifier.urihttp://hdl.handle.net/10754/562747en
dc.description.abstractWe discuss the theory, discretization, and numerics of curves which are evolving such that part of their shape, or at least their curvature as a function of arc length, remains unchanged. The discretization of a curve as a smooth sequence of circular arcs is well suited for such purposes, and allows us to reduce evolution of curves to the evolution of a control point collection in a certain finite-dimensional shape space. We approach this evolution by a 2-step process: linearized evolution via optimized velocity fields, followed by optimization in order to exactly fulfill all geometric side conditions. We give applications to freeform architecture, including "rationalization" of a surface by congruent arcs, form finding and, most interestingly, non-static architecture. © 2013 The Author(s) Computer Graphics Forum © 2013 The Eurographics Association and Blackwell Publishing Ltd.en
dc.description.sponsorshipThis research has in part been supported by the Austrian Science Fund (FWF, grant P23735). We also want to thank Florin Isvoranu for help with architectural realization.en
dc.publisherWileyen
dc.titleCircular arc snakes and kinematic surface generationen
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 Graphics Forumen
dc.contributor.institutionEvolute GmbH, Vienna, Austriaen
dc.contributor.institutionVienna University of Technology, Austriaen
dc.contributor.institutionGraz University of Technology, Austriaen
kaust.authorBarton, Michaelen
kaust.authorShi, Lingen
kaust.authorPottmann, Helmuten
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