Mathematical Methods for Curves and Surfaces : 7th International Conference, MMCS 2008 Tønsberg, Norway, June 26-July 1, 2008 Revised Selected Papers

TheSeventhInternationalConferenceonMathematicalMethodsforCurvesand SurfacestookplaceJune26-July 1,2008, inTønsberg, Norway. Theearlier conferences in the series took place in Oslo (1988), Biri (1991), Ulvik (1994), Lillehammer(1997), Oslo(2000), andTromsø(2004). Theconferencegathered 165participants fromalmost30countries who presenteda total of129talks. Thisincludesnineinvitedtalksandsevenmini-symposia. Thisbookcontains28originalarticlesbasedontalkspresentedattheconf- ence. Thetopicsrangefrommathematicalanalysisofvariousmethodstoprac- calimplementationonmoderngraphicsprocessingunits. Thepapersre?ectthe newestdevelopmentsinthese?eldsandalsopointtothelatestliterature. The papershavebeensubjecttotheusualpeerreviewprocess, andwethankboth theauthorsandthereviewersfortheirhardworkandhelpfulcollaboration. Wewishtothankthosewhohavesupportedandhelpedorganizetheconf- ence. Firstandforemostitisapleasuretoacknowledgethegenerous?nancial support from the Department of Informatics and the Centre of Mathematics forApplications(CMA)attheUniversityofOslo, andtheResearchCouncilof Norway. WewouldalsoliketothankAndrewMcMurryforhishelpwithwith technicalmatters, andSaraMørkenforhelpwiththeregistration. November2009 Theeditors Organization Organizing Commitee and Editors MortenDæhlen UniversityofOslo, Norway MichaelFloater UniversityofOslo, Norway TomLyche UniversityofOslo, Norway Jean-LouisMerrien INSAdeRennes, France KnutMørken UniversityofOslo, Norway LarryL. Schumaker VanderbiltUniversity, USA Invited Speakers Jean-DanielBoissonnat, SophiaAntipolis, France MassimoFornasier, Linz, Austria TomHughes, Austin, USA JörgPeters, Gainesville, USA RagniPiene, Oslo, Norway RobertSchaback, Göttingen, Germany PeterSchröder, Caltech, USA JonathanShewchuk, Berkeley, USA JoachimWeickert, Saarland, Germany Mini-Symposia Organizers OlegDavydov, Glasgow, UK TorDokken, Oslo, Norway BinHan, Edmonton, Canada ChuckHansen, SaltLakeCity, USA RimvydasKrasauskas, Vilnius, Lithuania TrondKvamsdal, Trondheim, Norway CarlaManni, Rome, Italy Sponsoring Institutions DepartmentofInformatics, UniversityofOslo CentreofMathematicsforApplications, UniversityofOslo ResearchCouncilofNorway Table of Contents MMCS 2008 Partial Di?erential Equations for Interpolation and Compression of Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Egil Bae and Joachim Weickert Construction of Rational Curves with Rational Rotation-Minimizing Frames via Mob ] ius Transformations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Michael Barton, ? Bert Juttl ] er, and Wenping Wang Fat Arcs for Implicitly De?ned Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Szilvia B´ ela and Bert Juttl ] er Geometric Properties of the Adaptive Delaunay Tessellation. . . . . . . . . . . 41 Tom Bobach, Alexandru Constantiniu, Paul Steinmann, and Georg Umlauf Quadrangular Parameterization for Reverse Engineering . . . . . . . . . . . . . . 55 David Bommes, Tobias Vossemer, and Leif Kobbelt A Comparison of Three Commodity-Level Parallel Architectures: Multi-core CPU, Cell BE and GPU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Andr´ e Rigland Brodtkorb and Trond Runar Hagen Mean Distance from a Curve to Its Control Polygon. . . . . . . . . . . . . . . . . . 81 Jesu ´s Carnicer and Jorge Delgado Compactly Supported Splines with Tension Properties on a Three-Direction Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008, held in Tønsberg, Norway, in June/July 2008.

The 28 revised full papers presented were carefully reviewed and selected from 129 talks presented at the conference. The topics addressed by the papers range from mathematical analysis of various methods to practical implementation on modern graphics processing units.