Morten Daehlen – författare

This volume contains more than 50 refereed and edited full-length papers on the theory and applications of mathematical methods in computer aided geometric design and related areas.

This book is entirely about triangulations. With emphasis on computational issues, we present the basic theory necessary to construct and manipulate triangulations. In particular, we make a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. We also discuss various data structures used for the representation of triangulations. Throughout the book we relate the theory to selected applications, in part- ular surface construction, meshing and visualization. The ?eld of triangulation is part of the huge area of computational ge- etry, and over many years numerous books and articles have been written on the subject. Important results on triangulations have appeared in theore- cal books and articles, mostly within the realm of computational geometry. However, many important results on triangulations have also been presented in publications within other research areas, where they have played and play an important role in solving speci?c scienti?c and applied problems. We will touch upon some of these areas in this book. Triangulations, almost everywhere. The early development of triangulation comes from surveying and the art of constructing maps – cartography. S- veyors and cartographers used triangles as the basic geometric feature for calculating distances between points on the Earth’s surface and a position’s elevation above sea level.

This book is entirely about triangulations. With emphasis on computational issues, we present the basic theory necessary to construct and manipulate triangulations. In particular, we make a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. We also discuss various data structures used for the representation of triangulations. Throughout the book we relate the theory to selected applications, in part- ular surface construction, meshing and visualization. The ?eld of triangulation is part of the huge area of computational ge- etry, and over many years numerous books and articles have been written on the subject. Important results on triangulations have appeared in theore- cal books and articles, mostly within the realm of computational geometry. However, many important results on triangulations have also been presented in publications within other research areas, where they have played and play an important role in solving speci?c scienti?c and applied problems. We will touch upon some of these areas in this book. Triangulations, almost everywhere. The early development of triangulation comes from surveying and the art of constructing maps – cartography. S- veyors and cartographers used triangles as the basic geometric feature for calculating distances between points on the Earth’s surface and a position’s elevation above sea level.

This book is entirely about triangulations. With emphasis on computational issues, we present the basic theory necessary to construct and manipulate triangulations. In particular, we make a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. We also discuss various data structures used for the representation of triangulations. Throughout the book we relate the theory to selected applications, in part- ular surface construction, meshing and visualization. The ?eld of triangulation is part of the huge area of computational ge- etry, and over many years numerous books and articles have been written on the subject. Important results on triangulations have appeared in theore- cal books and articles, mostly within the realm of computational geometry. However, many important results on triangulations have also been presented in publications within other research areas, where they have played and play an important role in solving speci?c scienti?c and applied problems. We will touch upon some of these areas in this book. Triangulations, almost everywhere. The early development of triangulation comes from surveying and the art of constructing maps – cartography. S- veyors and cartographers used triangles as the basic geometric feature for calculating distances between points on the Earth’s surface and a position’s elevation above sea level.

TheSeventhInternationalConferenceonMathematicalMethodsforCurvesand SurfacestookplaceJune26-July 1,2008,inTonsberg,Norway. Theearlier conferences in the series took place in Oslo (1988),Biri (1991), Ulvik (1994), Lillehammer(1997),Oslo(2000),andTromso(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,andSaraMorkenforhelpwiththeregistration.November2009 Theeditors Organization Organizing Commitee and Editors MortenDaehlen UniversityofOslo,Norway MichaelFloater UniversityofOslo,Norway TomLyche UniversityofOslo,Norway Jean-LouisMerrien INSAdeRennes,France KnutMorken UniversityofOslo,Norway LarryL. Schumaker VanderbiltUniversity,USA Invited Speakers Jean-DanielBoissonnat,SophiaAntipolis,France MassimoFornasier,Linz,Austria TomHughes,Austin,USA JorgPeters,Gainesville,USA RagniPiene,Oslo,Norway RobertSchaback,Gottingen,Germany PeterSchroder,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 ...