Mathematical Methods for Curves and Surfaces: 9th International Conference, MMCS 2016, Tønsberg, Norway, June 23–28, 2016, Revised Selected Papers

333 Pages·2017·8.829 MB·English

by  Michael Floater, Tom Lyche, Marie-Laurence Mazure, Knut Mørken, Larry L. Schumaker

Michael Floater · Tom Lyche
Marie-Laurence Mazure · Knut Mørken
Larry L. Schumaker (Eds.)
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Mathematical Methods
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C for Curves and Surfaces
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9th International Conference, MMCS 2016
Tønsberg, Norway, June 23–28, 2016
Revised Selected Papers
123
Lecture Notes in Computer Science 10521
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Michael Floater Tom Lyche
(cid:129)
ø
Marie-Laurence Mazure Knut M rken
(cid:129)
Larry L. Schumaker (Eds.)
Mathematical Methods
for Curves and Surfaces
9th International Conference, MMCS 2016
ø –
T nsberg, Norway, June 23 28, 2016
Revised Selected Papers
123
Editors
Michael Floater KnutMørken
University of Oslo University of Oslo
Oslo Oslo
Norway Norway
TomLyche Larry L.Schumaker
University of Oslo Vanderbilt University
Oslo Nashville, TN
Norway USA
Marie-Laurence Mazure
UniversitéJosephFourier
Grenoble
France
ISSN 0302-9743 ISSN 1611-3349 (electronic)
Lecture Notesin Computer Science
ISBN 978-3-319-67884-9 ISBN978-3-319-67885-6 (eBook)
https://doi.org/10.1007/978-3-319-67885-6
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Preface
The 9th International Conference on Mathematical Methods for Curves and Surfaces
took place during June 23–28, 2016, in Tønsberg, Norway. The earlier conferences in
the series took place in Oslo (1988), Biri (1991), Ulvik (1994), Lillehammer (1997),
Oslo(2000),Tromsø(2004),Tønsberg(2008),andOslo(2012).Thisconferenceseries
is integrated with the French conferences Curves and Surfaces organized by
SMAI-SIGMA (Signal-Image-Géométrie-Modélisation-Approximation), and the last
conference in France was in Paris in 2014.
Theconferencegathered140participantsfrom27countrieswhopresentedatotalof
115 talks. This includes nine invited talks and seven mini-symposia. This book con-
tains 17 original articles based on talks presented at the conference. The topics range
from mathematical theory to industrial applications. The papers have been subject to
theusualpeer-reviewprocess,andwethankboththeauthorsandthereviewersfortheir
hard work and helpful collaboration. We wish to thank all those who supported and
helped organize theconference. It is a pleasure to acknowledge thegenerous financial
support from the Research Council of Norway and the Department of Mathematics at
the University of Oslo. We also thank Elisabeth Seland, Espen Sande, and Espen
Lybekkfortheirhelpwithadministrativeandtechnicalmatters,andAnneBergFloater
for help with the registration.
June 2017 Michael Floater
Tom Lyche
Marie-Laurence Mazure
Knut Mørken
Larry L. Schumaker
Organization
Organizing Committee
Morten Dæhlen University of Oslo, Norway
Michael Floater University of Oslo, Norway
Tom Lyche University of Oslo, Norway
Marie-Laurence Mazure UJF Grenoble, France
Knut Mørken University of Oslo, Norway
Larry L. Schumaker Vanderbilt University, Nashville, TN, USA
Invited Speakers
Gershon Elber Technion, Israel
Greg Fasshauer Colorado School of Mines, USA
Leif Kobbelt RWTH Aachen University, Germany
Helmut Pottman Technical University Vienna, Austria
Ulrich Reif Technical University of Darmstadt, Germany
Giancarlo Sangalli University of Pavia, Italy
Scott Schaefer Texas A&M University, USA
Hal Schenk University of Illinois, USA
Wenping Wang University of Hong Kong, SAR China
Mini-Symposia Organizers
Heidi Dahl SINTEF, Norway
Carlotta Giannelli University of Florence, Italy
Ying He Nanyang Technological University, Singapore
Gitta Kutyniok Technical University of Berlin, Germany
Jean-Louis Merrien University of Rennes 1, France
Tomas Sauer University of Passau, Germany
Grady Wright Boise State University, USA
Contents
Computational Assessment of Curvatures and Principal Directions
of Implicit Surfaces from 3D Scalar Data. . . . . . . . . . . . . . . . . . . . . . . . . . 1
Eric Albin, Ronnie Knikker, Shihe Xin, Christian Oliver Paschereit,
and Yves D’Angelo
Coefficient–Based Spline Data Reduction by Hierarchical Spaces . . . . . . . . . 23
Cesare Bracco, Carlotta Giannelli, and Alessandra Sestini
A Versatile Strategy for the Implementation of Adaptive Splines. . . . . . . . . . 42
Andrea Bressan and Dominik Mokriš
Machinability of Surfaces via Motion Analysis. . . . . . . . . . . . . . . . . . . . . . 74
Robert J. Cripps, Ben Cross, Glen Mullineux, and Mat Hunt
Simplicial Complex Entropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
Stefan Dantchev and Ioannis Ivrissimtzis
Precise Construction of Micro-structures and Porous Geometry
via Functional Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Gershon Elber
Partially Nested Hierarchical Refinement of Bivariate Tensor-Product
Splines with Highest Order Smoothness. . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Nora Engleitner, Bert Jüttler, and Urška Zore
Regression Analysis Using a Blending Type Spline Construction . . . . . . . . . 145
Tatiana Kravetc, Børre Bang, and Rune Dalmo
On the Coupling of Decimation Operator with Subdivision Schemes
for Multi-scale Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
Zhiqing Kui, Jean Baccou, and Jacques Liandrat
Translation Surfaces and Isotropic Transport Nets on Rational
Minimal Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Jan Vršek and Miroslav Lávička
Towards Subdivision Surfaces C2 Everywhere . . . . . . . . . . . . . . . . . . . . . . 202
Malcolm Sabin
VIII Contents
Adaptivity with B-spline Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
Malcolm Sabin
Reconstructing Sparse Exponential Polynomials from Samples:
Difference Operators, Stirling Numbers and Hermite Interpolation. . . . . . . . . 233
Tomas Sauer
Reparameterization and Adaptive Quadrature for the Isogeometric
Discontinuous Galerkin Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Agnes Seiler and Bert Jüttler
Deconfliction and Surface Generation from Bathymetry Data
Using LR B-splines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
Vibeke Skytt, Quillon Harpham, Tor Dokken, and Heidi E.I. Dahl
Application of Longest Common Subsequence Algorithms
to Meshing of Planar Domains with Quadrilaterals . . . . . . . . . . . . . . . . . . . 296
Petra Surynková and Pavel Surynek
Order-Randomized Laplacian Mesh Smoothing. . . . . . . . . . . . . . . . . . . . . . 312
Ying Yang, Holly Rushmeier, and Ioannis Ivrissimtzis
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Computational Assessment of Curvatures
and Principal Directions of Implicit Surfaces
from 3D Scalar Data
B
Eric Albin1( ), Ronnie Knikker1, Shihe Xin1, Christian Oliver Paschereit2,
and Yves D’Angelo3
1 Univ. Lyon, CNRS, INSA-Lyon, Universit´e Claude Bernard Lyon 1,
CETHIL UMR5008, F-69621 Villeurbanne, France
[email protected]
2 Institute of Fluid Dynamics and Technical Acoustics, Hermann-F¨ottinger-Institut.,
Technische Universit¨at Berlin, Mu¨ller-Breslau-Str. 8, 10623 Berlin, Germany
3 Laboratoire de Math´ematiques J.A. Dieudonn´e, CNRS UMR 7351,
Universit´e de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice, France
Abstract. An implicit method based on high-order differentiation to
determine the mean, Gaussian and principal curvatures of implicit sur-
facesfromathree-dimensionalscalarfieldispresentedandassessed.The
method also determines normal vectors and principal directions. Com-
pared to explicit methods, the implicit approach shows robustness and
improved accuracy to measure curvatures of implicit surfaces. This is
evaluatedonsimplecaseswherecurvatureisknowninclosed-form.The
methodisappliedtocomputethecurvaturesofwrinkledflamesonlarge
triangularunstructuredmeshes(namelya3Disosurfaceoftemperature).
· · ·
Keywords: Implicitsurface Curvature Principaldirections Isosur-
· ·
face 3D scalar field Combustion analysis
Introduction
Curvatures play an important role in many areas of physics where interfaces
are encountered [13,20]. For instance, local curvatures can modify combustion
speed [1,8,9,38], surface tension [4] and evaporation speed [7]. Accurate meth-
ods for determining curvatures can then be of paramount importance for flow
analysis.IntherecentstudyofYuandBai[38],localmeanandGaussiancurva-
turesarecomputedtoanalysedeflagrationfrontsduringanauto-ignition.Strong
saddle front and small sphere front are shown to play an important role during
theauto-ignitionprocess.However,numericaltechniquesusedtoestimatecurva-
tures are not detailed and plots with curvatures show a large scattering of data.
The present work proposes implicit methods to improve such analyses. These
methods measure curvatures and principal directions of isosurfaces extracted
from 3D data. Many methods use an explicit representation of surfaces, where
(cid:2)c SpringerInternationalPublishingAG2017
M.Floateretal.(Eds.):MMCS2016,LNCS10521,pp.1–22,2017.
https://doi.org/10.1007/978-3-319-67885-6_1