Mathematical Methods for Curves and Surfaces: 8th International Conference, MMCS 2012, Oslo, Norway, June 28 – July 3, 2012, Revised Selected Papers

519 Pages·2014·44.835 MB·English

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

Michael Floater Tom Lyche
Marie-Laurence Mazure Knut Mørken
Larry L. Schumaker (Eds.)
7
7 Mathematical Methods
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8

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8th International Conference, MMCS 2012
Oslo, Norway, June 28 – July 3, 2012
Revised Selected Papers
123
Lecture Notes in Computer Science 8177
CommencedPublicationin1973
FoundingandFormerSeriesEditors:
GerhardGoos,JurisHartmanis,andJanvanLeeuwen
EditorialBoard
DavidHutchison
LancasterUniversity,UK
TakeoKanade
CarnegieMellonUniversity,Pittsburgh,PA,USA
JosefKittler
UniversityofSurrey,Guildford,UK
JonM.Kleinberg
CornellUniversity,Ithaca,NY,USA
AlfredKobsa
UniversityofCalifornia,Irvine,CA,USA
FriedemannMattern
ETHZurich,Switzerland
JohnC.Mitchell
StanfordUniversity,CA,USA
MoniNaor
WeizmannInstituteofScience,Rehovot,Israel
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UniversityofBern,Switzerland
C.PanduRangan
IndianInstituteofTechnology,Madras,India
BernhardSteffen
TUDortmundUniversity,Germany
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MicrosoftResearch,Cambridge,MA,USA
DemetriTerzopoulos
UniversityofCalifornia,LosAngeles,CA,USA
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UniversityofCalifornia,Berkeley,CA,USA
GerhardWeikum
MaxPlanckInstituteforInformatics,Saarbruecken,Germany
Michael Floater Tom Lyche
Marie-Laurence Mazure Knut Mørken
Larry L. Schumaker (Eds.)
Mathematical Methods
for Curves and Surfaces
8th International Conference, MMCS 2012
Oslo, Norway, June 28 – July 3, 2012
Revised Selected Papers
1 3
VolumeEditors
MichaelFloater
UniversityofOslo,Norway
E-mail:michaelf@ifi.uio.no
TomLyche
UniversityofOslo,Norway
E-mail:tom@ifi.uio.no
Marie-LaurenceMazure
UniversitéJosephFourier,Grenoble,France
E-mail:[email protected]
KnutMørken
UniversityofOslo,Norway
E-mail:knutm@ifi.uio.no
LarryL.Schumaker
VanderbiltUniversity,Nashville,TN,USA
E-mail:[email protected]
ISSN0302-9743 e-ISSN1611-3349
ISBN978-3-642-54381-4 e-ISBN978-3-642-54382-1
DOI10.1007/978-3-642-54382-1
SpringerHeidelbergNewYorkDordrechtLondon
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Preface
The8thInternationalConferenceonMathematicalMethodsforCurvesandSur-
facestookplaceJune28–July3,2012,inOslo,Norway.Theearlierconferences
in the series took place in Oslo (1988), Biri (1991), Ulvik (1994), Lillehammer
(1997), Oslo(2000), Tromsø (2004),and Tønsberg (2008). The conference gath-
ered 170 participantsfrom 31 countries who presenteda total of 135 talks. This
includesnineinvitedtalksandsixmini-symposia.Thisbookcontains28original
articlesbasedontalkspresentedattheconference.Thetopicsrangefrommath-
ematical analysis of various methods to practical implementation on modern
graphics processing units. The papers reflect the newest developments in these
fields and also point to the latest literature. The papers have been subject to
the usual peer-reviewprocess,andwethank both the authorsandthe reviewers
for their hardworkandhelpful collaboration.We wishto thank those who have
supportedandhelpedorganizetheconference.Firstandforemostitisapleasure
toacknowledgethegenerousfinancialsupportfromtheDepartmentofInformat-
ics and the Centre of Mathematics for Applications (CMA) at the University of
Oslo, and the Research Council of Norway. We would also like to thank Georg
Muntingh for his help with with technical matters, Katja Elisabeth Andersson
for help with the registration,and our students Helene Norheim Semmerud and
James Trotter for help with various practical matters.
October 2013 Michael Floater
Tom Lyche
Marie-Laurence Mazure
Knut Mørken
Larry Schumaker
Organization
Organizing Committee
Morten Dælen 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, USA
Invited Speakers
Albert Cohen, France Vin de Silva, USA
Oleg Davydov, UK Gabriele Steidl, Germany
Yaron Lipman, Israel Michael Unser, Switzerland
Charles Loop, USA Johannes Wallner, Austria
Carla Manni, Italy
Mini-Symposia Organizers
Rick Beatson, New Zealand Jens Gravesen, Denmark
Peter Binev, USA Tomas Sauer, Germany
Constanza Conti, Italy Tatyana Sorokina, USA
Sponsoring Institutions
Department of Informatics, University of Oslo
Centre of Mathematics for Applications, University of Oslo
Research Council of Norway
Table of Contents
Vibrational Error Extraction Method Based on Wavelet Technique ..... 1
Loay Alkafafi, Carsten Hamm, and Tomas Sauer
A Mathematical Model for Extremely Low Dose Adaptive Computed
Tomography Acquisition .......................................... 13
Oren Barkan, Amir Averbuch, Shai Dekel, and Yaniv Tenzer
Approximation of Implicit Blends by Canal Surfaces of Low
ParameterizationDegree.......................................... 34
Michal Bizzarri and Miroslav L´aviˇcka
Exploiting the Implicit Support Function for a Topologically Accurate
Approximation of Algebraic Curves ................................ 49
Eva Blaˇzkov´a and Zbynˇek Sˇ´ır
Non-regular Surface Approximation ................................ 68
Mira Bozzini, Licia Lenarduzzi, and Milvia Rossini
Piecewise Rational Parametrizationsof Canal Surfaces................ 88
Heidi E.I. Dahl
Macro-elementHierarchical Riesz Bases............................. 112
Oleg Davydov and Wee Ping Yeo
Generalized Metric Energies for Continuous Shape Deformation........ 135
Janick Martinez Esturo, Christian R¨ossl, and Holger Theisel
Least Squares Fitting of Harmonic Functions Based on Radon
Projections...................................................... 158
Irina Georgieva, Clemens Hofreither, and Rumen Uluchev
Generating Functions for Uniform B-Splines......................... 172
Ron Goldman
Planar Parametrizationin Isogeometric Analysis ..................... 189
Jens Gravesen, Anton Evgrafov, Dang-Manh Nguyen, and
Peter Nørtoft
Realistic Plant Modeling from Images Based
on Analysis-by-Synthesis.......................................... 213
J´erˆome Gu´enard, G´eraldine Morin, Fr´ed´eric Boudon, and
Vincent Charvillat
VIII Table of Contents
Hermite Interpolation with Rational Splines with Free Weights ........ 230
Carsten Hamm, Tomas Sauer, and Florian Zimmermann
Direct Pixel-Accurate Rendering of Smooth Surfaces ................. 238
Jon Hjelmervik
Non-uniform Interpolatory Subdivision Based on Local Interpolants
of Minimal Degree ............................................... 248
Kestutis Karˇciauskas and J¨org Peters
λ
Representation of Motion Spaces Using Spline Functions and Fourier
Series .......................................................... 265
Thomas Kronfeld, Jens Fankh¨anel, and Guido Brunnett
Bilinear Clifford-B´ezier Patches on Isotropic Cyclides ................. 283
Rimvydas Krasauskas, Severinas Zube˙, and Salvatore Cacciola
Algorithms and Data Structures for Truncated Hierarchical
B-Splines ....................................................... 304
G´abor Kiss, Carlotta Giannelli, and Bert Ju¨ttler
The LIR Space Partitioning System Applied to Cartesian Grids........ 324
Sven Linden, Hans Hagen, and Andreas Wiegmann
Local Hierarchical h-Refinements in IgA Based on Generalized
B-Splines ....................................................... 341
Carla Manni, Francesca Pelosi, and Hendrik Speleers
Exploring Matrix Generation Strategies in Isogeometric Analysis....... 364
Angelos Mantzaflaris and Bert Ju¨ttler
Commutator Estimate for Nonlinear Subdivision..................... 383
Peter Oswald and Tatiana Shingel
Joining Primal/Dual Subdivision Surfaces........................... 403
Sergey Podkorytov, Christian Gentil, Dmitry Sokolov, and
Sandrine Lanquetin
Reparametrization and Volume Mesh Generation for Computational
Fluid Dynamics Using Modified Catmull-Clark Methods .............. 425
Michael Rom and Karl-Heinz Brakhage
A Theoretical Analysis of an Improved Rational Scheme for Spherical
Camera Motions ................................................. 442
Maria Lucia Sampoli, Alessandra Sestini, Gaˇsper Jakliˇc, and
Emil Zˇagar
Construction and Analysis of Zone-Dependent Interpolatory/
Non-interpolatory Stochastic Subdivision Schemes for Non-regular
Data ........................................................... 456
Xiaoyun Si, Jean Baccou, and Jacques Liandrat
Table of Contents IX
Deriving Novel Formulas and Identities for the Bernstein Basis
Functions and Their Generating Functions .......................... 471
Yilmaz Simsek
Efficient Pixel-Accurate Rendering of Animated Curved Surfaces....... 491
Young In Yeo, Sagar Bhandare, and J¨org Peters
Author Index.................................................. 511
Vibrational Error Extraction Method
Based on Wavelet Technique
Loay Alkafafi1, Carsten Hamm1, and Tomas Sauer2
1 Siemens AG, Erlangen 91056, Germany
{loay.alkafafi,carsten.hamm}@siemens.com
2 University of Passau, Passau 94032, Germany
[email protected]
Abstract. Akeyfactorindevelopingandassessinganyvibrationatten-
uationtechniqueforelasticsystemsisthemeasurethatquantifiestheoc-
curringvibrations.Inthispaper,weproposeageneralandinstantaneous
vibration measurewhich allows for more subtlemethods of localized vi-
bration attenuationtechniques.Thismeasureisbasedonextractingthe
vibrationalpartfromtheconventionaltrackingerrorsignalusingwavelet
technique.The paperalso provides amethod for constructing a wavelet
functionbasedonthesystemimpulseresponse.Thiswaveletoutperforms
theexistingonesinrepresentingthesystembehaviorwhileguaranteeing
admissibility and providing sufficient smoothness and rate of decay in
both time and frequency domains.
Keywords: elasticsystem,vibrationattenuation,vibrationalerror,im-
pulse response, wavelet transform, admissibility.
1 Introduction
Suppressing the vibrations in numerically controlled mechanical systems is a
challenge in many industrial applications. Vibrations typically occur when an
elastic system is driven by positioning commands that contain frequencies close
tothesystem’scriticalfrequency.Therealreadyexistsavarietyoftechniquesto
treat such a problem, the most popular of which is the input shaping technique
[10]. In general, all existing techniques share the same idea of filtering out the
system’s critical frequency from the driving commands.
A primaryrequirementfor any suchvibrationsuppressiontechnique is to de-
riveameasurethatquantifiesthe occurringvibrations.Inliterature,discussions
are often limited to performance measures for the techniques in use rather than
forthe existingvibrations.Averygoodsurveyonthe availablekeyperformance
measuresisfoundin[3].Oneofthelimitationsoftheexistingperformancemea-
sures is that they “represent” the system vibrations merely after the command
completion and only for a specific type of input commands. On the other hand,
an instantaneous measure of vibration allows for more subtle methods for local
correctionsofthe input command.Providingsucha measurewill indeedbe use-
ful in many practical applications, e.g., the attenuation of vibrations in CNC
M.Floateretal.(Eds.):MMCS2012,LNCS8177,pp.1–12,2014.
(cid:2)c Springer-VerlagBerlinHeidelberg2014