skip to content
Effective computational geometry for curves and surfaces : with 1 table Preview this item
ClosePreview this item
Checking...

Effective computational geometry for curves and surfaces : with 1 table

Author: Jean-Daniel Boissonnat
Publisher: Berlin ; Heidelberg New York : Springer, 2007.
Series: Mathematics and visualization
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This book covers combinatorial data structures and algorithms, algebraic issues in geometric computing, approximation of curves and surfaces, and computational topology. Coverage includes references  Read more...

Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Jean-Daniel Boissonnat
ISBN: 9783540332589 3540332588
OCLC Number: 180913715
Notes: Literaturverz. S. 321 - 340.
Description: XII, 343 Seiten : Diagramme ; 24 cm.
Contents: 1 Arrangements Efi Fogel, Dan Halperin, Lutz Kettner, Monique Teillaud, Ron Wein, Nicola Wolpert 1.1 Introduction1.2 Chronicles1.3 Exact Construction of Planar Arrangements 1.3.1Construction by Sweeping 1.3.2 Incremental Construction1.4 Software for Planar Arrangements1.4.1 The Cgal Arrangements Package1.4.2 Arrangements Traits 1.4.3 Traits Classes from Exacus 1.4.4An Emerging Cgal Curved Kernel1.4.5 How To Speed UpYour Arrangement Computation in Cgal 1.5 Exact Construction in 3-Space 1.5.1 Sweeping Arrangements of Surfaces 1.5.2Arrangements of Quadricsin 3D1.6 Controlled Perturbation: Fixed-Precision Approximation of Arrangements1.7 Applications 1.7.1 Boolean Operations for Conics 1.7.2 Motion Planning for Discs 1.7.3 Lower Envelopes for Path Verification in Multi-Axis NC-Machining1.7.4 Maximal Axis-Symmetric Polygon Containedin a Simple Polygon 1.7.5 Molecular Surfaces1.7.6 Additional Applications 1.8 Further Reading and Open problems2 Curved Voronoi Diagrams Jean-Daniel Boissonnat, Camille Wormser, Mariette Yvinec2.1 Introduction2.2 Lower Envelopes and Minimization Diagrams 2.3 Affine Voronoi Diagrams 2.3.1 Euclidean Voronoi Diagrams of Points2.3.2 Delaunay Triangulation2.3.3 PowerDiagrams2.4 Voronoi Diagrams with Algebraic Bisectors 2.4.1 Moebius Diagrams2.4.2 Anisotropic Diagrams 2.4.3Apollonius Diagrams2.5 Linearization 2.5.1Abstract Diagrams2.5.2 Inverse Problem 2.6 Incremental Voronoi Algorithms2.6.1 Planar Euclidean diagrams2.6.2 Incremental Construction2.6.3 The Voronoi Hierarchy 2.7 Medial Axis 2.7.1 Medial Axis and Lower Envelope 2.7.2 Approximation of the Medial Axis 2.8 Voronoi Diagrams in Cgal 2.9 Applications 3 Algebraic Issues in Computational Geometry Bernard Mourrain, Sylvain Pion, Susanne Schmitt, Jean-Pierre Tecourt, Elias Tsigaridas, Nicola Wolpert 3.1 Introduction3.2 Computers and Numbers3.2.1 Machine Floating Point Numbers: the IEEE 754 norm........1193.2.2 Interval Arithmetic ......................................1203.2.3 Filters..................................................1213.3 Effective Real Numbers .......................................1233.3.1 Algebraic Numbers ......................................1243.3.2 Isolating Interval Representation of Real Algebraic Numbers 3.3.3 Symbolic Representation of Real Algebraic Numbers .........1253.4 Computing with Algebraic Numbers ............................1263.4.1 Resultant...............................................1263.4.2 Isolation................................................1313.4.3Algebraic Numbers of Small Degree ........................1363.4.4 Comparison.............................................1383.5 Multivariate Problems ........................................1403.6 Topology of Planar Implicit Curves.............................1423.6.1 The Algorithm from a Geometric Point of View .............1433.6.2 Algebraic Ingredients.....................................1443.6.3 How to Avoid Genericity Conditions .......................1453.7 Topology of 3d Implicit Curves.................................1463.7.1 Critical Points and Generic Position........................1473.7.2 The Projected Curves ....................................1483.7.3 Lifting a Point of the Projected Curve......................1493.7.4 Computing Points of the Curve above CriticalValues.........1513.7.5 Connecting the Branches .................................1523.7.6 The Algorithm ..........................................1533.8 Software ....................................................1544 Differential Geometry on Discrete Surfaces David Cohen-Steiner, Jean-Marie Morvan 4.1 Geometric Properties of Subsets of Points .......................1574.2 Length and Curvature of a Curve...............................1584.2.1 The Length of Curves ....................................1584.2.2 The Curvature of Curves .................................1594.3 The Area of a Surface.........................................1614.3.1 Definition of the Area ....................................1614.3.2 An Approximation Theorem ..............................1624.4 CurvaturesofSurfaces ........................................1644.4.1 The Smooth Case........................................1644.4.2 Pointwise Approximation of the Gaussian Curvature .........1654.4.3 From Pointwise to Local..................................1674.4.4 Anisotropic Curvature Measures...........................1744.4.5 o-samples on a Surface....................................1785 Meshing of Surfaces Jean-Daniel Boissonnat, David Cohen-Steiner, Bernard Mourrain, Gunter Rote, Gert Vegter 5.1 Introduction: What is Meshing?................................1815.1.1 Overview ...............................................1875.2 Marching Cubesand Cube-Based Algorithms ....................1885.2.1 Criteria for a Correct Mesh Inside a Cube ..................1905.2.2 Interval Arithmetic for Estimating the Range of a Function ...1905.2.3 Global Parameterizability: Snyder's Algorithm...............1915.2.4 Small Normal Variation ..................................1965.3 DelaunayRefinementAlgorithms...............................2015.3.1 Using the Local Feature Size ..............................2025.3.2 Using Critical Points.....................................2095.4 A Sweep Algorithm...........................................2135.4.1Meshing a Curve ........................................2155.4.2Meshing a Surface .......................................2165.5 Obtaining a Correct Mesh by Morse Theory .....................2235.5.1 Sweeping through Parameter Space ........................2235.5.2 Piecewise-Linear Interpolation of the Defining Function5.6 Research Problems............................................2276 Delaunay Triangulation Based Surface Reconstruction Frederic Cazals, Joachim Giesen 6.1 Introduction.................................................2316.1.1 Surface Reconstruction ...................................2316.1.2Applications ............................................2316.1.3 Reconstruction Using the Delaunay Triangulation............2326.1.4 A Classification of Delaunay Based Surface Reconstruction Methods6.1.5 Organization of the Chapter ..............................2346.2 Prerequisites.................................................2346.2.1Delaunay Triangulations, Voronoi Diagrams and Related Concepts6.2.2 Medial Axis and Derived Concepts.........................2446.2.3 Topological and Geometric Equivalences....................2496.2.4 Exercises ...............................................2526.3 Overview of the Algorithms....................................2536.3.1Tangent Plane Based Methods ............................2536.3.2Restricted Delaunay Based Methods .......................2576.3.3Inside/Outside Labeling.................................2616.3.4Empty Balls Methods ....................................2686.4 Evaluating Surface Reconstruction Algorithms 6.5 Software ....................................................2726.6 Research Problems ...........................................2737 Computational Topology: An Introduction Gunter Rote, Gert Vegter 7.1 Introduction.................................................2777.2 Simplicialcomplexes..........................................2787.3 Simplicial homology ..........................................2827.4 MorseTheory................................................2957.4.1 Smooth functions and manifolds ...........................2957.4.2 Basic Results from Morse Theory..........................3007.5 Exercises....................................................3107.6 Appendix:SomeBasicResultsfromLinearAlgebra...............3128 Appendix -Generic Programming and The Cgal Library Efi Fogel, Monique Teillaud .......................................3158.1 The Cgal OpenSourceProject ...............................3158.2 Generic Programming ........................................3168.3 Geometric Programming ......................................3188.4 Cgal ......................................................320References Index
Series Title: Mathematics and visualization
Responsibility: Jean-Daniel Boissonnat ; Monique Teillaud ed.
More information:

Reviews

Editorial reviews

Publisher Synopsis

From the reviews:"Boissonat and Teillaud have collected in this book the foundations of a computational geometry that no longer deals exclusively with linear objects but also with curved objects that Read more...

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/180913715> # Effective computational geometry for curves and surfaces : with 1 table
    a schema:Book, schema:CreativeWork ;
    library:oclcnum "180913715" ;
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/891708982#Place/heidelberg> ; # Heidelberg
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/gw> ;
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/891708982#Place/berlin> ; # Berlin
    library:placeOfPublication <http://dbpedia.org/resource/New_York_City> ; # New York
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/krommen_gtt> ; # Krommen.--gtt
    schema:about <http://id.worldcat.org/fast/940870> ; # Geometry--Data processing
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/curves_on_surfaces> ; # Curves on surfaces
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/krommen> ; # Krommen
    schema:about <http://id.loc.gov/authorities/subjects/sh2008105182> ; # Geometry--Data processing
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/computergraphics_gtt> ; # Computergraphics.--gtt
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/geometry_data_processing> ; # Geometry--Data processing
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/courbes_sur_les_surfaces> ; # Courbes sur les surfaces
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/computational_geometry> ; # Computational geometry
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/geometry_differential> ; # Geometry, Differential
    schema:about <http://id.worldcat.org/fast/940919> ; # Geometry, Differential
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/kurve> ; # Kurve
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/oppervlakken> ; # Oppervlakken
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/geometrie_differentielle> ; # Géométrie différentielle
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/geometrie_informatique> ; # Géométrie--Informatique
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/visualisatie_gtt> ; # Visualisatie.--gtt
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/algorithmische_geometrie> ; # Algorithmische Geometrie
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/computational_geometry_gtt> ; # Computational geometry.--gtt
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/computergraphics> ; # Computergraphics
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/oppervlakken_gtt> ; # Oppervlakken.--gtt
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/flache> ; # Fläche
    schema:about <http://id.worldcat.org/fast/885448> ; # Curves on surfaces
    schema:about <http://experiment.worldcat.org/entity/work/data/891708982#Topic/visualisatie> ; # Visualisatie
    schema:bookFormat bgn:PrintBook ;
    schema:datePublished "2007" ;
    schema:editor <http://viaf.org/viaf/110597108> ; # Jean-Daniel Boissonnat
    schema:exampleOfWork <http://worldcat.org/entity/work/id/891708982> ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/891708982#Series/mathematics_and_visualization> ; # Mathematics and visualization
    schema:name "Effective computational geometry for curves and surfaces : with 1 table" ;
    schema:productID "180913715" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/180913715#PublicationEvent/berlin_heidelbergnew_york_springer_2007> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/891708982#Agent/springer> ; # Springer
    schema:url <http://d-nb.info/979593913/04> ;
    schema:workExample <http://worldcat.org/isbn/9783540332589> ;
    umbel:isLike <http://d-nb.info/979593913> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/180913715> ;
    .


Related Entities

<http://dbpedia.org/resource/New_York_City> # New York
    a schema:Place ;
    schema:name "New York" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Series/mathematics_and_visualization> # Mathematics and visualization
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/180913715> ; # Effective computational geometry for curves and surfaces : with 1 table
    schema:name "Mathematics and visualization" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/algorithmische_geometrie> # Algorithmische Geometrie
    a schema:Intangible ;
    schema:name "Algorithmische Geometrie" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/computational_geometry> # Computational geometry
    a schema:Intangible ;
    schema:name "Computational geometry" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/computational_geometry_gtt> # Computational geometry.--gtt
    a schema:Intangible ;
    schema:name "Computational geometry.--gtt" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/computergraphics> # Computergraphics
    a schema:Intangible ;
    schema:name "Computergraphics" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/computergraphics_gtt> # Computergraphics.--gtt
    a schema:Intangible ;
    schema:name "Computergraphics.--gtt" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/courbes_sur_les_surfaces> # Courbes sur les surfaces
    a schema:Intangible ;
    schema:name "Courbes sur les surfaces" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/curves_on_surfaces> # Curves on surfaces
    a schema:Intangible ;
    schema:name "Curves on surfaces" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/geometrie_differentielle> # Géométrie différentielle
    a schema:Intangible ;
    schema:name "Géométrie différentielle" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/geometrie_informatique> # Géométrie--Informatique
    a schema:Intangible ;
    schema:name "Géométrie--Informatique" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/geometry_data_processing> # Geometry--Data processing
    a schema:Intangible ;
    schema:name "Geometry--Data processing" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/geometry_differential> # Geometry, Differential
    a schema:Intangible ;
    schema:name "Geometry, Differential" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/oppervlakken_gtt> # Oppervlakken.--gtt
    a schema:Intangible ;
    schema:name "Oppervlakken.--gtt" ;
    .

<http://experiment.worldcat.org/entity/work/data/891708982#Topic/visualisatie_gtt> # Visualisatie.--gtt
    a schema:Intangible ;
    schema:name "Visualisatie.--gtt" ;
    .

<http://id.loc.gov/authorities/subjects/sh2008105182> # Geometry--Data processing
    a schema:Intangible ;
    schema:name "Geometry--Data processing" ;
    .

<http://id.worldcat.org/fast/885448> # Curves on surfaces
    a schema:Intangible ;
    schema:name "Curves on surfaces" ;
    .

<http://id.worldcat.org/fast/940870> # Geometry--Data processing
    a schema:Intangible ;
    schema:name "Geometry--Data processing" ;
    .

<http://id.worldcat.org/fast/940919> # Geometry, Differential
    a schema:Intangible ;
    schema:name "Geometry, Differential" ;
    .

<http://viaf.org/viaf/110597108> # Jean-Daniel Boissonnat
    a schema:Person ;
    schema:familyName "Boissonnat" ;
    schema:givenName "Jean-Daniel" ;
    schema:name "Jean-Daniel Boissonnat" ;
    .

<http://worldcat.org/isbn/9783540332589>
    a schema:ProductModel ;
    schema:isbn "3540332588" ;
    schema:isbn "9783540332589" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.