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Lecture Notes of the Unione Matematica Italiana
cover

Smooth Bézier Surfaces over Unstructured Quadrilateral Meshes

Authors: Bercovier, Michel, Matskewich, Tanya

  • With a foreword by T.J.R. Hughes 
  • Represents a step forward in Isogeometric Analysis and its applications
  • Provides a bridge between Finite Element Methods and Isogeometric Analysis
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eBook 44,02 €
price for Spain (gross)
  • ISBN 978-3-319-63841-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
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  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-319-63840-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

Using an elegant mixture of geometry, graph theory and linear analysis, this monograph completely solves a problem lying at the interface of Isogeometric Analysis (IgA) and Finite Element Methods (FEM). The recent explosion of IgA, strongly tying Computer Aided Geometry Design to Analysis, does not easily apply to the rich variety of complex shapes that engineers have to design and analyse. Therefore new developments have studied the extension of IgA to unstructured unions of meshes, similar to those one can find in FEM. The following problem arises: given an unstructured planar quadrilateral mesh, construct a C1-surface, by piecewise Bézier or B-Spline patches defined over this mesh. This problem is solved for C1-surfaces defined over plane bilinear Bézier patches, the corresponding results for B-Splines then being simple consequences. The method can be extended to higher-order quadrilaterals and even to three dimensions, and the most recent developments in this direction are also mentioned here.

 

Reviews

“This well-written monograph provides a way to solve interpolation and partial differential problems for arbitrary structures of quadrilateral meshes. The solution has a linear form, which makes it relatively simple, fast, and stable. The whole theory is illustrated by numerous examples and instructive figures. This book is an important contribution to computer-aided design over unstructured meshes.” (Manfred Tasche, Mathematical Reviews, June, 2018)

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Introduction

    Pages 1-24

    Bercovier, Michel (et al.)

  • G 1-Smooth Surfaces

    Pages 25-42

    Bercovier, Michel (et al.)

  • MDS: Quadrilateral Meshes and Polygonal Boundary

    Pages 43-72

    Bercovier, Michel (et al.)

  • Global MDS

    Pages 73-91

    Bercovier, Michel (et al.)

  • MDS for a Smooth Boundary

    Pages 93-136

    Bercovier, Michel (et al.)

Buy this book

eBook 44,02 €
price for Spain (gross)
  • ISBN 978-3-319-63841-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-319-63840-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Smooth Bézier Surfaces over Unstructured Quadrilateral Meshes
Authors
Series Title
Lecture Notes of the Unione Matematica Italiana
Series Volume
22
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-63841-6
DOI
10.1007/978-3-319-63841-6
Softcover ISBN
978-3-319-63840-9
Series ISSN
1862-9113
Edition Number
1
Number of Pages
XX, 192
Number of Illustrations
5 b/w illustrations, 59 illustrations in colour
Topics