Lecture Notes of the Unione Matematica Italiana

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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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.

 

Buy this book

eBook $39.99
price for USA (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 $49.99
price for USA
  • ISBN 978-3-319-63840-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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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 and Tables
5 b/w illustrations, 59 illustrations in colour
Topics