Smooth Bézier Surfaces over Unstructured Quadrilateral Meshes

  • Michel Bercovier
  • Tanya Matskewich

Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 22)

Table of contents

  1. Front Matter
    Pages i-xx
  2. Michel Bercovier, Tanya Matskewich
    Pages 1-24
  3. Michel Bercovier, Tanya Matskewich
    Pages 25-42
  4. Michel Bercovier, Tanya Matskewich
    Pages 43-72
  5. Michel Bercovier, Tanya Matskewich
    Pages 73-91
  6. Michel Bercovier, Tanya Matskewich
    Pages 93-136
  7. Michel Bercovier, Tanya Matskewich
    Pages 137-143
  8. Michel Bercovier, Tanya Matskewich
    Pages 145-147
  9. Back Matter
    Pages 149-192

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.


Isogeometric analysis C1 surfaces Bézier patches B-Splines unstructured meshes finite element analysis

Authors and affiliations

  • Michel Bercovier
    • 1
  • Tanya Matskewich
    • 2
  1. 1.Rachel and Benin School of Computer Science and EngineeringHebrew University of JerusalemJerusalemIsrael
  2. 2.Microsoft CorporationRedmondUSA

Bibliographic information

Industry Sectors
Finance, Business & Banking
Energy, Utilities & Environment
Oil, Gas & Geosciences