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Smooth Bézier Surfaces over Unstructured Quadrilateral Meshes

  • Book
  • © 2017

Overview

Authors:
  1. Michel Bercovier

    1. Rachel and Benin School of Computer Science and Engineering, Hebrew University of Jerusalem, Jerusalem, Israel

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  2. Tanya Matskewich

    1. Microsoft Corporation, Redmond, USA

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    You can also search for this author in PubMed   Google Scholar

  • 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

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xx
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  2. Introduction

    • Michel Bercovier, Tanya Matskewich
    Pages 1-24

  3. G1-Smooth Surfaces

    • Michel Bercovier, Tanya Matskewich
    Pages 25-42

  4. MDS: Quadrilateral Meshes and Polygonal Boundary

    • Michel Bercovier, Tanya Matskewich
    Pages 43-72

  5. Global MDS

    • Michel Bercovier, Tanya Matskewich
    Pages 73-91

  6. MDS for a Smooth Boundary

    • Michel Bercovier, Tanya Matskewich
    Pages 93-136

  7. Computational Examples

    • Michel Bercovier, Tanya Matskewich
    Pages 137-143

  8. Conclusions and Further Research

    • Michel Bercovier, Tanya Matskewich
    Pages 145-147

  9. Back Matter

    Pages 149-192
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Keywords

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)

Authors and Affiliations

  • Rachel and Benin School of Computer Science and Engineering, Hebrew University of Jerusalem, Jerusalem, Israel

    Michel Bercovier

  • Microsoft Corporation, Redmond, USA

    Tanya Matskewich

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