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Computer-Aided Geometric Design

A Totally Four-Dimensional Approach

  • Book
  • © 2002

Overview

Authors:
  1. Fujio Yamaguchi

    1. Department of Mechanical Engineering School of Science and Engineering, Waseda University, Tokyo, Japan

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  • Offers a new system of geometric processing techniques that attain accurate, robust, and compact computations, and allow the construction of a systematically structured CAD system

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Table of contents (28 chapters)

  1. Presentation of a Solution —Four-dimensional Processing—

    1. Data Structures

      • Fujio Yamaguchi
      Pages 381-415

    2. Euclidean and Affine

      • Fujio Yamaguchi
      Pages 417-434

    3. Set Operations

      • Fujio Yamaguchi
      Pages 435-466

    4. Polyhedron Subdivisions

      • Fujio Yamaguchi
      Pages 467-487

    5. Reconstruction of 3-D Points

      • Fujio Yamaguchi
      Pages 489-494

    6. Display Process

      • Fujio Yamaguchi
      Pages 495-517

    7. Classical or Two-Sided?

      • Fujio Yamaguchi
      Pages 519-523

  2. Test Results

    1. Front Matter

      Pages 525-525
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    2. Various Tests

      • Fujio Yamaguchi
      Pages 527-557

  3. Conclusions

    1. Front Matter

      Pages 559-559
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    2. Evaluations

      • Fujio Yamaguchi
      Pages 561-569

    3. Role of Division Operations

      • Fujio Yamaguchi
      Pages 571-574

    4. Various Interpretations

      • Fujio Yamaguchi
      Pages 575-577

  4. Back Matter

    Pages 579-630
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Keywords

About this book

Computer graphics, computer-aided design, and computer-aided manufacturing are tools that have become indispensable to a wide array of activities in contemporary society. Euclidean processing provides the basis for these computer-aided design systems although it contains elements that inevitably lead to an inaccurate, non-robust, and complex system. The primary cause of the deficiencies of Euclidean processing is the division operation, which becomes necessary if an n-space problem is to be processed in n-space. The difficulties that accompany the division operation may be avoided if processing is conducted entirely in (n+1)-space. The paradigm attained through the logical extension of this approach, totally four-dimensional processing, is the subject of this book. This book offers a new system of geometric processing techniques that attain accurate, robust, and compact computations, and allow the construction of a systematically structured CAD system.

Authors and Affiliations

  • Department of Mechanical Engineering School of Science and Engineering, Waseda University, Tokyo, Japan

    Fujio Yamaguchi

Bibliographic Information

  • Book Title: Computer-Aided Geometric Design

  • Book Subtitle: A Totally Four-Dimensional Approach

  • Authors: Fujio Yamaguchi

  • DOI: https://doi.org/10.1007/978-4-431-67881-6

  • Publisher: Springer Tokyo

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Tokyo 2002

  • Hardcover ISBN: 978-4-431-70340-2Published: 14 October 2002

  • Softcover ISBN: 978-4-431-68007-9Published: 21 October 2012

  • eBook ISBN: 978-4-431-67881-6Published: 28 June 2011

  • Edition Number: 1

  • Number of Pages: XXXIX, 630

  • Additional Information: Original Japanese edition published by Nikkan Kogyo Shinbunsha, 1996

  • Topics: Computer-Aided Engineering (CAD, CAE) and Design, Software Engineering/Programming and Operating Systems

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