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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. Front Matter

    Pages ii-xxxix
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  2. Problem Definitions

    1. Front Matter

      Pages 1-1
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    2. Problems of Euclidean Approach

      • Fujio Yamaguchi
      Pages 3-11

    3. Homogeneous Coordinates

      • Fujio Yamaguchi
      Pages 13-20

    4. Classical Projective Space

      • Fujio Yamaguchi
      Pages 21-31

    5. Two-Sided Space

      • Fujio Yamaguchi
      Pages 33-65

    6. Processing in Projective Spaces

      • Fujio Yamaguchi
      Pages 67-69

    7. Transformations

      • Fujio Yamaguchi
      Pages 71-84

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

    1. Front Matter

      Pages 85-85
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    2. A Solution

      • Fujio Yamaguchi
      Pages 87-103

    3. Geometric Definitions in General

      • Fujio Yamaguchi
      Pages 105-121

    4. Geometric Element Definitions

      • Fujio Yamaguchi
      Pages 123-158

    5. Homogeneous Curves

      • Fujio Yamaguchi
      Pages 159-198

    6. Homogeneous Surfaces

      • Fujio Yamaguchi
      Pages 199-206

    7. Basic Intersections

      • Fujio Yamaguchi
      Pages 207-213

    8. 4 × 4 Determinant Methods

      • Fujio Yamaguchi
      Pages 215-246

    9. The Homogeneous Determinant Method

      • Fujio Yamaguchi
      Pages 247-297

    10. Geometric Newton-Raphson Method

      • Fujio Yamaguchi
      Pages 299-324

    11. Exact Arithmetic

      • Fujio Yamaguchi
      Pages 325-349

    12. Fundamentals of Topology

      • Fujio Yamaguchi
      Pages 351-380
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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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