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Computer-Aided Geometric Design

A Totally Four-Dimensional Approach

  • Fujio Yamaguchi

Table of contents

  1. Front Matter
    Pages ii-xxxix
  2. Problem Definitions

    1. Front Matter
      Pages 1-1
    2. Fujio Yamaguchi
      Pages 3-11
    3. Fujio Yamaguchi
      Pages 13-20
    4. Fujio Yamaguchi
      Pages 21-31
    5. Fujio Yamaguchi
      Pages 33-65
    6. Fujio Yamaguchi
      Pages 67-69
    7. Fujio Yamaguchi
      Pages 71-84
  3. Presentation of a Solution —Four-dimensional Processing—

    1. Front Matter
      Pages 85-85
    2. Fujio Yamaguchi
      Pages 87-103
    3. Fujio Yamaguchi
      Pages 105-121
    4. Fujio Yamaguchi
      Pages 123-158
    5. Fujio Yamaguchi
      Pages 159-198
    6. Fujio Yamaguchi
      Pages 199-206
    7. Fujio Yamaguchi
      Pages 207-213
    8. Fujio Yamaguchi
      Pages 215-246
    9. Fujio Yamaguchi
      Pages 247-297
    10. Fujio Yamaguchi
      Pages 299-324
    11. Fujio Yamaguchi
      Pages 325-349
    12. Fujio Yamaguchi
      Pages 351-380
    13. Fujio Yamaguchi
      Pages 381-415
    14. Fujio Yamaguchi
      Pages 417-434
    15. Fujio Yamaguchi
      Pages 435-466
    16. Fujio Yamaguchi
      Pages 467-487
    17. Fujio Yamaguchi
      Pages 489-494
    18. Fujio Yamaguchi
      Pages 495-517
    19. Fujio Yamaguchi
      Pages 519-523
  4. Test Results

    1. Front Matter
      Pages 525-525
    2. Fujio Yamaguchi
      Pages 527-557
  5. Conclusions

    1. Front Matter
      Pages 559-559
    2. Fujio Yamaguchi
      Pages 561-569
    3. Fujio Yamaguchi
      Pages 571-574
    4. Fujio Yamaguchi
      Pages 575-577
  6. Back Matter
    Pages 579-630

About this book

Introduction

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.

Keywords

CAM Computational Geometry Computer-Aided Geometric Design Four-dimensional Geometric Processing Homogeneous Coordinates Plucker Coordinates computer graphics computer-aided design (CAD) construction topology

Authors and affiliations

  • Fujio Yamaguchi
    • 1
  1. 1.Department of Mechanical Engineering School of Science and EngineeringWaseda UniversityTokyoJapan

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