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Geometric and Algorithmic Aspects of Computer-Aided Design and Manufacturing
Edited by: Ravi Janardan, University of Minnesota, Minneapolis, MN, Michiel Smid, Carleton University, Ottawa, ON, Canada, and Debasish Dutta, University of Michigan, Ann Arbor, MI
A co-publication of the AMS and DIMACS.

DIMACS: Series in Discrete Mathematics and Theoretical Computer Science
2005; 360 pp; hardcover
Volume: 67
ISBN-10: 0-8218-3628-5
ISBN-13: 978-0-8218-3628-6
List Price: US$109
Member Price: US$87.20
Order Code: DIMACS/67
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Computer-Aided Design and Manufacturing (CAD/CAM) is concerned with all aspects of the process of designing, prototyping, manufacturing, inspecting, and maintaining complex geometric objects under computer control. As such, there is a natural synergy between this field and Computational Geometry (CG), which involves the design, analysis, implementation, and testing of efficient algorithms and data representation techniques for geometric entities such as points, polygons, polyhedra, curves, and surfaces. The DIMACS Center (Piscataway, NJ) sponsored a workshop to further promote the interaction between these two fields. Attendees from academia, research laboratories, and industry took part in the invited talks, contributed presentations, and informal discussions. This volume is an outgrowth of that meeting.

Topics covered in this volume include geometric modeling, computational topology, computational metrology, geometric constraint solving, part immobilization, geometric aspects of machining, layered manufacturing, and algebraic methods.

The book is suitable for graduate students and researchers interested in geometric and algorithmic aspects of computer-aided design and manufacturing.

Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with the Association for Computer Machinery (ACM).


Graduate students and researchers interested in geometric and algorithmic aspects of computer-aided design and manufacturing.

Table of Contents

  • I. Boier-Martin, D. Zorin, and F. Bernardini -- A survey of subdivision-based tools for surface modeling
  • T. K. Dey -- Sample based geometric modeling
  • D. Blackmore, Y. Mileyko, M. C. Leu, W. C. Regli, and W. Sun -- Computational topology and swept volumes
  • V. Srinivasan -- Elements of computational metrology
  • M. Sitharam -- Combinatorial approaches to geometric constraint solving: Problems, progress and directions
  • A. F. van der Stappen -- Immobilization: Analysis, existence, and output-sensitive synthesis
  • R. Janardan and M. Smid -- Geometric algorithms for layered manufacturing
  • P. Singh and D. Dutta -- A process planning framework for multi-direction layered deposition
  • T. Kim and S. E. Sarma -- Machinability: Geometric reasoning for cutting
  • D. Misra, V. Sundararajan, and P. K. Wright -- Zig-zag tool path generation for sculptured surface finishing
  • I. Z. Emiris and I. S. Kotsireas -- Implicitization exploiting sparseness
  • J. Keyser, K. Ouchi, and J. M. Rojas -- The exact rational univariate representation for detecting degeneracies
  • W. R. Franklin -- Mass properties of the union of millions of identical cubes
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