DIMACS Series in
Discrete Mathematics and Theoretical Computer Science

VOLUME Sixty seven
TITLE: "Geometric and Algorithmic Aspects of Computer-Aided Design and Manufacturing"
EDITORS: Ravi Janardan, Michiel Smid, and Debasis Dutta

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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. On the one hand, CG can bring about significant performance improvements in CAD/CAM, while, on the other hand, CAD/CAM can be a rich source of interesting problems that can spur new research in CG. Indeed, such two-way interaction has already been witnessed in recent years in areas such as numerically-controlled machining, casting and injection molding, rapid prototyping and layered manufacturing, metrology, and mechanism/linkage design, to name just a few.

To further promote the interaction between the two fields, we organized a Workshop on "Computer-Aided Design and Manufacturing" at the DIMACS Center in Piscataway, NJ, from Oct. 7-9, 2003. The Workshop, which was attended by about fifty-five individuals from academia, research laboratories, and industry, was organized around a series of invited talks, contributed presentations, and informal discussions geared towards fostering collaborative research. Details about the Workshop can be found at http://dimacs.rutgers.edu/archive/Workshops/CompAided/.

Subsequently, authors of papers presented at the Workshop were invited to submit expanded and polished versions of their research to this Volume. The intent was to provide, in one place, a set of self-contained papers that could serve as the starting point for further research. All submissions were refereed. The papers in this Volume are an outgrowth of this process and cover topics such as geometric modeling, computational topology, computational metrology, geometric constraint solving, part immobilization, geometric aspects of machining, layered manufacturing, and algebraic methods.

We thank Fred Roberts (DIMACS Director) and Steve Fortune (Member, DIMACS Executive Council) for their support and encouragement, DIMACS and AMS staff members for organizational help, the referees for their help with the reviews, and, of course, the authors for their research contributions. We are grateful to the National Science Foundation for financial support for the Workshop.

Ravi Janardan (Minneapolis, MN)
Michiel Smid (Ottawa, Canada)
Debasish Dutta (Ann Arbor, MI)
July 2004



Forward                                             vii
Preface                                              ix

A Survey of Subdivision-Based Tools for Surface
     I. Boier-Martin, D. Zorin, and F. Bernardini     1

Sample Based Geometric Modeling
     T. Dey                                          29

Computational Topology and Swept Volumes
     D. Blackmore, Y. Mileyko, M. Leu, W. Regli,
        and W. Sun                                   53

Elements of Computational Metrology
     V. Srinivasan                                   79

Combinatorial Approaches to Geometric Constraint
   Solving: Problems, Progress, and Directions
     M. Sitharam                                    117

Immobilization: Analysis, Existence, and Output-
   Sensitive Synthesis                              
     F. van der Stappen                             165

Geometric Algorithms for Layered Manufacturing
     R. Janardan and M. Smid                        189

Towards a Process Planning Framework for Multi-
   Direction Layered Deposition
     P. Singh and D. Dutta                          221

Machinability: Geometric Reasoning for Cutting
     T. Kim and S. Sarma                            245

Zig-Zag Tool Path Generation for Sculptured Surface
     D. Misra, V. Sundararajan and P. Wright        265

Implicitization Exploiting Sparseness
     I. Emiris and I. Kotsireas                     281

The Exact Rational Univariate Representation for
   Detecting Degeneracies
     J. Keyser, K. Ouchi and J.M. Rojas             299

Mass Properties of the Union of Millions of
   Identical Cubes
     W.R. Franklin                                  329

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Document last modified on July 19, 2005.