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Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

List of Contributors

Agarwal, P.K., Duke University, Durham, NC (Chs. 1, 2)

Alt, H., Freie Universitdt Berlin, Berlin (Ch. 3)

Asano, T., Japan Advanced Institute of Science and Technology, Ishikawa (Ch. 19)

Atallah, M.J., Purdue University, West Lafayette, IN (Ch. 4)

Aurenhammer, R, Technische Universitdt Graz, Graz (Ch. 5)

Bern, M., Xerox Palo Alto Research Center, Palo Alto, CA (Ch. 6)

Chen, D.Z., University of Notre Dame, Notre Dame, IN (Ch. 4)

De Floriani, L., Universita di Genova, Genova (Ch. 7)

Djidjev, H.N., University of Warwick, Coventry (Ch. 12)

Dobkin, D.P., Princeton University, Princeton, NJ (Ch. 8)

Eppstein, D., University of California, Irvine, CA (Ch. 9)

Ghosh, S.K., Tata Institute of Fundamental Research, Bombay (Ch. 19)

Goodrich, M.T., Johns Hopkins University, Baltimore, MD (Ch. 10)

Guibas, L.J., Stanford University, Stanford, CA (Ch. 3)

Hausner, A., Princeton University, Princeton, NJ (Ch. 8)

Keil, J.M., University of Saskatchewan, Saskatoon, SK (Ch. 11)

Klein, R., Fern Universitdt Hagen, Hagen (Ch. 5)

Magillo, P., Universita di Genova, Genova (Ch. 7)

Maheshwari, A., Carleton University, Ottawa, ON (Ch. 12)

Matousek, J., Charles University, Praha (Ch. 13)

Mitchell, J.S.B., State University of New York, Stony Brook, NY (Ch. 15)

Mulmuley, K., The University of Chicago, Chicago, IL, and LIT, Bombay (Ch. 16)

Nievergelt, J., ETH Zurich, Zurich (Ch. 17)

Plassmann, P., Pennsylvania State University, University Park, PA (Ch. 6)

Puppo, E., Universita di Genova, Genova (Ch. 7)

Ramaiyer, K., Informix Software, Oakland, CA (Ch. 10)

Reif, J.H., Duke University, Durham, NC (Ch. 18)

Sack, J.-R., Carleton University, Ottawa, ON (Ch. 12)

Schirra, S., Max-Planck-InstitutfUr Informatik, SaarbrUcken (Ch. 14)

Sen, S., Indian Institute of Technology, New Delhi (Ch. 18)

Sharir, M., Tel Aviv University, Tel Aviv, and New York University, New York, NY (Chs. 1,2)

Shermer, T.C., Simon Fraser University, Bumaby, BC (Ch. 19)

Smid, M., University of Magdeburg, Magdeburg (Ch. 20)

Tamassia, R., Brown University, Providence, RI (Ch. 21)

Urrutia, J., Universidad Nacional Autonoma de Mexico, Mexico (Ch. 22)

Widmayer, P., ETH Zurich, Zurich (Ch. 17)

List of Contributors vii
1. Davenport-Schinzel sequences and their geometric applications 1
P.K. Agarwal and M. Sharir
2. Arrangements and their applications 49
P.K. Agarwal andM. Sharir
3. Discrete geometric shapes: Matching, interpolation, and approximation 121
H. Alt and L.J. Guihas
4. Deterministic parallel computational geometry 155
M.J. Atallah and D.Z. Chen
5. Voronoi diagrams 201
F. Aurenhammer and R. Klein
6. Mesh generation 291
M. Bern and P. Plassmann
7. Applications of computational geometry to geographic information systems 333
L. de Floriani, P. Magillo and E. Puppo
8. Making geometry visible: An introduction to the animation of geometric
algorithms 389
A. Hausner and D.P Dohkin
9. Spanning trees and spanners 425
D. Eppstein
10. Geometric data structures 463
M.T. Goodrich and K Ramaiyer
11. Polygon decomposition 491
J.M. Keil
12. Link distance problems 519
A. Maheshwari, J. -R. Sack and H.N. Djidjev
13. Derandomization in computational geometry 559
/. Matousek
14. Robustness and precision issues in geometric computation 597
S. Schirra
15. Geometric shortest paths and network optimization 633
J.S.B. Mitchell
16. Randomized algorithms in computational geometry 703
K. Mulmuley
17. Spatial data structures: Concepts and design choices 725
/. Nievergelt and P. Widmayer
18. Parallel computational geometry: An approach using randomization 765
J,H.ReifandS.Sen
19. Visibility in the plane 829
T Asano, S.K. Ghosh and T.C. Shermer
20. Closest-point problems in computational geometry 877
M. Smid
21. Graph drawing 937
R. Tamassia
22. Art gallery and illumination problems 973
/. Urrutia
Author Index I-l
Subject Index 1-35
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