Apollonius tenth problem as a point location problem

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2073, Issue , 2001, Pages 728-737

  Kim, Deok Soo ^a   Kim, Donguk ^a   Sugihara, Kokichi ^b   Ryu, Joonghyun ^a  

^a Hanyang University   (South Korea)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR TRANSFORMATIONS;

APOLLONIUS TENTH PROBLEMS; CAD SYSTEM; COMPLEX SPACE; DEGENERATE CASE; GEOMETRIC COMPUTATIONS; LINEAR FRACTIONAL TRANSFORMATIONS; POINT LOCATION PROBLEMS; VORONOI DIAGRAMS;

MATHEMATICAL TRANSFORMATIONS;

EID: 69549115344     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45545-0_84     Document Type: Conference Paper

References (18)

1. Altshiller-Court, N., The problem of Apollonius. College Geometry, 2nd Ed., Barnes and Noble, New York, (1952) 173-181.
2. Boyer, C. B., A History of Mathematics, Wiley, New York (1968).
3. Capelli, R. Circle tangential to 3 cicles or lines. Posting No. 35067, Usenet newsgroup comp.graphics.algorithms, 2 pages, (1996).
4. Courant, R. and Robbins, H., What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd edition, Oxford University Press, Oxford (1996).
5. Dörrie, H., 100 Great Problems of Elementary Mathematics: Their History and Solutions, Dover, New York (1965).
6. Gavrilova, M. and Rokne, J., Swap conditions for dynamic Voronoi diagram for circles and line segments, Computer Aided Geometric Design, Vol. 16 (1999) 89-106.
7. Gavrilova, M. and Rokne, J., Apollonius' Tenth Problem Revisited, Special Session on Recent Progress in Elementary Geometry, 941st American Mathematical Society Conference (1999) 64.
8. Kim, D.-S., Hwang, I.-K. and Park, B.-J., Representing the Voronoi diagram of a simple polygon using rational quadratic Bézier curves, Computer-Aided Design, Vol. 27, No. 8 (1995) 605-614.
9. Kim, D.-S., Lee, S.-W. and Shin, H., A cocktail algorithm for planar Bézier curve intersections, Computer-Aided Design, Vol. 30, No. 13 (1998) 1047-1051.
10. Kim, D.-S., Kim, D. and Sugihara, K., Voronoi diagram of a circle set from Voronoi diagram of a point set: I. Topology, (Submitted to Computer Aided Geometric Design 2001).
11. Kim, D.-S., Kim, D. and Sugihara, K., Voronoi diagram of a circle set from Voronoi diagram of a point set: II. Geometry, (Submitted to Computer Aided Geometric Design 2001).
12. Kreyszig, E., Advanced Engineering Mathematics, 7th Edition, John Wiley & Sons (1993).
13. Lee, D.T. and Drysdale, R.L., III, Generalization of Voronoi diagrams in the plane, SIAM J. COMPUT., Vol. 10, No. 1 (1981) 73-87.
14. Moise, E.E., Elementary Geometry from an Advanced Standpoint, 3rd. ed., Addison- Wesley Publ. Co., Reading (1990).
15. Okabe, A., Boots, B. and Sugihara, K., Spatial Tessellations Concepts and Applications of Voronoi Diagram, John Wiley & Sons (1992).
16. Rokne, J., Appolonius’s 10th problem, Graphics Gems II, ed. James Arvo, Academic Press, (1991) 19-24.
17. Sevici, C.A., Solving the problem of Apollonius and other related problems, Graphics Gems III, ed. David Kirk, Academic Press, San Diego (1992) 203-209.
18. Sharir, M., Intersection and closest-pair problems for a set of planar discs, SIAM J. COMPUT., Vol. 14, No. 2 (1985) 448-468.