- 1.P. K. Agarwal and J. Erickson. Geometric ranso searching and its relatives. Technical report CS-1997-11, Duke University, May 1997. To appear in Discrete # C'omputatzonal Geome#y: Ten Years Later, B. Chazelle, J. E. Goodman, and R. Pollack, editors, American Mathematical Society Prcsa, 1998. (http://www.cs.duke.edu/"jeffe/pub#/survey.ht ml).Google Scholar
- 2.P. K. Agarwal and J. Matou#ek. Dynamic half-space range reporting and its applications. Algorithmica 13:325-345, 1995.Google ScholarCross Ref
- 3.P. K. Agarwal and J. Matou#ek. Ray shooting and parametric search. SIAM J. Compu#,. 22(4):794-806, 1993. Google ScholarDigital Library
- 4.P. K. Agarwal and J. Matou#ek. On range searching with semialgebraic sets. Discrete Comput. Geom. 11:393-418, 1994.Google ScholarDigital Library
- 5.P. K. Agarwal and M. Shark. Applications of a new spacepartitioning technique. Discrete Oomput. Geom. 9:11-38, 1993. Google ScholarDigital Library
- 6.A. Aggarwal, L. J. Gniba#, J. Saxe, and P. W. Shor. A linear-time algorithm for computing the Voronoi diagram of a convex polygon. Discrete Comput. Geom. 4(6):591-604, 1989.Google ScholarDigital Library
- 7.O. Aichholzer and F. Aurenhammer. Straight skcletonu for general polygonal figures in the plane. Prec. 2nd Annu. Internat. Conf. Computing and Combina#orics, pp. 117-126. Lecture Notes in Computer Science 1090, Sprin#er, 1996. Google ScholarDigital Library
- 8.O. Aichhoher, F. Aurenhammer, D. Alberts, and B. G#tncr. A novel type of skeleton for polygons. J. Universal Comput. Sci. 1(12):752-761, 1995. (http://vnvw.iicm.edu}juco#l.12/ amoveLt3rpe_of).Google Scholar
- 9.M, J0 Atallah, P, Callahan# and M. T. Goodrich. P-complete geometric problems. Internal J. Comput. Geom. AppL 3:443-462, 1993,Google ScholarCross Ref
- 10.D, Baraff, Interactive simulation of solid rigid bodies. IEEE Gomput. Graph. AppL 15(3):63-75, May 1995. Google ScholarDigital Library
- 11.J, BaBch, L. Gulbas, and J. Hershberger. Data structures for mobile data. Proc. 8th ACM-SIAM Sympos. Discrete Algorithm% pp. 747-756, 1997. Google ScholarDigital Library
- 12.J, Batch, L. Gulbas, and L. Zhang. Proximity problems on moving points. Proc, iSth Annu. ACM Sympos. Comput. Geom,, pp, 344-351, 1997'. Google ScholarDigital Library
- 13.M, de Berg, D, Halperin, M. Overmars, J. Snoeyink, and M. van Kreveld. Efficient ray shooting and hidden surface removal, Algorithmica 12:30-53, 1994.Google ScholarCross Ref
- 14.H. Blum, A transformation for extracting new descriptors of #hape, Models for the Perception of Speech and Visual Form, pp, 362-380. HIT Press, 1967.Google Scholar
- 15.F, L, BookDtein, The line-skeleton. CompuL Graph. Image Proceso. II:123-137, 1979.Google Scholar
- 16.L. Calabt and W, E. Hartnett. Shape recognition, prairie flreu, convex deficiencies and skeletons. Amer. Math. Monthly 75:335-342, 1968.Google ScholarCross Ref
- 17.T, M. Ohm. Geometric applications of a randomized optimization technique. To appear in Prec. 14th Annu. ACM #~ympoo, Oomput Geom,, 1998. Google ScholarDigital Library
- 18.B, Chazelle, H. Edelsbrunner, L. Guibas, and M. Shaxir. A Dingly.exponential stratification #cheme for real semialgebraic varieties and its applications. Theoret. CompuL #qci, 84:77-105, 1991. Google ScholarDigital Library
- 19.B, Chazelle, H. Edelsbrunner, L. J. Guibas, M. Sharir, and J, Stolfl, Lines in apace: Combinatorics and algorithms. Algorithmica 15:428-447, 1996,Google ScholarDigital Library
- 20.L, P, Chert. Building Voronoi diagrams for convex polygons In linear e:vpected time. Technical Report PCS-TR90-147, Dept. Math. Comput. Sci., Dartmouth College, 1986.Google Scholar
- 21.F, Chin, J. Snoeyink, and C.-A. Wang. Finding the medial axi# of a simple polygon in linear time. Prec. 6th Annu. Intcrnat, Sympoo. Algorithms CompuL, pp. 382-391. Lecture Note0 Comput. Sci. 1004, Springer-Verlag, 1995. Google Scholar
- 22.J, D, Cohen, M. C. Lin, D. Manocha, and M. K. Ponamgi. I.colltde: An interactive and exact collision detection system for large-scale environments. Prec. A CM Interactive 3D Graphic8 Gonf,, pp. 189-196, 1995. Google ScholarDigital Library
- 23.J, Czyzowlcz, I, Rival, and J. Urrutia. Gallerie% light matchtng0 and vlBibility graphs. Prec. 1st Workshop Algorithms Data #truct., pp0 316-324. Lecture Notes CompuL Sci. 382, #pringer-Verlag, 1989, Google ScholarDigital Library
- 24.O, Devlllers. Randomization yields simple O{nlog* n) algorlthm# for difficult F2{n) problems. Internal J. CompuL Geom. AppL 2(1):97-111, 1992. (http://www.mria.fr/ prtQme/blblio/search,html).Google ScholarCross Ref
- 25.D, Eppsteln. Dynamic Euclidean minimum spanning trees and extrema of binary functions. Discrete CompuL Geom. 13:111-122, 1995,Google ScholarDigital Library
- 26.D, Eppstein. Fast hierarchical clustering and other applications of dynamic closes# pairs. Prec. 9th Annu. ACM-SIAM #ympoa, Discrete Algorffhn#, pp. 619-628, 1998. Google Scholar
- 27.A. Foloy, V, Hayv/ard, and S. Aubry. The use of awareness in collloton prediction. Prec. 1990 IEEE Internal Conf. Robotics and Automation, pp. 338-343# 1990.Google Scholar
- 28.E. Fredkin and T, Toffoli. Conservative logic. In#ernat. J. Theoret, Phy8. 21:219-253, 1981/82. Proceedings of Conference on PhyBics of Computation, Dedham, Mass., 1981.Google Scholar
- 29.D, Grlffeath and C. Moore. Life Without Death is P- complete. Working Paper 97-05-044, Santa Fe Institute, 1997, To appear in Complex Systems. (http:// p0oup, math.wiac.edu/java/lwodpc/lwodpc.html).Google Scholar
- 30.L. J. Guibas. Kinetic data structures: A state of the art report. To appear in Prec. 3rd Workshop on Algorithmic Foundations of Robotics, P. K. Aganval, L. Kavraki, and M. Mason, editors, A. K. Peters, 1998. Google ScholarDigital Library
- 31.H. N. Gfimoy and N. M. Patrikalakis. An automatic coarse and fine surface mesh generation scheme based on medial axis transform, Part h Algorithms. Engineering with Computers 8:121-137, 1992.Google ScholarDigital Library
- 32.M. Held. Voronoi diagrams and offset curves of curvilinear polygons. To appear in CompuL Aided Design. (http:// www.cosy.sbg.ac.at/'held/papers/cad96.p#.#).Google Scholar
- 33.M. Held, G. Luk#cs, and L. Andor. Pocket machining based on contour-parallel tool paths generated by means of proximity maps. GompuL Aided Design 26(3):189--203, Mar. 1994.Google ScholarCross Ref
- 34.P. M. Hubbard. Collision detection for interactive graphics applications. IEEE Trans. Visualization and Compu#ar Graphi# 1(3):218--230, Sept. 1995. Google ScholarDigital Library
- 35.D. Kim, b. Guibas, and S. Shin. Fas# collision detection among multiple moving spheres. Pwc. 13th Annu. ACM Sympos. GompuL Geom., pp. 373-375. 1997. Google ScholarDigital Library
- 36.R. Klein. Goncrefe and Abstract Voronoi Diagrams. Lecture Notes Comput. Sci. 400. Springer-Verlag, 1989.Google Scholar
- 37.tL J. Lang. A computational algorithm for origami design. Prec. 12th Annu. ACM Sympos. Comput. Geom., pp. 93- 105# 1996. Google ScholarDigital Library
- 38.D. T. Lee. Medial axis transformation of a planar shape. IEEE Trans. Pa#ern Anal. Mach. InteU. PAMI-4:363-369, 1982.Google ScholarDigital Library
- 39.S. Lisberger, director. Tron. Walt Disney Productions, 1932. Motion picture, 96 minutes.Google Scholar
- 40.J. Matou#ek. Reporting points in half, paces. GompuL Geom. Theory AppL 2(3):169--186, 1992. Google ScholarDigital Library
- 41.J. Matou#ek. Range searching with efficient hierarchical cuttings. D#scre#e CompuL Geom. 10(2):157-182, 1993.Google Scholar
- 42.M. McAllister, D. Kirkpatrick, and J. Snoeyink. A compact piecewise-linear Voronoi diagram for convex site# in the plane. Discrete Comput. Geom. 15:73-I05, 1996.Google ScholarDigital Library
- 43.N. Megiddo. Applying parallel computation algorithms in the design of serial algorithms. J. ACM 30:852-865, 1983. Google ScholarDigital Library
- 44.B. Mir#ich and J. Canny. Impul#e-ba#ed simulation of rigid bodies. S#npos{um on Interadive 3D Graphics. ACM Press, 1995. Google ScholarDigital Library
- 45.C. 6'Ddnlaing and C. K. Yap. A "retraction" method for planning the motion of a disk. J. Algorithms 6:104--111, 1985.Google ScholarCross Ref
- 46.A. Recuaero and J. P. Gutidrre#. Sloped roofs for archEecrural CAD systems. Microcomputers in Civil Engineering 8:147-159, 1993.Google ScholarCross Ref
- 47.V. Srinivasan, L. R. Nadunan, J.-M. Tang, and S. N. Meshkat. Automatic mesh generation using the symmetric axis transform of polygonal domains. Prec. IEEE 80(9):1485--1501, Sept. 1992.Google ScholarCross Ref
- 48.J. Stolfi. Or/ended Prajective Geometry: A Framework for Geometric Computabions. Academic Pre#, New York, NY, 1991. Google ScholarDigital Library
- 49.J.A. Storer and J. H. Reif. Shortest paths in the plane with polygonal obstacles. J. ACM 41(5):982-1012# 1994. Google ScholarDigital Library
- 50.A. Sudhaltmr, L. Gumoz, and F. Prinz. B#-skeletons of discrete solids. CompuL Aided Design 28:507-517, 1996.Google ScholarCross Ref
- 51.T. K. H. Tam and C. G. Armstrong. 2D finite element mesh generation by" medial axis subdivision. Advances in Engi. neering Software and Workstations 13(5-6):313-324# SepL 1991.Google Scholar
- 52.P. J. Venneer. MedioJ Axis Transform to Boundary R#re. sensation Conv#rsio# Ph.D. thesis, CS Dept., Purdue University, West Lafayette, Indiana 47907-1398, USA, 1994.Google Scholar
Index Terms
- Raising roofs, crashing cycles, and playing pool: applications of a data structure for finding pairwise interactions
Recommendations
Realistic roofs over a rectilinear polygon
Given a simple rectilinear polygon P in the xy-plane, a roof over P is a terrain over P whose faces are supported by planes through edges of P that make a dihedral angle @p/4 with the xy-plane. According to this definition, some roofs may have faces ...
Constructive Roofs from Solid Building Primitives
Transactions on Computational Science XXVI - Volume 9550The creation of building models has high importance, due to the demand for detailed buildings in virtual worlds, games, movies and geo information systems. Due to the high complexity of such models, especially in the urban context, their creation is ...
Chorded Cycles
A chord is an edge between two vertices of a cycle that is not an edge on the cycle. If a cycle has at least one chord, then the cycle is called a chorded cycle, and if a cycle has at least two chords, then the cycle is called a doubly chorded cycle. ...
Comments