- 4. Conclusions We have presented an optimal algorithm for determining the visibility of a polygon from a
- between two crossing convex polygons,'' Computing, vol. 32, 1984, pp. 357364. [To85a] Toussaint, G. T., ed., Computational Geometry, NorthHolland, 1985.
- tion of parts," Proc. IEEE Int. Conf. Robotics and Automation, Cincinnati, OH, USA, May 13-18, 1990, pp. 1284-1289.
- Experimental Results on Quadrangulations of Sets of Fixed Points Prosenjit Bose
- It turns out however that the pair of vertices determining d min , surprisingly, is neither a copodal nor an antipodal pair and thus the techniques used with success on d max fail on d min . Finding an
- In-Place Planar Convex Hull Algorithms ? Herv e Bronnimann 1 , John Iacono 1 , Jyrki Katajainen 2 , Pat Morin 3 , Jason
- The ErdosNagy Theorem and its Ramifications Godfried Toussaint \Lambda
- Lower Bounds for Computing Statistical Greg Aloupis Carmen Cort es y Francisco G omez z
- Contemporary Mathematics Convexifying Polygons in 3D: a Survey
- 4. Applications Meisters' [Me] TwoEars Theorem was motivated by the problem of triangulating a simple
- Algorithmic, Geometric, and Combinatorial Problems in Computational Music Theory
- Geometric Decision Rules for High Binay Bhattacharya
- Interlocking Rhythms, Duration Interval Content, Cyclotomic Sets, and the Hexachordal Theorem
- 5. References 1. Chazelle B (1980) Computational geometry and convexity. Ph.D. thesis, Carnegie-Mel-
- 98, 1991, pp. 3135. [To3] Toussaint, G. T., ``New results in computational geometry relevant to pattern recognition
- 4. Conclusions We have presented an optimal algorithm for determining the visibility of a polygon from a
- The Euclidean Algorithm Generates Traditional Musical Rhythms Godfried Toussaint
- Convexifying Polygons with Simple Projections Jorge Alberto Calvo Danny Krizanc y Pat Morin z
- [2] Schwartz, J. T.: Finding the minimum distance between two convex polygons. Informa tion Processing Letters 1981, 168 170.
- Geometry, to appear in 1991. [To92] Toussaint, G. T., ed., Proceedings of the IEEE, Special Issue on Computational Geo
- Filling Polyhedral Molds \Lambda Prosenjit Bose Marc van Kreveld Godfried Toussaint
- Symposium of the Interface, Atlanta, Georgia, 1984. [To76a] Tomek, I., ``Two modifications of CNN,'' IEEE Trans. Systems, Man and Cybernetics,
- Computational Theoryand Applications
- A Note on Linear Expected Time Algorithms for Finding Convex Hulls
- On Reconfiguring Tree Linkages: Trees can Lock
- An Algorithm for Computing the Restriction Scaffold Assignment Problem in Computational Biology
- [10] F. P. Preparata and S. J. Hong, ``Convex hulls of finite sets of points in two and three di mensions,'' Communications of the ACM, vol. 20, pp. 8793, 1977.
- Computing Simple Circuits from a Set of Line Segments David Rappaport \Lambda
- dal polygons,'' Information Processing Letters, vol. 31, June 1989, pp. 243247. [Ra88] J. D. Radke, ``On the shape of a set of points,'' in Computational Morphology, Tous
- An O(n log n)-Time Algorithm for the Restricted Scaffold Assignment Problem
- Faster Algorithms for Computing Distances between One-Dimensional Point Sets
- [Ba] Bykat, A., ``Convex hull of a finite set of points in two dimensions,'' Info. Proc. Lett. 7 (1978), 296298.
- mal vectors,'' Proc. Symposium on Computational Geometry, Baltimore, June 57 1985, pp. 8996.
- [Va53] Valentine, F. A., ``Minimal sets of visibility,'' Proc. American Mathematical Society, vol. 4, 1953, pp. 917921.
- Some constrained minimax and maximin location Ferran Hurtado 1 Vera Sacrist'an 1 Godfried Toussaint 2
- 8. References [1] H. Freeman and S. P. Morse, ``On searching a contour map for a given terrain elevation
- An Efficient Algorithm for Decomposing a Polygon into StarShaped PolygonsDecember 9, 1999 1 An Efficient Algorithm for Decomposing a
- [41] B. Chazelle, "The polygon containment problem", in Computational Geometry, Ed., F. P. Preparata, Advances on Computing Research, vol. 1, JAI Press, Inc., 1983, pp 1-33.
- Geometry, to appear in 1991. [To92] Toussaint, G. T., ed., Proceedings of the IEEE, Special Issue on Computational Geo
- Computing the Constrained Euclidean, Geodesic and Link Centre of a Simple Polygon with Applications
- Nice Perspective Projections* Escuela Universitaria de Inform atica, U.P.M., Madrid, Spain
- Illinois, pp. 3540, October 1980. [22] G. T. Toussaint and B. K. Bhattacharya, ``Optimal algorithms for computing the mini
- Computational Polygonal Entanglement Theory \Lambda
- [Gr] Grunbaum, B., ``On common transversals,'', Arch. Math., Vol. 9, 1958, pp. 465469. [HV] Horn, A., and Valentine, F.A., ``Some properties of Lsets in the plane,'', Duke Mathematics
- [8] K. J. Supowit, ``The relative neighborhood graph with an application to minimum span ning trees,'' Tech. Rept., Department of Computer Science, University of Illinois, Urba
- Robot Motion, Ablex Publishing Corporation, Norwood, New Jersey, 1987. [St91] Stolfi, J., Oriented Projective Geometry: A Framework for Geometric Computations,
- A simple O(n log n) algorithm for finding the maximum distance between two finite planar sets
- 5. References 1. Chazelle B (1980) Computational geometry and convexity. Ph.D. thesis, CarnegieMel
- Tech. Rept. SOCS88.10, McGill University, May 1988. [To88d] Toussaint, G. T., ``Separating two simple polygons by a single translation,'' Journal of
- Relative Neighborhood Graphs and Their Relatives
- cs.CG/9910009 Locked and Unlocked
- Characterizing and Efficiently Computing Quadrangulations of Planar Prosenjit Bose \Lambda Godfried Toussaint y
- A Comparison of Rhythmic Similarity Godfried Toussaint
- [Gu] Guggenheimer, H., "The Jordan and Schoenflies theorems in axiomatic geometry," Ameri-can Mathematical Monthly, vol. 85, 1978, pp.753-756.
- Illinois, pp. 35-40, October 1980. [22] G. T. Toussaint and B. K. Bhattacharya, "Optimal algorithms for computing the mini-
- The Complexity of Computing Nice Viewpoints of Objects in Godfried T. Toussaint
- ApertureAngle Optimization Problems in 3 Dimensions \Lambda Elsa Oma~naPulido
- [Gu] Guggenheimer, H., ``The Jordan and Schoenflies theorems in axiomatic geometry,'' Ameri can Mathematical Monthly, vol. 85, 1978, pp.753756.
- Efficient Many-To-Many Point Matching in One Dimension Justin Colannino1
- The Geometry of Musical Rhythm Godfried Toussaint
- Mathematical Features for Recognizing Preference in Sub-Saharan African Traditional
- Computational Geometric Aspects of Musical Rhythm Godfried Toussaint
- Algorithmic, Geometric, and Combinatorial Problems in Computational Music Theory
- !"#$%&'$)(021 3547698@BADCFE
- Fig. 5 A polygon on which the DSW algorithm fails.
- Symposium of the Interface, Atlanta, Georgia, 1984. [To76a] Tomek, I., "Two modifications of CNN," IEEE Trans. Systems, Man and Cybernetics,
- 4. Applications Meisters' [Me] Two-Ears Theorem was motivated by the problem of triangulating a simple
- ceton University Press, 1970. [Pe76] Pedoe, D., Geometry and the Liberal Arts, Penguin Books, Inc., 1976.
- Robot Motion, Ablex Publishing Corporation, Norwood, New Jersey, 1987. [St91] Stolfi, J., Oriented Projective Geometry: A Framework for Geometric Computations,
- [Va53] Valentine, F. A., "Minimal sets of visibility," Proc. American Mathematical Society, vol. 4, 1953, pp. 917-921.
- 98, 1991, pp. 31-35. [To3] Toussaint, G. T., "New results in computational geometry relevant to pattern recognition
- Geometry, to appear in 1991. [To92] Toussaint, G. T., ed., Proceedings of the IEEE, Special Issue on Computational Geo-
- [Ba] Bykat, A., "Convex hull of a finite set of points in two dimensions," Info. Proc. Lett. 7 (1978), 296-298.
- Tech. Rept. SOCS-88.10, McGill University, May 1988. [To88d] Toussaint, G. T., "Separating two simple polygons by a single translation," Journal of
- [Gr] Grunbaum, B., "On common transversals,", Arch. Math., Vol. 9, 1958, pp. 465-469. [HV] Horn, A., and Valentine, F.A., "Some properties of L-sets in the plane,", Duke Mathematics
- dal polygons," Information Processing Letters, vol. 31, June 1989, pp. 243-247. [Ra88] J. D. Radke, "On the shape of a set of points," in Computational Morphology, Tous-
- [10] F. P. Preparata and S. J. Hong, "Convex hulls of finite sets of points in two and three di-mensions," Communications of the ACM, vol. 20, pp. 87-93, 1977.
- gons considered in this note. Acknowledgement: The authors are grateful to Hossam ElGindy for stimulating discussions on
- [8] K. J. Supowit, "The relative neighborhood graph with an application to minimum span-ning trees," Tech. Rept., Department of Computer Science, University of Illinois, Urba-
- Receivd 31 Octobw 1977, awisedwdon received28 December1977 Convexhid, &orithm
- Pattern Recognition Vol. tO. pp. 189-204. Pergamon Press Ltd. 1978. Printed in Great Britain.
- 8. References [1] H. Freeman and S. P. Morse, "On searching a contour map for a given terrain elevation
- Algorithms for Bivariate Medians and a Fermat-Torricelli Problem for Lines
- On Reconfiguring Tree Linkages: Trees can Lock
- [41] B. Chazelle, ``The polygon containment problem'', in Computational Geometry, Ed., F. P. Preparata, Advances on Computing Research, vol. 1, JAI Press, Inc., 1983, pp 133.
- Finding Hamiltonian Circuits in Arrangements of Jordan Curves is NPComplete
- On the Role of Kinesthetic Thinking in Computational Geometry J. Antoni Sellar es y and Godfried Toussaint z
- Geometric Decision Rules for Instance-based Learning Problems
- GACT Symposium, Los Angeles, California (1980). [36] G. T. Toussaint, Solving geometric problems with the rotating calipers, Proc. ME-
- It turns out however that the pair of vertices determining dmin, surprisingly, is neither a co-podal nor an antipodal pair and thus the techniques used with success on dmax fail on dmin. Finding an
- GACT Symposium, Los Angeles, California (1980). [36] G. T. Toussaint, Solving geometric problems with the rotating calipers, Proc. ME
- Constructing Convex 3-Polytopes from Two Triangulations of a Polygon
- Pattern Recognition Letters 3 (1985) 29-34 January 1985 North-Holland
- Converting Triangulations to Quadrangulations \Lambda Suneeta Ramaswami
- Analisis filogenetico del compas flamenco Jose-Miguel Diaz-Ba~nez *
- [2] Schwartz, J. T.: Finding the minimum distance between two convex polygons. Informa-tion Processing Letters 1981, 168 -170.
- A Faster Algorithm for Computing the Link Distance Between Two Point Sets on the Real Line
- lishers, New York, 1989. [Mu90]Muraski, S. J., "Make it in a minute," Machine Design, February 1990, pp. 127-
- Advances in Computational Geometry for Document Analysis
- Growing a Tree from its Branches \Lambda Prosenjit Bose and Godfried Toussaint
- On Degeneracies Removable by Perspective Projections
- between two crossing convex polygons," Computing, vol. 32, 1984, pp. 357-364. [To85a] Toussaint, G. T., ed., Computational Geometry, North-Holland, 1985.
- pp. 595-645. [Sw72] Swonger, C.W., "Sample set condensation for a condensed nearest neighbor decision
- Fig. 3 The density function governing r for six values of d. to distinguish high counts then determines the confidence level with which we reject the null hy-
- Proximity Graphs for Nearest Neighbor Decision Rules: Recent Progress
- A New Class of Stuck Unknots in P ol 6 Godfried Toussaint
- Fig. 5 A polygon on which the DSW algorithm fails.
- El Compas Flamenco: A Phylogenetic Analysis J. Miguel Diaz-Ba~nez
- [11] G. T. Toussaint, "On translating a set of spheres" Technical Report SOCS-84.4, School of Computer Science, McGill University (March, 1984).
- Geometric and Computational Aspects of Polymer Recon guration
- Experimental Results on Quadrangulations of Sets of Fixed Points Prosenjit Bose # Suneeta Ramaswami + Godfried Toussaint # Alain Turki
- guarding problems,'' Tech. Rept. B9308, Free University of Berlin, June 1993. [Hof] F. Hoffmann, "On the rectilinear art gallery problem," in Proc. Int. Colloq. Automata,
- mal vectors," Proc. Symposium on Computational Geometry, Baltimore, June 5-7 1985, pp. 89-96.
- pp. 595645. [Sw72] Swonger, C.W., ``Sample set condensation for a condensed nearest neighbor decision
- Wiley 1977, pp. 267311. [25] H. Abelson and A. di Sessa, Turtle Geometry, MIT Press, 1980.
- Computing a Geometric Measure of the Similarity Between two Greg Aloupis Thomas Fevens y Stefan Langerman z Tomomi Matsui x
- Fig. 3 The density function governing r for six values of d. to distinguish high counts then determines the confidence level with which we reject the null hy
- On the Sectional Area of Convex Polytopes \Lambda David Avis 1 Prosenjit Bose 2 Thomas C. Shermer 3
- On the Role of Kinesthetic Thinking in Computational Geometry J. Antoni Sellar es y and Godfried Toussaint z
- CONVEX HULLS FOR RANDOM LINES Luc Devroye
- gons considered in this note. Acknowledgement: The authors are grateful to Hossam ElGindy for stimulating discussions on
- Algorithmic, Geometric, and Combinatorial Problems in Computational Music Theory
- Scripta Mathematica, vol. 14, 1948, pp. 189-264. [Si1756] Simson, R., Los Seis Primeros Libros, y el Undcimo, y Duodcimo de los Elementos
- lection,'' SIAM Journal on Computing, Vol. 18, No. 4, 1989, pp. 792810. [DT93] Devroye, L. and Toussaint, G. T., ``Convex hulls for random lines,'' Journal of Algo
- division,'' SIAM Journal on Computing, vol. 18, 1989, pp. 811830. [QS90] Quak, E. and Schumaker, L. L., ``Cubic spline fitting using data dependent triangu
- [He] Helly, E., ``Uber Mengen konvexer Korper mit gemeinshaftlichen Punkten,'' Jber. Deut sch. Math. Verein. vol. 32, 1923, 175176.
- Scripta Mathematica, vol. 14, 1948, pp. 189264. [Si1756] Simson, R., Los Seis Primeros Libros, y el Undcimo, y Duodcimo de los Elementos
- Computational Theoryand Applications
- Mathematical Notation, Representation, and Visualization of Musical Rhythm: A Comparative Perspective
- Camp. & Morhs. with A&T Vol. 9. No. 6. pp. 747-754. 1983 Pnnted m Great Bntain.
- Geometry, to appear in 1991. [To92] Toussaint, G. T., ed., Proceedings of the IEEE, Special Issue on Computational Geo-
- Implicit Convex Polygons Francisco G omez 1 Ferran Hurtado 2 Suneeta Ramaswami 3 Vera Sacrist an 2
- On Removing Extrinsic Degeneracies in Computational Geometry \Lambda
- OUTPUT-SENSITIVE ALGORITHMS FOR COMPUTING NEAREST-NEIGHBOUR DECISION BOUNDARIES
- An Efficient Algorithm for Decomposing a Polygon into Star-Shaped PolygonsDecember 9, 1999 1 An Efficient Algorithm for Decomposing a