Associate Professor Gill Barequet
 Contact information
 Homepage:
 http://www.cs.technion.ac.il/~barequet/
 Email:
 barequetcs.technion.ac.il
 Office:
 428
 Phone:
 3219
 Office Hours:
 By appointmen via email
 Research interests
 Discrete and computational geometry; geometric computing; combinatorics;computeraided geometric design; computer graphics and visualization.
 Selected publications

Book Chapters
 G. Barequet, Geometric hashing and its applications, in: Database and Data Communication Network Systems: Techniques and Applications (C.T. Leondes, ed.), vol. I, ch. 8, pp. 277287, Elsevier, June 2002. (.ps.gz 85K)
 G. Barequet, Computer techniques and applications in rapid prototyping, in: Computer Aided and Integrated Manufacturing Systems (C.T. Leondes, ed.), vol. 4 (CAD/CAM), ch. 6, pp. 281295, World Scientific Publishing Co., September 2003. (.ps.gz 247K)
 G. Barequet, S.W. Golomb, and D.A. Klarner, Polyominoes, in: Handbook of Discrete and Computational Geometry (E. Goodman, J. O'Rourke, and C.D. Tóth, eds.), 3rd ed., Chapman and Hall/CRC, expected 2016.
Journal Papers
 G. Barequet and M. Sharir, Filling gaps in the boundary of a polyhedron, ComputerAided Geometric Design (CAGD), 12 (2), 207229, March 1995.
 G. Barequet and M. Sharir, Piecewiselinear interpolation between polygonal slices, Computer Vision and Image Understanding (CVIU), 63 (2), 251272, March 1996.
 G. Barequet, B. Chazelle, L.J. Guibas, J.S.B. Mitchell, and A. Tal, BOXTREE: A hierarchical representation for surfaces in 3D, Computer Graphics Forum (CGF), 15 (3), C387396, August 1996.
 G. Barequet and M. Sharir, Partial surface and volume matching in three dimensions, IEEE Trans. on Pattern Analysis and Machine Intelligence (TPAMI), 19 (9), 929948, September 1997.
 G. Barequet, M. Dickerson, and P. Pau, Translating a convex polygon to contain a maximum number of points, Computational Geometry: Theory and Applications (CGTA), 8 (4), 167179, September 1997.
 G. Barequet, Using geometric hashing to repair CAD objects, IEEE Computational Science & Engineering (CS&E), 4 (4), 2228, OctoberDecember 1997.
 G. Barequet and Y. Kaplan, A data frontend for layered manufacturing, ComputerAided Design (CAD), 30 (4), 231243, April 1998.
 G. Barequet, C.A. Duncan, and S. Kumar, RSVP: A geometric toolkit for controlled repair of solid models, IEEE Trans. on Visualization and Computer Graphics (TVCG), 4 (2), 162177, AprilJune 1998.
 G. Barequet and B. Wolfers, Optimizing a strip separating two polygons, Graphical Models and Image Processing (GMIP), 60 (3), 214221, May 1998.
 G. Barequet, M. Dickerson, and D. Eppstein, On triangulating threedimensional polygons, Computational Geometry: Theory and Applications (CGTA), 10 (3), 155170, June 1998.
 G. Barequet, DCEL: A polyhedral database and programming environment, Int. J. of Computational Geometry and Applications (IJCGA), 8 (56), 619636, OctoberDecember 1998.
 G. Barequet, A.J. Briggs, M.T. Dickerson, and M.T. Goodrich, Offsetpolygon annulus placement problems, Computational Geometry: Theory and Applications (CGTA), 11 (34), 125141, December 1998.
 G. Barequet and M. Sharir, Partial surface matching by using directed footprints, Computational Geometry: Theory and Applications (CGTA), 12 (12), 4562, February 1999.
 G. Barequet, C.A. Duncan, M.T. Goodrich, S.S. Bridgeman, and R. Tamassia, GeomNet: Geometric computing over the Internet, IEEE Internet Computing (IC), 3 (2), 2129, MarchApril 1999.
 G. Barequet, D. Shapiro, and A. Tal, Multilevel sensitive reconstruction of polyhedral surfaces from parallel slices, The Visual Computer (TVC), 16 (2), 116133, March 2000.
 G. Barequet and S. HarPeled, Efficiently approximating the minimumvolume bounding box of a point set in three dimensions, J. of Algorithms (JoA), 38 (1), 91109, January 2001.
 G. Barequet, M.T. Dickerson, and M.T. Goodrich, Voronoi diagrams for polygonoffset distance functions, Discrete & Computational Geometry (DCG), 25 (2), 271291, January 2001.
 T. Surazhsky, V. Surazhsky, G. Barequet, and A. Tal, Metamorphosis of polygonal shapes with different topologies, Computers & Graphics (C&G), 25 (1), 2939, February 2001.
 G. Barequet, A lower bound for Heilbronn's triangle problem in d dimensions, SIAM J. on Discrete Mathematics (SIDMA), 14 (2), 230236, 2001.
 G. Barequet, A duality between smallface problems in arrangements of lines and Heilbronntype problems, Discrete Mathematics (DM), 237 (13), 112, June 2001.
 G. Elber, G. Barequet, and M.S. Kim, Bisectors and αsectors of rational varieties, Computing (Suppl.), in: Geometric Modelling (G. Brunnett, H. Bieri, and G. Farin, eds.), 14, 7388, 2001, SpringerVerlag, Wien.
 G. Barequet and S. HarPeled, Polygoncontainment and translational minHausdorffdistance between segment sets are 3SUMhard, Int. J. of Computational Geometry and Applications (IJCGA), 11 (4), 465474, August 2001.
 G. Barequet, D.Z. Chen, O. Daescu, M.T. Goodrich, and J. Snoeyink, Efficiently approximating polygonal paths in three and higher dimensions, Algorithmica (ALG), 33 (2), 150167, January 2002.
 V. Makhervaks, G. Barequet, and A. Bruckstein, Image flows and oneliner graphical image representation, in: Visualization and Imaging in Transport Phenomena (S. Sideman and A. Landesberg, eds.), Anals of the New York Academy of Sciences (NYAS), 972, 1018, October 2002.
 G. Barequet, M.T. Dickerson, and R.L.S. Drysdale, 2point site Voronoi diagrams, Discrete Applied Mathematics (DAM), 122 (13), 3754, October 2002.
 G. Barequet, The online Heilbronn's triangle problem, Discrete Mathematics (DM), 283 (13), 714, June 2004.
 G. Barequet, M.T. Goodrich, A. LeviSteiner, and D. Steiner, Contour interpolation by straight skeletons, Graphical Models (GM), 66 (4), 245260, July 2004.
 G. Barequet, M.T. Goodrich, and C. Riley, Drawing planar graphs with large vertices and thick edges, J. of Graph Algorithms and Applications (JGAA), 8 (1), 320, 2004.
 G. Barequet and G. Elber, Optimal bounding cones of vectors in three dimensions, Information Processing Letters (IPL), 93 (1), 8389, January 2005.
 G. Barequet, P. Bose, M.T. Dickerson, and M.T. Goodrich, Optimizing a constrained convex polygonal annulus, J. of Discrete Algorithms (JDA), 3 (1), 126, March 2005.
 G. Barequet, G. Elber, and M.S. Kim, Computing the minimum enclosing circle of a set of planar curves, ComputerAided Design and Applications (CADA), 2 (14), 301308, June 2005.
 E. Ackerman, G. Barequet, R.Y. Pinter, and D. Romik, The number of guillotine partitions in d dimensions, Information Processing Letters (IPL), 98 (4), 162167, May 2006.
 E. Ackerman, G. Barequet, and R.Y. Pinter, A bijection between permutations and floorplans, and its applications, Discrete Applied Mathematics (DAM), 154 (12), 16741685, July 2006.
 E. Ackerman, G. Barequet, and R.Y. Pinter, On the number of rectangulations of a planar point set, J. of Combinatorial Theory, Series A (JCTA), 113 (6), 10721091, August 2006.
 G. Barequet and J. Naor, Large kD simplices in the ddimensional unit cube, Far East J. of Applied Mathematics (FJAM), 24 (3), 343354, September 2006.
 G. Barequet, M. Moffie, A. Ribó, and G. Rote, Counting polyominoes on twisted cylinders, Integers: Electronic J. of Combinatorial Number Theory (INT), 6, #A22, 37 pp., September 2006.
 G. Barequet and V. Rogol, Maximizing the area of an axiallysymmetric polygon inscribed in a simple polygon, Computers & Graphics (C&G), 31 (1), 127136, January 2007.
 G. Barequet and M. Moffie, On the complexity of Jensen's algorithm for counting fixed polyominoes, J. of Discrete Algorithms (JDA), 5 (2), 348355, June 2007.
 G. Barequet and A. Shaikhet, The online Heilbronn's triangle problem in d dimensions, Discrete & Computational Geometry (DCG), 38 (1), 5160, July 2007.
 G. Barequet, M.T. Dickerson, and Y. Scharf, Covering points with a polygon, Computational Geometry: Theory and Applications (CGTA), 39 (3), 143162, April 2008.
 G. Barequet and A. Vaxman, Nonlinear interpolation between slices, Int. J. of Shape Modeling (IJSM), 14 (1), 3960, June 2008.
 G. Barequet and A. Steiner, On the matability of polygons, Int. J. of Computational Geometry and Applications (IJCGA), 18 (5), 469506, October 2008.
 G. Aleksandrowicz and G. Barequet, Counting ddimensional polycubes and nonrectangular planar polyominoes, Int. J. of Computational Geometry and Applications (IJCGA), 19 (3), 215229, June 2009.
 G. Aleksandrowicz and G. Barequet, Counting polycubes without the dimensionality curse, Discrete Mathematics (DM), 309 (13), pp. 45764583, July 2009.
 G. Barequet and A. Vaxman, Reconstruction of multilabel domains from partial planar crosssections, Computer Graphics Forum (CGF), 28 (5), 13271337, July 2009.
 R. Barequet, G. Barequet, and G. Rote, Formulae and growth rates of highdimensional polycubes, Combintorica (COMB), 30 (3), 257275, May 2010.
 S. Biasotti, G. Patanè, M. Spagnuolo, B. Falcidieno, and G. Barequet, Shape approximation by differential properties of scalar functions, Computers & Graphics (C&G), 34 (3) 252262, June 2010.
 I. Hanniel and G. Barequet, On the triangleperimeter twosite Voronoi diagram, Trans. on Computational Science (TCS), IX, Lecture Notes in Computer Science, 6290, SpringerVerlag, 5475, 2010.
 R. Muthuganapathy, G. Elber, G. Barequet, and M.S. Kim, Computing the minimum enclosing sphere of freeform hypersurfaces in arbitrary dimensions, ComputerAided Design (CAD), 43 (3), 247257, March 2011.
 K. Vyatkina and G. Barequet, On multiplicatively weighted Voronoi diagrams for lines in the plane, Trans. on Computational Science (TCS), XIII, Lecture Notes in Computer Science, 6750, SpringerVerlag, 4471, 2011.
 G. Aleksandrowicz, A. Asinowski, and G. Barequet, A polyominoespermutations injection and treelike convex polyominoes, J. of Combinatorial Theory, Series A (JCTA), 119 (3), 503520, April 2012.
 A. Asinowski, G. Barequet, R. Barequet, and G. Rote, Proper ncell polycubes in n3 dimensions, J. of Integer Sequences (JIS), 15, #12.8.4, 16 pp., October 2012.
 M. AlJubeh, G. Barequet, M. Ishaque, D.L. Souvaine, C.D. Tóth, and A. Winslow, Constrained triconnected planar straight line graphs, in: Thirty Essays on Geometric Graph Theory (J. Pach, ed.), Springer, 4970, 2013.
 G. Barequet, N. Benbernou, D. Charlton, E.D. Demaine, M.L. Demaine, M. Ishaque, A. Lubiw, A. Schulz, D.L. Souvaine, G.T. Toussaint, and A. Winslow, Boundeddegree polyhedronization of point sets, Computational Geometry: Theory and Applications (CGTA), 46 (2), 148153, February 2013.
 G. Barequet, M.T. Dickerson, D. Eppstein, D. Hodorkovsky, and K. Vyatkina, On 2site Voronoi diagrams under geometric distance functions, J. of Computer Science and Technology (JCST), 28 (2), 267277, March 2013.
 G. Aleksandrowicz, A. Asinowski, and G. Barequet, Permutations with forbidden patterns and polyominoes on a twisted cylinder of width 3, Discrete Mathematics (DM), 313 (10), 10781086, May 2013.
 A. Asinowski, G. Barequet, M. BousquetMélou, T. Mansour, and R.Y. Pinter, Orders induced by segments in floorplan partitions and (2143,3412)avoiding permutations, Electronic J. of Combinatorics (ElJC), 20 (2), #P35, 43 pp., May 2013.
 G. Aleksandrowicz and G. Barequet, The growth rate of highdimensional tree polycubes, European J. of Combinatorics (EuJC), 35, 3238, January 2014.
 G. Barequet and A. Goryachev, Offset polygon and annulus placement problems, Computational Geometry: Theory and Applications (CGTA), 47 (3), 407434, April 2014.
 A. Asinowski, G. Barequet, T. Mansour, and R.Y. Pinter, Cut equivalence of ddimensional guillotine partitions, Discrete Mathematics (DM), 331, 165173, November 2014.
 G. Barequet, G. Rote, and M. Shalah, λ > 4: An improved lower bound on the growth constant of polyominoes, Comm. of the ACM (CACM), 59 (7), July 2016, to appear.
 G. Barequet, S.M. Cannon, E. FoxEpstein, B. Hescott, D.L. Souvaine, C.D. Tóth, and A. Winslow, Diffuse reflection diameter in simple polygons, Discrete Applied Mathematics (DAM), accepted.
 E. Ackerman, M. Allen, G. Barequet, M. Löffler, J. Mermelstein, D.L. Souvaine, and C.D. Tóth, The flip diameter of rectangulations and convex subdivisions, Discrete Mathematics and Theoretical Computer Science (DMTCS), accepted.
 Center for Graphics and Geometric Computing
 Head of the CGGC (Center for Graphics and Geometric Computing) from October 2001 to March 2014.