Gill Barequet's
A picture taken many years ago -
now I have much smaller glasses...;
"Barequet" is the biblic word for
emerald (Be3Al2(SiO3)6::Cr) !
Gill Barequet's home page 4.5

barequet at cs dot technion dot ac dot il

Arabic name     x     Hebrew name


Vice Dean for Graduate Studies
Dept. of Computer Science
Technion - Israel Inst. of Technology

Former Vice Dean for Curriculum (CS Dept.), 2014-2017
Former Head of the CGGC (Center for Graphics and Geometric Computing), 2001-2014

[CGGC seminar program; brochure;
articles: Technion Focus (1/2002), Technion Magazine (3/2002), CS Homepage Magazine (2/2009)]

Hot News

(24/Jul/2023) Shauli was very right (in Hebrew)

(24/Aug/2020) Prof. Lowenstein (a.k.a. as "Prof") is the manager of the ophthalmology (eyes) department of Ichilov hospital in Tel Aviv. A lady named Ilanit, the public-inquiries coordinator of the hopital, forwarded to Prof an inquiry about Dana, a resident (מתמחה) at the department, who also happens to be my daughter!

(10/Mar/2020)      λ < 4.5252      (Klarner's constant)
Trying hard to fix a miserable bug I had a few years ago (see below), my former PhD student Mira Shalah and I showed that λ (Klarner's constant) is strictly less than 4.53. As a byproduct, we imrpoved significantly the upper bound on λ3 to 9.39, and found a general method for setting an efficient lower bound in any dimension.

(31/Jan/2020) Yet another Technion CS team, Volodymyr Polosukhin, Artem Shtefan, Evgenii Zheltonozhskii, and coaches Nofar Carmeli and Gil Ben-Shachar, and supposedly under my virtual supervision, did well and won bronze medals (11th place out of 95) in the prestigious ICPC contest (Southwestern Europe region) held in January 26, 2020 in Paris, France.

(28/Jan/2019) My former Ph.D. student Mira Shalah appears in Forbes list of the 30 most promising young researchers.

(27/Nov/2017) One more Technion CS team, Dean Leitersdorf, Volodymyr Polosukhin, Artem Shtefan, and Coach Eden Saig, and under my virtual supervision, performed extremely well and won silver medals (6th place out of 75) in the prestigious ACM/ICPC contest (Southwestern Europe region) held in November 26, 2017 in Paris, France.

(11/Feb/2016) Günter Rote found a gap in the proof of the upper bound on λ claimed below; We are working on fixing the proof...

(16/Dec/2015)       λ < 4.5685       (Klarner's constant)
A new upper bound on λ (4.5685) was obtained; see paper in EuroComb'15. A few more tricks reduced the bound further, and it continues to go down.

(20/Nov/2013) Again, the Technion CS team, Roei Gelbhart, Alexander Goltman, Oleg Zlotnik, and under my virtual supervision, performed very nicely, winning this time bronze medals (10th place out of 44) in the prestigious ACM/ICPC contest (Southwestern Europe region) held in November 17, 2013 in Valencia, Spain.

(23/May/2013)      λ > 4.0025      (Klarner's constant)
Closing a 10-year effort, Günter Rote and I showed that the leading decimal digit of λ (Klarner's constant, the asymptotic growth rate [or growth constant] of site animals in the planar cubical lattice) is 4. My Ph.D. student Mira Shalah participated in the last step of this research. See more details here.

(23/Nov/2012) Once again, the Technion CS team, Idan Elad, Olivier Hofman, and Mike Harris, with its coach Noa Korner and under my virtual supervision, performed nicely, winning this time bronze medals (12th place) in the prestigious ACM/ICPC contest (Southwestern Europe region) held in November 18, 2012 in Valencia, Spain.

(22/Nov/2010) The Technion CS team, Shahar Papini, Yaniv Sabo, and Carmi Grushko, with its coach Kolman Vornovitsky and under my supervision, won gold medals (2nd place) in the prestigious ACM/ICPC contest (Southwestern Europe region) held in November 21, 2010 in Madrid, Spain. (Shahar almost did not compete since he lost both his passport and his contest badge. Worldwide efforts to restore both items were successful.)

(04/Mar/2009) The Technion awarded me the Henri Taub prize for academic excellence for a few polyomino and polycube-related works. (The background of the picture in the above link is completely unrelated to the things I do. 8-)

Information for Prospective Graduate Students

x Just want to be a CGGC student and then decide? Click Here.
x Would like to consider a thesis topic in Computational Geometry? Take my Computational Geometry course and send me a message!
x Here is a nice research problem for a thesis: Read this paper (journal #26) and rethink about the 3D case. Can it be improved to Ω(1/n³) by sharpening the argument for the inner-most cylinder?
x For perspective, here is (completely out of context!) how Eli O'Hana was quoted in Yediot Akhronot in an interview in May 1999.

Major Interests

x Computational geometry
x Graph theory and combinatorics
x Discrete mathematics
x Geometric and solid modeling
x Geometric algorithms for medical imaging
x Geometric algorithms for computer graphics
Lungs Heart

Current Research

x Polyominoes and polycubes: x The running time of Jensen's Algorithm x λ (Klarner's constants) ≥ 3.9801 x Redelmeier's algorithm on any lattice x Redelmeier's algorithm without the dimensionality curse x Formulas enumerating polycubes x Tree-like convex polyominoes x Exact formula for DX(n,n-3) x Permutations count polyominoes on twisted cylinders x Growth constant of tree polycubes x λ (Klarner's constants) ≥ 4 (!)
x Object reconstruction from slices: x Geometric-hashing algorithm x Context-enabled interpolation x Smooth blending of slices x Straight-skeleton algorithm x Matability of polygons x Moving polygons around x Nonplanar interpolation x Multicolor interpolation

Biographic Details

Here are links to a short résumé and a list of publications.
My academic genealogy goes back to Gauss, Bessel, and Weierstrass.

Post-Doctoral Fellows:

Graduate Students

  1. Eyal Ackerman (Ph.D., Computer Science, secondary advisor: R.Y. Pinter)
    Counting problems for geometric structures: Rectangulations, floorplans, and quasi-planar graphs
    (dissertation; defense held September 3, 2006; now [8/2023] at Haifa University at Oranim, Israel)
    M.Sc. in Sciences obtained while passing the Ph.D.-candidacy exam in the direct track, January 1, 2004
  2. Amir Vaxman (Ph.D., Computer Science)
    General techniques for interpolation, reconstruction, and morphing of polyhedral surfaces
    (dissertation; defense held April 3, 2011; now [8/2023] at Univ. of Edinburgh, UK)
  3. Gadi Aleksandrowicz (Ph.D., Computer Science)
    Enumeration of lattice animals
    (dissertation; defense held July 17, 2011; now [8/2023] at IBM Research Labs, Haifa, Israel)
    M.Sc. in Sciences obtained while passing the Ph.D.-candidacy exam in the direct track, March 9, 2008
  4. Mira Shalah (Ph.D., Computer Science)
    Formulae and growth rates of animals on cubical and triangular lattices
    (dissertation; defense held October 15, 2017; now [8/2023] co-founder and CTO, BeautAI)
    M.Sc. in Sciences obtained while passing the Ph.D.-candidacy exam in the direct track, May 4, 2015
  5. Gil Ben-Shachar (Ph.D., Computer Science)
    Extremal properties of polyominoes
    (dissertation; defense held December 4, 2022; now [8/2023] at Sparkware Technologies)
    M.Sc. in Sciences obtained while passing the Ph.D.-candidacy exam in the direct track, December 24, 2018
  1. Vadim Makhervaks (M.Sc., Mathematics, primary advisor: A. Bruckstein)
    Image flows and one-liner graphical image representations
    (thesis; defense held November 5, 2002; now [8/2023] at Microsoft, Seattle, WA)
  2. Daniel Brunstein (M.Sc., Computer Science, secondary advisor: C. Gotsman)
    Animating a camera for viewing a planar polygon
    (thesis; defense held June 18, 2003; now [8/2023] at Intel, Haifa, Israel)
  3. Vadim Rogol (M.Sc., Electrical Engineering)
    Maximizing the area of an axially-symmetric polygon inscribed by a simple polygon
    (thesis; defense held June 30, 2003; now [8/2023] at General Electric, Tirat Carmel, Israel)
  4. Micha Moffie (M.Sc., Computer Science)
    Counting polyominoes in two and three dimensions
    (thesis; defense held December 31, 2003; now [8/2023] at IBM Research Labs, Haifa, Israel)
  5. Evgeny Yakersberg (M.Sc., Computer Science)
    Morphing between geometric shapes using straight-skeleton-based interpolation
    (thesis; defense held May 14, 2004; now [1/2012] self-employed in Pattaya, Thailand)
  6. Yuval Scharf (M.Sc., Computer Science)
    Covering points with a polygon
    (thesis; defense held September 27, 2004; now [8/2023] in San Francisco, CA)
  7. Aya Steiner (M.Sc., Mathematics)
    Matability of polygons
    (thesis; defense held February 28, 2005; now [2016] in Haifa, Israel)
  8. Alex Goryachev (M.Sc., Computer Science)
    Offset polygon and annulus placement problems
    (thesis; defense held November 16, 2005; now [4/2013] at IBM Research Labs, Haifa, Israel)
  9. Dimitry Kloper (M.Sc., Computer Science, secondary advisor: with C. Gotsman)
    Geometries and topologies of triangulations of point sets
    (thesis; defense held December 21, 2005; now [8/2023] at Intel, Haifa, Israel)
  10. David Hodorkovsky (M.Sc., Mathematics)
    2-point site Voronoi diagrams
    (thesis; defense held December 22, 2005; now [9/2011] at Imagine, Natanya, Israel)
  11. Jonathan Naor (M.Sc., Computer Science)
    d-dimensional variants of Heilbronn's triangle problem
    (thesis; defense held January 8, 2006; now [9/2011] at Elbit Systems, Haifa, Israel)
  12. Avishay Sidlesky (M.Sc., Computer Science, secondary advisor: C. Gotsman)
    Polygon reconstruction from line cross-sections
    (thesis; defense held June 11, 2006; now [9/2023] at VTM Technologies, Atlit, Israel)
  13. Amir Vaxman (M.Sc., Computer Science)
    Nonlinear interpolation between slices
    (thesis; defense held November 22, 2006; see also a Ph.D. entry)
  14. Alina Shaikhet (M.Sc., Computer Science)
    The on-line Heilbronn's triangle problem in d dimensions
    (thesis; defense held June 20, 2007; now [8/2023] at Carleton University, Ottawa, Canada)
  15. Alik Zamansky (M.Sc., Computer Science)
    A framework for surface reconstruction of sparsely-sampled objects
    (thesis; defense held June 26, 2007; now [10/2011] at BIRD Aerosystems, Herzlia, Israel)
  16. Asenath Tal (M.Sc., Computer Science)
    Algorithms for Heilbronn's triangle problem
    (thesis; defense held April 19, 2009; now [9/2023] at Sisense, Tel Aviv, Israel)
  17. Shahar Tal (M.Sc., Computer Science, The Open University)
    Solving general lattice puzzles
    (thesis; defense held May 1, 2011; now [3/2023] at HP, Israel)
  18. Raeda Naamnieh (M.Sc., Computer Science)
    Fair multi-label reconstruction from cross-sections
    (thesis; defense held November 7, 2013; now [9/2023] at Google, Israel)
  19. Abraham Stiefel (M.Sc., Computer Science)
    Motion planning in the presence of mobile obstacles
    (thesis; defense held October 26, 2015; now [9/2023] at Momentis Surgical, Or Yehuda, Israel)
  20. Yufei Zheng (M.Sc., Computer Science)
    Two researches on lattice animals
    (thesis; defense held June 27, 2018; now [8/2023] a Ph.D. student at Princeton, NJ)
  21. Bar Magal (M.Sc., Computer Science)
    Enumerating polyominoes with fixed perimeter defect
    (thesis; defense held September 1, 2021; now [8/2023] at Exodigo, Tel Aviv, Israel)
  22. Matan Eyn-Avi (M.Sc., Computer Science)
    A new lower bound on the growth constant of polycubes in three dimensions
    (thesis; defense held September 12, 2022; now [8/2023] at IDF)
  23. Amani Shhadi (M.Sc., Computer Science)
    Topology-controlled reconstruction from partial planar cross-sections
    (thesis; defense held September 12, 2022; now [9/2023] at Qualcomm, Haifa, Israel)
  24. Antoine Vinciguerra (M.Sc., Computer Science)
    On the structure of Heilbronn's configurations
    (thesis; defense held October 23, 2022; now [8/2023] a Ph.D. student at The Technion, Haifa, Israel)

Publicly-Available Resources

x My electronic collection of human organs and digital terrains (in polygonal-slices format), and related software
x My partial surface matching and object registration software
x My polyhedral environment and database software (DCEL)
x Software for approximating the minimum-volume bounding box of a spatial point set (with Sariel Har-Peled)


x Computational Geometry (236719, announcement)
x Project in Copmutational Geometry (236729)
x Discrete Algorithmic Geometry (238739)
x Seminar in Discrete Geometry (236831)
x Computer Graphics 1 (234325)
x Introduction to System Programming (234122)

Courses I Teach in the Current Semester (2016-17 I תשע"ז)

  1. Computational Geometry (236719, Tuesday 12:30-14:30, Taub ??)
  2. Introduction to System Programming (234122, Monday 12:30-14:30, Taub ??)
  3. Project in Computational Geometry (236729, continuously)

Where did I come from?

x PhD and Postdoc, CS, Tel Aviv University (Tel Aviv, Israel, 1991-96)
x Postdoc, CS, Johns Hopkins University (Baltimore, MD, 1996-98)
x Sabbatical, CS, Tufts University (Medford, MA, 2009-10)


Office address:

Dept. of Computer Science
     (New Taub bldg., fl. 4, rm. 430)
Technion---Israel Inst. of Technology
Haifa 32000
x   +972 (4) 829-3219 x (ask Inbal below)
  x   (center) +972 (4) 829-5538     (dept.) +972 (4) 829-3900

CGGC administrative assistant:

Inbal Barazani
New Taub bldg., fl. 4, rm. 427
x phone: +972 (4) 829-4906; fax: +972 (4) 829-5538

View in and from the Technion:

The new Taub building, hosting the department of computer science:
(Click on the picture to see it full sized)
Taub bldg. at night Taub bldg. during the day
When the visibility is perfect, this is how the Hermon mountain (60 miles [96.5 KM] from Haifa) is seen from my office:
(Click on the picture to see the full sight [Dani B., 07/01/2003],
and a new picture shot ten years later [Mira S., 29/01/2013])
Hermon picture shot January 7, 2003

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