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

barequet at cs dot technion dot ac dot il

Arabic name         Hebrew name

Associate Professor and Vice Dean, Dept. of Computer Science
Head of the CS Curriculum Committee
Technion - Israel Inst. of Technology
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

(11/Feb/16) 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/15)       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/13) Again, the Technion CS team, Roei Gelbhart, Alexander Goltman, Oleg Zlotnik, and under my virtual supervision, performed very nicely, winning this time a bronze medal (10th place out of 44) in the prestigious ACM/ICPC contest (Southwestern Europe region) held in November 17, 2013 in Valencia, Spain.

(23/May/13)       λ > 4.0025       (Klarner's constant)
Closing a 10-year effort, Günter Rote and I showed that the leading decomal 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/12) 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 a bronze medal (12th place) in the prestigious ACM/ICPC contest (Southwestern Europe region) held in November 18, 2012 in Valencia, Spain.

(22/Nov/10) The Technion CS team, Shahar Papini, Yaniv Sabo, and Carmi Grushko, with its coach Kolman Vornovitsky and under my supervision, won a gold medal (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/09) 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

Just want to be a CGGC student and then decide? Click Here.
Would like to consider a thesis topic in Computational Geometry? Take my Computational Geometry course and send me a message!
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?
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

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

Current Research

Polyominoes and polycubes: The running time of Jensen's Algorithm λ (Klarner's constants) ≥ 3.9801 Redelmeier's algorithm on any lattice Redelmeier's algorithm without the dimensionality curse Formulas enumerating polycubes Tree-like convex polyominoes Exact formula for DX(n,n-3) Permutations count polyominoes on twisted cylinders Growth constant of tree polycubes λ (Klarner's constants) ≥ 4 (!)
Object reconstruction from slices: Geometric-hashing algorithm Context-enabled interpolation Smooth blending of slices Straight-skeleton algorithm Matability of polygons Moving polygons around Nonplanar interpolation 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 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 at Vienna University of Technology, Austria)
  3. Gadi Aleksandrowicz (Ph.D., Computer Science)
    Enumeration of lattice animals
    (dissertation; defense held July 17, 2011; now 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
  1. Vadim Makhervaks (M.Sc., Mathematics, primary advisor: A. Bruckstein)
    Image flows and one-liner graphical image representations
    (thesis; defense held November 5, 2002)
  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 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 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 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 in Pattaya, Thailand)
  6. Yuval Scharf (M.Sc., Computer Science)
    Covering points with a polygon
    (thesis; defense held September 27, 2004; now in Mountain View, CA)
  7. Aya Steiner (M.Sc., Mathematics)
    Matability of polygons
    (thesis; defense held February 28, 2005; now in Haifa, Israel)
  8. Alex Goryachev (M.Sc., Computer Science)
    Offset polygon and annulus placement problems
    (thesis; defense held November 16, 2005; now 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 at Microsoft, Haifa, Israel)
  10. David Hodorkovsky (M.Sc., Mathematics)
    2-point site Voronoi diagrams
    (thesis; defense held December 22, 2005; now 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 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)
  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 in 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 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 at Red Bend Software, Hod HaSharon, Israel)
  17. Shahar Tal (M.Sc., Computer Science, The Open University)
    Solving general lattice puzzles
    (thesis; defense held May 1, 2011; now at HP, Israel)
  18. Raeda Naamnieh (M.Sc., Computer Science)
    Fair multi-label reconstruction from cross-sections
    (thesis; defense held November 7, 2013)
  19. Abraham Stiefel (M.Sc., Computer Science)
    Motion planning in the presence of mobile obstacles
    (thesis; defense held October 26, 2015)
In progress:
  1. Mira Shalah (Ph.D., Computer Science)
    On the growth constants of polyominoes and polycubes
  2. Yufei Zheng (M.Sc., Computer Science)

Publicly-Available Resources

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


Computational Geometry (236719, announcement):
       Fall 15-16, Fall 14-15, Fall 12-13, Fall 11-12, Fall 10-11, Fall 09-10 (Tufts University), Fall 08-09, Spring 07-08, Spring 06-07, Spring 05-06, Spring 04-05, Spring 03-04, Fall 02-03, Spring 01-02, Spring 00-01, Spring 99-00 (236603), Spring 98-99 (236601)

Project in Copmutational Geometry (236729):
       Continuously (Technion), Fall 95-96 (TAU, project)

Discrete Algorithmic Geometry (238739):
       Spring 15-16, Spring 14-15, Spring 12-13, Spring 10-11, Fall 07-08 (236739), Fall 05-06 (236604), Spring 02-03 (236601)

Advanced Seminar on Geometric Computing:
       Graphics: Spring 01-02 (236801)
       Object reconstruction: Fall 06-07 (236801), Spring 04-05 (236801), Spring 03-04 (236801), Spring 95-96 (TAU)
       Polyominoes and polycubes: Fall 15-16 (236803), Fall 14-15 (236804), Spring 11-12 (236801), Fall 08-09 (236803)

Computer Graphics 1 (234325):
       Fall 03-04

Introduction to System Programming (234122):
       Fall 16-17, Fall 13-14, Fall 12-13, Fall 11-12, Fall 10-11, Spring 09-10, Spring 08-09, Fall 07-08, Fall 06-07, Fall 05-06, Fall 04-05, Fall 03-04, Fall 02-03, Fall 01-02, Fall 00-01, Fall 99-00, Fall 98-99, Spring 94-95 (TAU), Fall 94-95 (TAU), Spring 93-94 (TAU)

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?

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

Office address:

Dept. of Computer Science
     (New Taub bldg., fl. 4, rm. 428)
Technion---Israel Inst. of Technology
Haifa 32000
  +972 (4) 829-3219 (ask Inbal below)
    (center) +972 (4) 829-5538     (dept.) +972 (4) 829-3900

CGGC administrative assistant:

Inbal Barazani
New Taub bldg., fl. 4, rm. 427
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

You are viewer number     (and counting) of this page.

Your comment:

to let Gill know this!

    Stop/Resume These Annoying Moving Colored Balloons!