SMI 2012
Shape Modeling International 2012
May 22-25 2012
College Station, Texas, USA
Technical Papers Sculpting/Fabrication Papers Courses Exhibition
Technical Paper Submission Sculpting/Fabrication Papers Course Submission Submission for Exhibition
Venue Registration Travel Accomodations
Presentation Videos Conference Program
Technical Papers Committee Sculpting/Fabrication Committee Courses Committee Exhibition Committee
Helmut Pottman Greg N. Frederickson Carlo Séquin
SMI'2013, Bournemouth, GB SMI'2011, Herzia, Israel SMI'2010, Aix-En Provence, France SMI'2009, Beinjin, China SMI'2008, Stony Brook, NW, USA SMI'2007, Lyon, France SMI'2006, Matsushima, Japan SMI'2005, Cambridge, MA, USA SMI'2004, Genova, Italy SMI'2003, Seoul Korea SMI'2002, Banff, Alberta, Canada SMI'2001, Genoa, Italy SMI'1999, Aizu, Japan SMI'1997, Aizu, Japan Shape Modeling 1994, Aizu, Japan

Keynote Speaker

Greg N. Frederickson

Beyond Swinging: Hinged Dissections that Twist or Fold

A geometric dissection is a cutting of a geometric figure into pieces that can be rearranged to form another figure. Some dissections can be connected with hinges so that the pieces form one figure when swung one way on the hinges, and form the other figure when swung another way. In addition to using "swing hinges", which allow rotation in the plane, we can use "twist hinges", which allow one piece to be flipped over relative to another piece via rotation by 180 degrees through a third dimension. Furthermore, we can use "fold hinges", which allow rotation along a shared edge, a motion that is akin to folding.

This talk will introduce a variety of twist-hinged and fold-hinged dissections of regular polygons and stars, and other figures such as polyominoes. The emphasis will be on both appreciating and understanding these fascinating mathematical recreations. I will employ algorithmic and tessellation-based techniques, as well as symmetry and other geometric properties, to design the dissections. The goal will be to minimize the number of pieces, subject to the dissection being suitably hinged. Animations and video will be used to demonstrate the hinged dissections, in addition to actual physical models.

Short Biography

Greg N. Frederickson is a Professor of Computer Science at Purdue University, in West Lafayette, Indiana. His primary area of research is the design and analysis of algorithms, and he has served on the editorial boards of SIAM Journal on Computing, SIAM Journal on Discrete Mathematics, Algorithmica, and IEEE Transactions on Computers. He also pursues interests in mathematical recreations, specifically geometric dissection. On this topic he has published three books and a number of articles. He has twice won the George Polya Award from the Mathematical Association of America.

The Bridges Organization:
Art and Mathematics
ISAMA: The international Society of the Arts, Mathematics and Architecture

Texas A&M University
College of Architecture
Texas A&M University
Visualization Department
Texas A&M University
Computer Science Department