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Research

My research is in the areas of computational geometry and computer science education. My current interests include algorithms for reconfiguring modular robots, placement of wireless transmitters, and polyhedra unfolding. The animation below is from some previous work on sequential triangulations. It shows a two guard walk around a polygon and the corresponding sequential triangulation that it produces. Click here to see some tools I've developed with students for teaching computer graphics concepts. I also do a lot of independent studies with undergraduates, so check out their projects too.



Publications

"Unfolding orthogonal polyhedra with quadratic refinement: The delta-unfolding algorithm," M. Damian, Erik Demaine, and R. Flatland. Graphs and Combinatorics, 30(1):125-140, 2014.

"Spanning Properties of Graphs Induced by Directional Antennas," M. Damian and R. Flatland. Discrete Mathematics, Algorithms and Applications, 5(3):1-16, 2013.

"Switching to directional antennas with constant increase in radius and hop distance," Prosenjit Bose, Paz Carmi, Mirela Damian, Robin Flatland, Matthew Katz, and Anil Maheshwari. Algorithmica, 56(1):1-15, 2013.

"Coverage with k-Transmitters in the Presence of Obstacles," B. Ballinger, N. Benbernou, P. Bose, M. Damian, E. Demaine, V. Dujmović, R. Flatland, F. Hurtado, J. Iacono, A. Lubiw, P. Morin, V. Sacristan, D. Souvaine, and R. Uehara. Journal of Combinatorial Optimization, 25(2):208-233, 2013.

"Efficient Reconfiguration of Lattice-Based Modular Robots," G. Aloupis, N. Benbernou, M. Damian, E. D. Demaine, R. Flatland, J. Iacono, S. Wuhrer. Computational Geometry: Theory and Applications, 46(8):917-928, 2013.

"Establishing strong connectivity using optimal radius half-disk antennas," Greg Aloupis, Mirela Damian, Robin Flatland, Matias Korman, Ozgur Ozkan, David Rappaport, Stefanie Wuhrer. Computational Geometry:Theory and Applications, 46(3):328-339, April 2013.

"Unfolding Orthogrids with Constant Refinement," Mirela Damian, Erik Demaine and Robin Flatland. In Proc. of the 23rd Fall Workshop in Computational Geometry, 2013.

"Algorithms for Collective Construction of 2D Block Structures with Holes," Z. Fitzsimmons, and R. Flatland. American Journal of Undergraduate Research (AJUR), 10:2, pp.1-10, 2011.

"Establishing Strong Connectivity using Optimal Radius Half-Disk Antennas," G. Aloupis, M. Damian, R. Flatland, M. Korman, O. Ozkan, D. Rappaport and S. Wuhrer. In Proc. of the 23rd Canadian Conference on Computational Geometry, CCCG'11, pages 361-366, 2011.

"Switching to Directional Antennas with Constant Increase in Radius and Hop Distance," P. Bose, P. Carmi, M. Damian, R. Flatland, M. Katz, and A. Maheshwari. In Proc. of the 12th Intl. Conf. on Algorithms and Data Structures Symposium (WADS), pages 134-146, 2011.

"Efficient Constant-Velocity Reconfiguration of Crystalline Robots," G. Aloupis, S. Collette, M. Damian, E. D. Demaine, D. El-Khechen, R. Flatland, S. Langerman, J. O'Rourke, V. Pinciu, S. Ramaswami, V. Sacristan, and S. Wuhrer. In Robotica, 29(1):59-71, January 2011.

"Coverage with k-Transmitters in the Presence of Obstacles," Brad Ballinger, Nadia Benbernou, Prosenjit Bose, Mirela Damian, Erik Demaine, Vida Dujmovic, Robin Flatland, Ferran Hurtado, John Iacono, Anna Lubiw, Pat Morin, Vera Sacristan, Diane Souvaine, and Ryuhei Uehara. In Proc. of the 4th International Conference on Combinatorial Optimization and Applications - Volume Part II, COCOA'10, pages 1-15, Berlin, Heidelberg, 2010. Springer-Verlag.

"Spanning Properties of Graphs Induced by Directional Antennas," Mirela Damian and Robin Y. Flatland. In Proceedings of the 20th Annual Fall Workshop on Computational Geometry , 2010.

" Connecting Polygonizations via Stretches and Twangs," Mirela Damian, Robin Y. Flatland, Joseph O’Rourke, and S. Ramaswami. In Theory of Computing Systems, 47(3):674-695, 2010.

" Shape Replication through Self-Assembly and RNase Enzymes," Zachary Abel, Nadia Benbernou, Mirela Damian, Erik D. Demaine, Martin L. Demaine, Robin Flatland, Scott D. Kominers, and Robert Schweller. Symposium on Discrete Algorithms, pages 1045-1064, 2010.

" Using Modes of Inquiry and Engaging Problems to Link Computer Science and Mathematics," Robin Flatland and James R. Matthews. In Proceedings of the 40th ACM Technical Symposium on Computer Science Education, pages 387-391, 2009.

" Linear Reconfiguration of Cube-Style Modular Robots," G. Aloupis, S. Collette, M. Damian, E. D. Demaine, R. Flatland, S. Langerman, J. O'Rourke, S. Ramaswami, V. Sacristan, and S. Wuhrer. In Computational Geometry: Theory and Applications, 42(6-7):652-663, 2009.

" Efficient Reconfiguration of Lattice Robots," Nadia Benbernou, Mirela Damian, Erik Demaine, Robin Flatland, John Iacono and Stefanie Wuhrer. European Conference on Mobile Robotics, pages 81-86, 2009.

" Realistic Reconfiguration of Crystalline (and Telecube) Robots," Greg Aloupis, Sebastien Collette, Mirela Damian, Erik Demaine, Dania El-Khechen, Robin Flatland, Stefan Langerman, Joseph O'Rourke, Val Pinciu, Suneeta Ramaswami, Vera Sacristan, Stefanie Wuhrer. Eighth Annual Workshop on the Algorithmic Foundations of Robotics (WAFR), 2008.

" Unfolding Manhattan Towers," Mirela Damian, Robin Y. Flatland, and Joseph O’Rourke. Computational Geometry: Theory and Applications, 40:102-114, 2008.

" Grid Vertex-Unfolding Orthogonal Polyhedra," Mirela Damian, Robin Flatland and Joseph O'Rourke. Discrete and Computational Geometry, 39:213-238, 2008.

" Connecting polygonizations via stretches and twangs," M. Damian, R. Flatland, S. Ramaswami and J. O'Rourke. In Proceedings of the 25th Annual Symposium on Theoretical Aspects of Computer Science, pages 217—228, 2008.

" Epsilon-Unfolding Orthogonal Polyhedra," Mirela Damian, Robin Flatland, and Joseph O’Rourke. Graphs and Combinatorics, 23[Supplemental]: 179-194, 2007.

" Exploring the Polygonizations of a Point Set via Stretches and Twangs," M. Damian, R. Flatland, S. Ramaswami and J. O'Rourke. Abstracts of the 17th Fall Workshop on Computational and Combinatorial Geometry, November 2007.

" A New Lower Bound on Guard Placement for Wireless Localization," M. Damian, R. Flatland, S. Ramaswami and J. O'Rourke. Abstracts of the 17th Fall Workshop on Computational and Combinatorial Geometry, November 2007.

" Exploring the Polygonizations of a Point Set via Stretches and Twangs," M. Damian, R. Flatland, S. Ramaswami and J. O'Rourke. Abstracts of the 17th Fall Workshop on Computational and Combinatorial Geometry, November 2007.

" Linear Reconfiguration of Cube-Style Modular Robots," G. Aloupis, S. Collette, M. Damian, E. D. Demaine, R. Flatland, S. Langerman, J. O'Rourke, S. Ramaswami, V. Sacristan, and S. Wuhrer. In International Symposium of Algorithms and Computation (ISAAC), 2007.

" Vertex Pops and Popturns," G. Aloupis, B. Ballinger, P. Bose, M. Damian, E. Demaine, M. Demaine, R. Flatland, F. Hurtado, S. Langerman, J. O'Rourke, P. Taslakian, and G. Toussaint. In Proceedings of the Nineteenth Canadian Conference on Computational Geometry, pages 137-140, 2007.

" Grid Vertex-Unfolding Orthogonal Polyhedra," Mirela Damian, Robin Flatland and Joseph O'Rourke. In 23rd Annual Symposium on Theoretical Aspects of Computer Science (STACS), Marseille, France. In Lecture Notes in Computer Science, vol. 3884, Springer, Berlin/Heidelberg, vol. 3884, pp. 264-276, Feb. 2006.

" Curves in the Sand," M. Damian, E. Demaine, M. Demaine, V. Dujmovic, D. El-Khechen, R. Flatland, J. Iacono, S. Langerman, H. Meijer, S. Ramaswami, D. Souvaine, P. Taslakian, and G. Toussaint. In Proceedings of the Eightenth Canadian Conference on Computational Geometry, pages 11-14, 2006.

" Unfolding Well-Separated Orthotrees," Mirela Damian, Robin Flatland, Henk Meijer, and Joseph O'Rourke. In 15th Annual Fall Workshop on Computational Geometry and Visualization, 2005, pp 25-26.

" Unfolding Manhattan Towers ," Mirela Damian, Robin Flatland, and Joseph O'Rourke. In Proceedings of the 17th Canadian Conference on Computational Geometry, 2005, pp 204-207.

" On Sequential Triangulations of Simple Polygons ," Robin Flatland. In Proceedings of the 16th Canadian Conference on Computational Geometry, 2004, pp 112-115.

"Using Visualization Tools To Develop Geometric Reasoning Skills in a Computer Graphics Course," Robin Y. Flatland., The Journal of Computing in Small Colleges, 17(6): 150-160, 2002.

"Maintaining Valid Topology with Active Contours: Theory and Application," Amita Perera, C. Tsai, R. Flatland, and Charles V. Stewart. In Proceedings of IEEE Computer Vision and Pattern Recognition, pages 496-502, 2000.

"Extending Range Queries and Nearest Neighbors," Robin Y. Flatland and Charles V. Stewart. Computational Geometry: Theory and Applications, 17: 3-24, 2000.

"Using MINIX in the Closed Lab Environment," Robin Y. Flatland., The Journal of Computing in Small Colleges, 14(4): 9-17, 1999.

"Extending Rectangular Range Reporting with Query Sensitive Analysis," Robin Y. Flatland and Charles V. Stewart. In Proceedings of the 8th Canadian Conference on Computational Geometry, 1996, pp 319-324.

"Geometric Constraints and Stereo Disparity Computation," Charles V. Stewart, Robin Y. Flatland, and Kishore Bubna. International Journal of Computer Vision, 20(3): 143-168, 1996

"Extending Range Queries and Nearest Neighbors," Robin Y. Flatland and Charles V. Stewart. In Proceedings of the 7th Canadian Conference on Computational Geometry, 1995, pp 267-272.

"Simulation and Visualization Tools for Teaching Parallel Merge Sort," Robin Y. (Trahan) Flatland and Susan Rodger. In 24th SIGCSE Technical Symposium on Computer Science Education, 1993, pp 237-241.