All Outputs (6)

Computing invariants of knotted graphs given by sequences of points in 3-dimensional space (2017)
Conference Proceeding
Kurlin, V., Carr, H., Garth, C., & Weinkauf, T. (2017). Computing invariants of knotted graphs given by sequences of points in 3-dimensional space. In Topological methods in data analysis and visualization IV : theory, algorithms, and applications (349-363). https://doi.org/10.1007/978-3-319-44684-4_21

We design a fast algorithm for computing the fundamental group of the complement to any knotted polygonal graph in 3-space. A polygonal graph consists of straight segments and is given by sequences of vertices along edge-paths. This polygonal model i... Read More about Computing invariants of knotted graphs given by sequences of points in 3-dimensional space.

Relaxed disk packing (2015)
Conference Proceeding
Edelsbrunner, E., Iglesias-Ham, M., Kurlin, V., Kouhestani, B., & Rappaport, D. (2015). Relaxed disk packing. In Proceedings of the 27th Canadian Conference on Computational Geometry, August 10-12, 2015, Queen’s University, Kingston, Ontario Canada (128-135)

Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexago... Read More about Relaxed disk packing.

A Linear Time Algorithm for Visualizing Knotted Structures in 3 Pages (2015)
Conference Proceeding
Kurlin, V. (2015). A Linear Time Algorithm for Visualizing Knotted Structures in 3 Pages. In Proceedings of the 6th International Conference on Information Visualization Theory and Applications, IVAPP-2015, 11-14 March 2015, Berlin, Germany (5-16). https://doi.org/10.5220/0005259900050016

We introduce simple codes and fast visualization tools for knotted structures in molecules and neural networks. Knots, links and more general knotted graphs are studied up to an ambient isotopy in Euclidean 3-space. A knotted graph can be represented... Read More about A Linear Time Algorithm for Visualizing Knotted Structures in 3 Pages.

A fast and robust algorithm to count topologically persistent holes in noisy clouds (2014)
Conference Proceeding
Kurlin, V. (2014). A fast and robust algorithm to count topologically persistent holes in noisy clouds.

Preprocessing a 2D image often produces a noisy cloud of interest points. We study the problem of counting holes in noisy clouds in the plane. The holes in a given cloud are quantified by the topological persistence of their boundary contours when th... Read More about A fast and robust algorithm to count topologically persistent holes in noisy clouds.

Computing a configuration skeleton for motion planning of two round robots on a metric graph (2014)
Conference Proceeding
Kurlin, V., & Safi-Samghabadi, M. (2014). Computing a configuration skeleton for motion planning of two round robots on a metric graph. In International Conference on Robotics and Mechatronics Conference (ICROM 2014) : digest book : October 15-17, 2014, Khajeh Nasir Toosi University, Tehran, Iran (723-729). https://doi.org/10.1109/icrom.2014.6990989

A connected metric graph G with n vertices and without loops and multiple edges is given as an n × n-matrix whose entry aij is the length of a single edge between vertices i ≠ j. A robot in the metric graph G is the metric ball with a center x ϵ G an... Read More about Computing a configuration skeleton for motion planning of two round robots on a metric graph.

Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence (2014)
Conference Proceeding
Kurlin, V., Winkler, F., Negru, V., Ida, T., Jebelean, T., Petcu, D., …Zaharie, D. (2014). Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence. In SYNASC 2014 : 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (594-601). https://doi.org/10.1109/synasc.2014.85

We design a new fast algorithm to automatically complete closed contours in a finite point cloud on the plane. The only input can be a scanned map with almost closed curves, a hand-drawn artistic sketch or any sparse dotted image in 2D without any ex... Read More about Auto-completion of Contours in Sketches, Maps and Sparse 2D Images Based on Topological Persistence.