Diane L. Souvaine

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It is well known that, given two simple n-sided polygons, it may not be possible to triangulate the two polygons in a compatible fashion, if one's choice of triangulation vertices is restricted to polygon corners. Is it always possible to produce compatible triangulations if additional vertices inside the polygon are allowed? We give a positive answer and(More)
We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are motivated by a practical nanofabrication scenario through protein-based bioengineering. Staging allows us to break through(More)
Pointed pseudo-triangulations are planar minimally rigid graphs embedded in the plane with <i>pointed</i> vertices (incident to an angle larger than <i>p</i>). In this paper we prove that the opposite statement is also true, namely that planar minimally rigid graphs always admit pointed embeddings, even under certain natural topological and combinatorial(More)
The concept of location depth was introduced in statistics as a way to extend the univariate notion of ranking to a bivariate configuration of data points. It has been used successfully for robust estimation, hypothesis testing, and graphical display. These require the computation of depth regions, which form a collection of nested polygons. The center of(More)
The goal of this paper is to show that the concept of the shortest path inside a polygonal region contributes to the design of eecient algorithms for certain geometric optimization problems involving simple polygons: computing optimum separators, maximum area or perimeter inscribed triangles, a minimum area circumscribed concave quadrilateral, or a maximum(More)
We have developed techniques which contribute to efficient algorithms for certain geometric optimization problems involving simple polygons: computing minimum separators, maximum inscribed triangles, a minimum circumscribed concave quadrilateral, or a maximum contained triangle. The structure for our algorithms is as follows: a) decompose the initial(More)
jcolan@cs.mcgill.ca 2 Department of Computer Science, Villanova University, Villanova, USA. e-mail: mirela.damian@villanova.edu 3 Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, Barcelona, Spain. Partially supported by projects MCYT BFM2003-00368, MEC MTM2006-01267 and Gen. Cat. 2005SGR00692. e-mail: Ferran.Hurtado@upc.edu 4(More)
For a set R of n red points and a set B of n blue points, a <i>BR-matching</i> is a non-crossing geometric perfect matching where each segment has one endpoint in B and one in R. Two BR-matchings are compatible if their union is also non-crossing. We prove that, for any two distinct BR-matchings M and M', there exists a sequence of BR-matchings M =(More)