Jorge Urrutia Galicia is a Mexican mathematician and computer scientist in the Institute of Mathematics of the National Autonomous University of Mexico (UNAM). [1] His research primarily concerns discrete and computational geometry.
Jorge Urrutia Galicia is a Mexican mathematician and computer scientist in the Institute of Mathematics of the National Autonomous University of Mexico (UNAM). [1] His research primarily concerns discrete and computational geometry.
Urrutia earned his Ph.D. from the University of Waterloo in 1980, under the supervision of Ronald C. Read. [2] He worked for many years at the University of Ottawa before moving to UNAM in 1999. [3] With Jörg-Rüdiger Sack in 1991, he was founding co-editor-in-chief of the academic journal Computational Geometry: Theory and Applications . [4]
Urrutia is a member of the Mexican Academy of Sciences. [5] The Mexican Conference on Discrete Mathematics and Computational Geometry, held in 2013 in Oaxaca, was dedicated to Urrutia in honor of his 60th birthday. [6]
In computational geometry, polygon triangulation is the partition of a polygonal area P into a set of triangles, i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P.
A Euclidean minimum spanning tree of a finite set of points in the Euclidean plane or higher-dimensional Euclidean space connects the points by a system of line segments with the points as endpoints, minimizing the total length of the segments. In it, any two points can reach each other along a path through the line segments. It can be found as the minimum spanning tree of a complete graph with the points as vertices and the Euclidean distances between points as edge weights.
The art gallery problem or museum problem is a well-studied visibility problem in computational geometry. It originates from the following real-world problem:
In mathematics, Scheinerman's conjecture, now a theorem, states that every planar graph is the intersection graph of a set of line segments in the plane. This conjecture was formulated by E. R. Scheinerman in his Ph.D. thesis (1984), following earlier results that every planar graph could be represented as the intersection graph of a set of simple curves in the plane. It was proven by Jeremie Chalopin and Daniel Gonçalves (2009).
Víctor Neumann-Lara (1933–2004) was a Mexican mathematician, pioneer in the field of graph theory in Mexico. His work also covers general topology, game theory and combinatorics.
In graph theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order. Comparability graphs have also been called transitively orientable graphs, partially orderable graphs, containment graphs, and divisor graphs. An incomparability graph is an undirected graph that connects pairs of elements that are not comparable to each other in a partial order.
The Euclidean shortest path problem is a problem in computational geometry: given a set of polyhedral obstacles in a Euclidean space, and two points, find the shortest path between the points that does not intersect any of the obstacles.
In computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge length. That is, an input polygon or the convex hull of an input point set must be subdivided into triangles that meet edge-to-edge and vertex-to-vertex, in such a way as to minimize the sum of the perimeters of the triangles. The problem is NP-hard for point set inputs, but may be approximated to any desired degree of accuracy. For polygon inputs, it may be solved exactly in polynomial time. The minimum weight triangulation has also sometimes been called the optimal triangulation.
In mathematics, a topological graph is a representation of a graph in the plane, where the vertices of the graph are represented by distinct points and the edges by Jordan arcs joining the corresponding pairs of points. The points representing the vertices of a graph and the arcs representing its edges are called the vertices and the edges of the topological graph. It is usually assumed that any two edges of a topological graph cross a finite number of times, no edge passes through a vertex different from its endpoints, and no two edges touch each other. A topological graph is also called a drawing of a graph.
In computational geometry, a polyhedral terrain in three-dimensional Euclidean space is a polyhedral surface that intersects every line parallel to some particular line in a connected set or the empty set. Without loss of generality, we may assume that the line in question is the z-axis of the Cartesian coordinate system. Then a polyhedral terrain is the image of a piecewise-linear function in x and y variables.
Prosenjit K. "Jit" Bose is a Canadian mathematician and computer scientist who works at Carleton University as a professor in the School of Computer Science and associate dean of research and graduate studies for the Faculty of Science. His research concerns graph algorithms and computational geometry, including work on geometric spanners and geographic routing in wireless ad hoc networks.
In matroid theory, a mathematical discipline, the girth of a matroid is the size of its smallest circuit or dependent set. The cogirth of a matroid is the girth of its dual matroid. Matroid girth generalizes the notion of the shortest cycle in a graph, the edge connectivity of a graph, Hall sets in bipartite graphs, even sets in families of sets, and general position of point sets. It is hard to compute, but fixed-parameter tractable for linear matroids when parameterized both by the matroid rank and the field size of a linear representation.
In geometry, a partition of a polygon is a set of primitive units, which do not overlap and whose union equals the polygon. A polygon partition problem is a problem of finding a partition which is minimal in some sense, for example a partition with a smallest number of units or with units of smallest total side-length.
Computational Geometry, also known as Computational Geometry: Theory and Applications, is a peer-reviewed mathematics journal for research in theoretical and applied computational geometry, its applications, techniques, and design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects, as well as fundamental problems in various areas of application of computational geometry: in computer graphics, pattern recognition, image processing, robotics, electronic design automation, CAD/CAM, and geographical information systems.
Isabel Alicia Hubard Escalera is a Mexican mathematician in the Institute of Mathematics of the National Autonomous University of Mexico (UNAM).
In the mathematical area of graph theory, a contact graph or tangency graph is a graph whose vertices are represented by geometric objects, and whose edges correspond to two objects touching according to some specified notion. It is similar to the notion of an intersection graph but differs from it in restricting the ways that the underlying objects are allowed to intersect each other.
Ferran Hurtado Díaz was a Spanish mathematician and computer scientist known for his research in computational geometry.
Patrick Ryan Morin is a Canadian computer scientist specializing in computational geometry and data structures. He is a professor in the School of Computer Science at Carleton University.
In the geometry of convex polyhedra, blooming or continuous blooming is a continuous three-dimensional motion of the surface of the polyhedron, cut to form a polyhedral net, from the polyhedron into a flat and non-self-overlapping placement of the net in a plane. As in rigid origami, the polygons of the net must remain individually flat throughout the motion, and are not allowed to intersect or cross through each other. A blooming, reversed to go from the flat net to a polyhedron, can be thought of intuitively as a way to fold the polyhedron from a paper net without bending the paper except at its designated creases.
