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Geometrical Problems And Computations (F.2.2...)
Euclidean distance geometry: an introduction
Liberti L., Lavor C., Springer International Publishing, New York, NY, 2017. 133 pp. Type: Book (978-3-319607-91-7)
If someone has a set of objects whose positions are known, calculating the distances between them is not a problem. However, the inverse problem is difficult, that is, given a set of distances between objects, determine their positions...
May 14 2019
An introduction to distance geometry applied to molecular geometry
Lavor C., Liberti L., Lodwick W., da Costa T., Springer Publishing Company, Incorporated, New York, NY, 2017. 54 pp. Type: Book (978-3-319571-82-9)
The most common way of determining the structures of molecules in a solution is nuclear magnetic resonance (NMR). The signals measured are caused by the flipping of the spins of paramagnetic nuclei in a magnetic field. The strengths of...
Jun 7 2018
Representing 3-manifolds by filling Dehn surfaces
Vigara R., Lozano-Rojo A., World Scientific Publishing Co, Inc., River Edge, NJ, 2016. 350 pp. Type: Book
In many applications we encounter manifolds, that is, topological spaces that are locally homeomorphic to the usual Euclidean space. Probably the most well-known example is general relativity, according to which our space-time is a man...
Sep 2 2016
Digital and discrete geometry: theory and algorithms
Chen L., Springer Publishing Company, Incorporated, New York, NY, 2014. 322 pp. Type: Book (978-3-319120-98-0)
The discipline of digital geometry studies the geometric properties of models of objects that are conceptually defined in Euclidean space and discretized onto integer grid subsets of the space. While digital geometry is generally consi...
Sep 9 2015
Representing finite convex geometries by relatively convex sets
Adaricheva K. European Journal of Combinatorics 3768-78, 2014. Type: Article
with a closure operator
is called a convex geometry if the empty set is closed and if it satisfies the anti-...
Sep 10 2014
On kinetic Delaunay triangulations: a near quadratic bound for unit speed motions
Rubin N. FOCS 2013 (Proceedings of the 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, Berkeley, CA, Oct 26-29, 2013) 519-528, 2013. Type: Proceedings
Robotics, video games, simulations, virtual reality, and many other domains that involve motion planning rely on kinetic triangulation data structures of a set of moving points. Delaunay triangulation is a method in which no point in t...
Apr 16 2014
Symmetry and pattern in projective geometry
Lord E., Springer Publishing Company, Incorporated, London, UK, 2013. 195 pp. Type: Book (978-1-447146-30-8)
Artists who wanted to represent 3D scenes on 2D canvases developed projective geometry. While it isn’t studied much these days, it has enjoyed some renewed interest with the development of computer graphics and games. This bo...
Jul 3 2013
A generalisation of Tverberg’s theorem
Soberón P., Strausz R. Discrete & Computational Geometry 47(3): 455-460, 2012. Type: Article
Tverberg’s theorem is a result from discrete geometry, which states that, in any
-dimensional vector space for any set of (
+1)+1 points in that vector space, the...
Dec 3 2012
Sphere and dot product representations of graphs
Kang R., Müller T. SoCG 2011 (Proceedings of the 27th Annual ACM Symposium on Computational Geometry, Paris, France, Jun 13-15, 2011) 308-314, 2011. Type: Proceedings
Kang and M¿ller, in this paper, prove two important positive results, and one partially negative result, on graph representation. A graph
) consists of a set of vertices
Sep 27 2011
A tree traversal algorithm for decision problems in knot theory and 3-manifold topology
Burton B., Ozlen M. SoCG 2011 (Proceedings of the 27th Annual ACM Symposium on Computational Geometry, Paris, France, Jun 13-15, 2011) 145-152, 2011. Type: Proceedings
Burton and Ozlen describe a kind of backtracking algorithm, which circumvents the complexity of the restricted vertex problem (nondeterministic polynomial-time (NP) complete). They use a domination test, which imposes a partial (but no...
Aug 3 2011
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