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Geometric Algorithms, Languages, And Systems (I.3.5...)
Stochastic geometry: modern research frontiers
Coupier D., Springer International Publishing, New York, NY, 2019. 248 pp. Type: Book (978-3-030135-46-1)
In the era BC (“before computers”), the standard way to reason about geometric objects, dating back to Euclid, was a logical proof system based on axioms. This approach is symbolic, dealing with entities such as points and lines. It le...
Apr 13 2021
Topology-oriented incremental algorithm for the robust construction of the Voronoi diagrams of disks
Lee M., Sugihara K., Kim D. ACM Transactions on Mathematical Software 43(2): 1-23, 2016. Type: Article
Voronoi diagrams are important in many applications that range from theoretical computing to computational geometry, to computer graphics and computer vision. The relatively new problem of computing the Voronoi diagram for a set of geometry primit...
Jan 20 2017
Leading a continuation method by geometry for solving geometric constraints
Imbach R., Schreck P., Mathis P. Computer-Aided Design 46138-147, 2014. Type: Article
Though not obvious from the title, this paper is concerned with 3D geometric constraints, as arise in, say, molecular modeling. This is definitely not a straightforward generalization of the commonly treated 2D case. The authors give many reasons ...
May 6 2015
Fast oriented bounding box optimization on the rotation group
Chang C., Gorissen B., Melchior S. ACM Transactions on Graphics 30(5): 1-16, 2011. Type: Article
Fitting oriented bounding boxes (OBBs) in real-time applications, such as the rapid rendering of 3D scenes and the discovery of interference, is an open research problem. Hierarchical OBB trees are used to minimize the computational time in the de...
Aug 28 2013
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 book is not a text...
Jul 3 2013
Power allocation with max-min and min-max fairness for cognitive radio networks with imperfect CSI
Lun T., Jing-Lin Y., Qing L., Qian-Bin C., Huan W. Wireless Personal Communications: An International Journal 65(3): 671-687, 2012. Type: Article
Cognitive radio (CR) technology emerged to enable efficient utilization of the existing radio spectrum. Devices using CR are capable of accessing frequency bands that are not currently being used by the primary user. This paper proposes three powe...
Nov 29 2012
Circular arc structures
Bo P., Pottmann H., Kilian M., Wang W., Wallner J. ACM Transactions on Graphics 30(4): 1-12, 2011. Type: Article
A circular arc structure (CAS) is a mesh of a surface with edges realized by circular arcs, such that all edges incident to a vertex are tangent to a common plane, and form a repeatable pattern of angles about interior vertices so that all vertice...
Feb 23 2012
Mathematics for computer graphics
Vince J., Springer, New York, NY, 2010. 312 pp. Type: Book (978-1-849960-22-9)
Many computer graphics students have difficulty understanding and applying the applicable mathematics. The mathematics required for computer graphics does not normally involve calculus, but it can be intense nonetheless. Extensive applications of ...
Sep 29 2010
Geometric folding algorithms: linkages, origami, polyhedra
Demaine E., O’Rourke J., Cambridge University Press, New York, NY, 2007. 496 pp. Type: Book
While origami may be the first thing that comes to mind when someone talks about folding, there are other things that are governed by similar physical rules, including protein folding, the movement of rods connected by joints, and how to cut out m...
Jun 12 2009
Freeform surfaces from single curved panels
Pottmann H., Schiftner A., Bo P., Schmiedhofer H., Wang W., Baldassini N., Wallner J. ACM Transactions on Graphics 27(3): 1-10, 2008. Type: Article
Freeform surfaces are increasingly used in spectacular steel and glass architectural designs. Constructing such a surface from flat pieces renders it polyhedral, diminishing the aesthetics of curved surfaces. Constructing it from doubly curved pan...
Jan 16 2009
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