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008 130107s2013 xxk| s |||| 0|eng d
020 _a9781447148173
_9978-1-4471-4817-3
024 7 _a10.1007/978-1-4471-4817-3
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aJoswig, Michael.
_eauthor.
245 1 0 _aPolyhedral and Algebraic Methods in Computational Geometry
_h[electronic resource] /
_cby Michael Joswig, Thorsten Theobald.
264 1 _aLondon :
_bSpringer London :
_bImprint: Springer,
_c2013.
300 _aX, 250 p. 67 illus., 17 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _aIntroduction and Overview -- Geometric Fundamentals -- Polytopes and Polyhedra -- Linear Programming -- Computation of Convex Hulls -- Voronoi Diagrams -- Delone Triangulations -- Algebraic and Geometric Foundations -- Gröbner Bases and Buchberger’s Algorithm -- Solving Systems of Polynomial Equations Using Gröbner Bases -- Reconstruction of Curves -- Plücker Coordinates and Lines in Space -- Applications of Non-Linear Computational Geometry -- Algebraic Structures -- Separation Theorems -- Algorithms and Complexity -- Software -- Notation.
520 _aPolyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry.   The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations.   The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics.   Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established.  Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.
650 0 _aMathematics.
650 0 _aComputer science
_xMathematics.
650 0 _aComputer mathematics.
650 0 _aAlgorithms.
650 0 _aGeometry.
650 0 _aConvex geometry.
650 0 _aDiscrete geometry.
650 1 4 _aMathematics.
650 2 4 _aGeometry.
650 2 4 _aConvex and Discrete Geometry.
650 2 4 _aMathematical Applications in Computer Science.
650 2 4 _aMathematics of Computing.
650 2 4 _aSymbolic and Algebraic Manipulation.
650 2 4 _aAlgorithms.
700 1 _aTheobald, Thorsten.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781447148166
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4471-4817-3
912 _aZDB-2-SMA
942 _2Dewey Decimal Classification
_ceBooks
999 _c43664
_d43664