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020 _a9781441909992
_9978-1-4419-0999-2
024 7 _a10.1007/978-1-4419-0999-2
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
082 0 4 _a516.35
_223
100 1 _aEmiris, Ioannis Z.
_eeditor.
245 1 0 _aNonlinear Computational Geometry
_h[electronic resource] /
_cedited by Ioannis Z. Emiris, Frank Sottile, Thorsten Theobald.
250 _a1.
264 1 _aNew York, NY :
_bSpringer New York,
_c2010.
300 _bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aThe IMA Volumes in Mathematics and its Applications,
_x0940-6573 ;
_v151
505 0 _aSpectral Techniques to Explore Point Clouds in Euclidean Space, with Applications to Collective Coordinates in Structural Biology -- Rational Parametrizations, Intersection Theory, and Newton Polytopes -- Some Discrete Properties of the Space of Line Transversals to Disjoint Balls -- Algebraic Geometry and Kinematics -- Rational Offset Surfaces and their Modeling Applications -- A List of Challenges for Real Algebraic Plane Curve Visualization Software -- A Subdivision Method for Arrangement Computation of Semi-Algebraic Curves -- Invariant-Based Characterization of the Relative Position of Two Projective Conics -- A Note on Planar Hexagonal Meshes -- List of Workshop Participants.
520 _aAn original motivation for algebraic geometry was to understand curves and surfaces in three dimensions. Recent theoretical and technological advances in areas such as robotics, computer vision, computer-aided geometric design and molecular biology, together with the increased availability of computational resources, have brought these original questions once more into the forefront of research. One particular challenge is to combine applicable methods from algebraic geometry with proven techniques from piecewise-linear computational geometry (such as Voronoi diagrams and hyperplane arrangements) to develop tools for treating curved objects. These research efforts may be summarized under the term nonlinear computational geometry. This volume grew out of an IMA workshop on Nonlinear Computational Geometry in May/June 2007 (organized by I.Z. Emiris, R. Goldman, F. Sottile, T. Theobald) which gathered leading experts in this emerging field. The research and expository articles in the volume are intended to provide an overview of nonlinear computational geometry. Since the topic involves computational geometry, algebraic geometry, and geometric modeling, the volume has contributions from all of these areas. By addressing a broad range of issues from purely theoretical and algorithmic problems, to implementation and practical applications this volume conveys the spirit of the IMA workshop.
650 0 _aMathematics.
650 0 _aGeometry, algebraic.
650 0 _aAlgebra.
650 0 _aComputer science
_xMathematics.
650 0 _aGeometry.
650 1 4 _aMathematics.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aComputational Mathematics and Numerical Analysis.
650 2 4 _aGeometry.
650 2 4 _aGeneral Algebraic Systems.
700 1 _aSottile, Frank.
_eeditor.
700 1 _aTheobald, Thorsten.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441909985
830 0 _aThe IMA Volumes in Mathematics and its Applications,
_x0940-6573 ;
_v151
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-0999-2
912 _aZDB-2-SMA
999 _c110293
_d110293