000 03933nam a22005535i 4500
001 978-3-642-13648-1
003 DE-He213
005 20160302170053.0
007 cr nn 008mamaa
008 100825s2010 gw | s |||| 0|eng d
020 _a9783642136481
_9978-3-642-13648-1
024 7 _a10.1007/978-3-642-13648-1
_2doi
050 4 _aQA150-272
072 7 _aPBD
_2bicssc
072 7 _aMAT008000
_2bisacsh
082 0 4 _a511.1
_223
100 1 _aSabin, Malcolm.
_eauthor.
245 1 0 _aAnalysis and Design of Univariate Subdivision Schemes
_h[electronic resource] /
_cby Malcolm Sabin.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aXIV, 218 p. 68 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aGeometry and Computing,
_x1866-6795 ;
_v6
505 0 _aPrependices -- Functions and Curves -- Differences -- B-Splines -- Eigenfactorisation -- Enclosures -- H�lder Continuity -- Matrix Norms -- Joint Spectral Radius -- Radix Notation -- z-transforms -- Dramatis Personae -- An introduction to some regularly-appearing characters -- Analyses -- Support -- Enclosure -- Continuity 1 - at Support Ends -- Continuity 2 - Eigenanalysis -- Continuity 3 - Difference Schemes -- Continuity 4 - Difference Eigenanalysis -- Continuity 5 - the Joint Spectral Radius -- What Converges ? -- Reproduction of Polynomials -- Artifacts -- Normalisation of Schemes -- Summary of Analysis Results -- Design -- The Design Space -- Linear Subspaces of the Design Space -- Non-linear Conditions -- Non-Stationary Schemes -- Geometry Sensitive Schemes -- Implementation -- Making Polygons -- Rendering -- Interrogation -- End Conditions -- Modifying the Original Polygon -- Appendices -- Proofs -- Historical Notes -- Solutions to Exercises -- Coda.
520 _aThis book covers the theory of subdivision curves in detail, which is a prerequisite for that of subdivision surfaces. The book reports on the currently known ways of analysing a subdivision scheme (i.e. measuring criteria which might be important for the application of a scheme to a given context). It then goes on to consider how those analyses can be used in reverse to design a scheme best matching the particular criteria for a given application. The book is presented in an accessible fashion, even for those whose mathematics is a tool to be used, not a way of life. It should provide the reader with a full and deep understanding of the state-of-the-art in subdivision analysis, and separate sections on mathematical techniques provide revision for those needing it. The book will be of great interest to those starting to do research in CAD/CAE. It will also appeal to those lecturing in this subject and industrial workers implementing these methods. The author has spent his professional life on the numerical representation of shape and his book fills a need for a book covering the fundamental ideas in the simplest possible context, that of curves.
650 0 _aMathematics.
650 0 _aComputer simulation.
650 0 _aComputer graphics.
650 0 _aComputer-aided engineering.
650 0 _aVisualization.
650 0 _aGeometry.
650 0 _aDiscrete mathematics.
650 1 4 _aMathematics.
650 2 4 _aDiscrete Mathematics.
650 2 4 _aGeometry.
650 2 4 _aSimulation and Modeling.
650 2 4 _aVisualization.
650 2 4 _aComputer-Aided Engineering (CAD, CAE) and Design.
650 2 4 _aComputer Graphics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642136474
830 0 _aGeometry and Computing,
_x1866-6795 ;
_v6
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-13648-1
912 _aZDB-2-SMA
999 _c193168
_d193168