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Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics, Series Number 7) 1st Edition
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- ISBN-100521793092
- ISBN-13978-0521793094
- Edition1st
- PublisherCambridge University Press
- Publication dateMay 28, 2001
- LanguageEnglish
- Dimensions6.25 x 0.75 x 9 inches
- Print length190 pages
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- Publisher : Cambridge University Press; 1st edition (May 28, 2001)
- Language : English
- Hardcover : 190 pages
- ISBN-10 : 0521793092
- ISBN-13 : 978-0521793094
- Item Weight : 14.4 ounces
- Dimensions : 6.25 x 0.75 x 9 inches
- Best Sellers Rank: #6,827,749 in Books (See Top 100 in Books)
- #1,622 in Topology (Books)
- #2,238 in Geometry
- #2,365 in Differential Equations (Books)
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- Reviewed in the United States on July 23, 2004OK, I must admit, I know the author personally, like his work a lot. And so I can only recommend this book. But that's not what you're looking for in a review, nor am I talking to freinds or collegues who already know hime too. This book will introduce you to simplicial complexes, and deep mathematical constructs, along with some topology and geometry, while at the same time remaining hands-on and simpler. Mostly, the notation is clean, simple, and yet rigorous enough that you'll really be in terrific shape one you integrate it. It's actually amazing that it comes so clean given how powerful it can be. Meshes are the basis for many of the computer graphics and CAD/CAM modern methods, and are an indispensible tool. That's the real value of reading this book: you'll get some real good tools for manipulating meshes (whether what you want to do is the same or different than the author), and especially you'll get a mathematically correct and rigorous treatment.
At the same time this book is quite manageable even (and foremost) if you don't have a PhD in algebraic topology (all you need is a good bachelor in some computational science with good mathematics foundations). Although it might challenge you at times, it is basically self-contained and does not rely on any other book. (Additional knowledge is always useful, but this is a good starting point.)
You'll earn about simplicial complexes not from an abstract algebraic topology point of view (although the author is well-acquainted with them) but as a tool for representing surfaces and solids. The topics revolve around reconstructing a surface from a point cloud (using so-called Delaunay triangulations, which is one of the prevalent methods for that problem). It starts simply with 2D and moves on to 3D. It builds on the research of the author for more than a decade.
I should mention in fine that the author is the creator of Alpha-Shapes(a well known Delaunay-based method for reconstruction) and of the succesful startup Raindrop Geomagic which uses these methods in an essential way. His current interests are linked to biogeometry. Most of the research in this book somehow made it in one way or the other in their products. So this is excellent reading and a must for anyone interested in meshes, whether from computer graphics, CAD/CAM, or scientific computation / finite elements.
- Reviewed in the United States on February 22, 2010And much more pleasant to read than Edelsbrunner's Computational Geometry book. I have very little interest in Mesh Generation, but most of the book is not about that, but is rather a rather lucid introduction to central topics in modern discrete and computational geometry.
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Pleased readerReviewed in Italy on November 19, 2011
4.0 out of 5 stars Libro didattico, ma concettuale
Una monografia di taglio didattico -e nato appunto come elaborazione degli appunti di un corso- sui metodi per la generazione di mesh. E' un'eccellente introduzione ad alcuni concetti di geometria conputazionale e discreta come i diagrammi di Voronoi, la triangolazione/tetraedralizzazione di Delaunay, i complessi simpliciali e le varietà -presentate dal punto di vista della disciplina. Potrebbe deludere, però, chi è alla ricerca di un libro di algoritmi pronti per l'uso: nonostante il taglio sia didattico (ben diverso dal più complesso "Algorithms in Combinatorial Geometry" dello stesso autore!), l'enfasi è sui concetti. A questi ultimi consiglio "Computational geometry in C" di O'Rourke oppure "Computational Geometry: Algorithms and Applications" di De Berg et al., che però si focalizzano poco sull'argomento specifico della generazione di mesh.
Nota: Edelsbrunner è considerato un pioniere nel campo della geometria computazionale e tra i suoi contributi più significativi -oltre ai lavori sulla triangolazione di Delaunay- ci sono il metodo degli alpha-shape, la simulation of simplicity per gestire le eccezioni (accennata in un paragrafo di questo testo) e gli arrangement of line.