Polygon Mesh Processing, Botsch

Автор: Jacques Tits; Richard M. Weiss
Название: Moufang Polygons
ISBN: 3642078338 ISBN-13(EAN): 9783642078330
Издательство: Springer
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Цена: 93130.00 T
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Описание: Spherical buildings are certain combinatorial simplicial complexes intro- duced, at first in the language of "incidence geometries," to provide a sys- tematic geometric interpretation of the exceptional complex Lie groups. (The definition of a building in terms of chamber systems and definitions of the various related notions used in this introduction such as "thick," "residue," "rank," "spherical," etc. are given in Chapter 39. ) Via the notion of a BN-pair, the theory turned out to apply to simple algebraic groups over an arbitrary field. More precisely, to any absolutely simple algebraic group of positive rela- tive rank is associated a thick irreducible spherical building of the same rank (these are the algebraic spherical buildings) and the main result of Buildings of Spherical Type and Finite BN-Pairs 101] is that the converse, for:::: 3, is almost true: (1. 1) Theorem. Every thick irreducible spherical building of rank at least three is classical, algebraic' or mixed. Classical buildings are those defined in terms of the geometry of a classical group (e. g. unitary, orthogonal, etc. of finite Witt index or linear of finite dimension) over an arbitrary field or skew-field. (These are not algebraic if, for instance, the skew-field is of infinite dimension over its center. ) Mixed buildings are more exotic; they are related to groups which are in some sense algebraic groups defined over a pair of fields k and K of characteristic p, where KP eke K and p is two or (in one case) three.

Автор: Hendrik,van Maldeghem
Название: Generalized Polygons
ISBN: 3034897898 ISBN-13(EAN): 9783034897891
Издательство: Springer
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Цена: 74530.00 T
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Описание: They are the prototypes and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge- ometries, near polygons, Moore geometries, etc. The main examples of generalized polygons are the natural geometries associated with groups of Lie type of relative rank 2.

Автор: Michel Bercovier; Tanya Matskewich
Название: Smooth B?zier Surfaces over Unstructured Quadrilateral Meshes
ISBN: 3319638408 ISBN-13(EAN): 9783319638409
Издательство: Springer
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Цена: 51230.00 T
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Описание: Using an elegant mixture of geometry, graph theory and linear analysis, this monograph completely solves a problem lying at the interface of Isogeometric Analysis (IgA) and Finite Element Methods (FEM).