Übersicht			Auf mobile öffnen

Lieferstatus:	Auf Bestellung (Lieferzeit unbekannt)
Veröffentlichung:	Juni 2008
Genre:	Schulbücher
	B / Computational Mathematics and Numerical Analysis / Computer Imaging, Vision, Pattern Recognition and Graphics / Computer mathematics / Computer Vision / Differential Geometry / Image processing / Mathematics and Statistics / Numerical analysis / Optical data processing
ISBN:	9783540737919
EAN-Code:	9783540737919
Verlag:	Springer Nature EN
Einband:	Gebunden
Sprache:	English
Serie:	#02 - Geometry and Computing
Dimensionen:	H 235 mm / B 155 mm / D
Gewicht:	588 gr
Seiten:	266
Illustration:	XI, 266 p. 107 illus., 36 illus. in color., schwarz-weiss Illustrationen, farbige Illustrationen
Bewertung:	Titel bewerten / Meinung schreiben

Inhalt:

The central object of this book is the measure of geometric quantities describing N a subset of the Euclidean space (E ,), endowed with its standard scalar product. Let us state precisely what we mean by a geometric quantity. Consider a subset N S of points of the N-dimensional Euclidean space E , endowed with its standard N scalar product. LetG be the group of rigid motions of E . We say that a 0 quantity Q(S) associated toS is geometric with respect toG if the corresponding 0 quantity Q[g(S)] associated to g(S) equals Q(S), for all g?G . For instance, the 0 diameter ofS and the area of the convex hull ofS are quantities geometric with respect toG . But the distance from the origin O to the closest point ofS is not, 0 since it is not invariant under translations ofS. It is important to point out that the property of being geometric depends on the chosen group. For instance, ifG is the 1 N group of projective transformations of E , then the property ofS being a circle is geometric forG but not forG , while the property of being a conic or a straight 0 1 line is geometric for bothG andG . This point of view may be generalized to any 0 1 subsetS of any vector space E endowed with a groupG acting on it.