Grundlagen der geometrischen Datenverarbeitung. (German) Zbl 0682.68002

Hoschek, Josef; Lasser, Dieter

Stuttgart: Teubner. 462 p. DM 52.00 (1989).

Geometric data processing (computer aided geometric design CAGD) yields mathematical foundations of graphical data processing. Mathematical methods, which are necessary for curve and surface modelling, are developed, and especially the Bézier- and B-spline-methods, which are used for computer aided design of free-form curves and surfaces, are studied. The authors start with elements of the theory of transformations and projections and develop essential parts of the theory of curves and surfaces including general methods of approximation and interpolation. A detailed and extensive representation of several general types of spline curves, Bézier curves, B-spline curves, Bézier surfaces, B-spline surfaces and generalized types such as \(\beta\)- and \(\gamma\)-splines follows. The authors study Gordon-Coons-patches, scattered data interpolation and approximation, and questions arising in the fields of transformations between several forms of curve- and surface-presentation. In the last two chapters algorithms for curve- and surface-section and smoothing methods for curves and surfaces are described. Many additional hints and applications to ray-traicing, blending of surfaces, visibility- tests, and other topics complete this interesting overview about the fascinating topic of computer aided geometric design. References to about 500 recent related papers and books are given.

Reviewer: H.D.Hecker

MSC:

68-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
68U99	Computing methodologies and applications

Keywords:

shapes; computer aided geometric design; spline-methods; free-form curves; surfaces; Bézier curves