By Dr. R. E. Barnhill, Dr. T. M. Frost (auth.), Prof. Dr. H. Hagen, Prof. Dr. G. Farin, Prof. Dr. H. Noltemeier (eds.)
Experts from college and are proposing new applied sciences for fixing business difficulties and giving many vital and workable impulses for brand spanking new examine. issues explored comprise NURBS, product engineering, item orientated modelling, good modelling, floor interrogation, function modelling, variational layout, scattered info algorithms, geometry processing, mixing tools, smoothing and fairing algorithms, spline conversion. This selection of 24 articles offers a cutting-edge survey of the appropriate difficulties and matters in geometric modelling.
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Additional info for Geometric Modelling: Dagstuhl 1993
Sample text
A polyhedral set is normally defined as the intersection of a finite number of closed halfspaces [17]. Therefore, all polyhedral sets are Nef polyhedra. • The set of all points belonging to the simplices of an m-dimensional simplicial complex in ~d(O :s; m :s; d) is normally called a linear d-polyhedron [25]. Hence, all linear d-polyhedra are Nef polyhedra. With regard to Geometric Modeling it is probably most natural to introduce Nef polyhedra within the context of Constructive Solid Geometry (CSG).
Schneider, F. : Optimal approximate conversion of spline surfaces. Comput. Aided Geom. Des. 6, 293-306 (1989). : An offset spline approximation for plane cubic splines. Comput. Aided Des. 15, 297~299 (1983). : Knot refinement algorithms for tensor product B-spline surfaces. Comput. Aided Geom. Des. 2, 133~139 (1985). [19] Patrikalakis, N. , Prakash, P. : Free-form plate modeling using offset surfaces. In: Computers in offshore and arctic engineering-1987 (Chung, 1. ), pp. 37-44. : Offset approximation of uniform B-splines.
Moreover, there is a recursive evaluation algorithm for curves written in terms of Ball's basis which is more efficient than de Casteljau's recursive evaluation algorithm for curves of the same degree represented in Bezier form [5,8]. Ball first introduced his basis for cubic polynomials [1-3]. Later this basis was generalized to polynomials of arbitrary odd degrees by Goodman and Said [6,8J, who also noted that these generalized basis functions are closely related to two point Hermite interpolation.