Get Geometric Modeling: Methods and Applications PDF

Nonfiction 8

By Robert E. Barnhill, Thomas A. Foley (auth.), Prof. Dr. Hans Hagen, Dr. Dieter Roller (eds.)

This e-book is predicated on lectures provided at a global workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. overseas specialists from academia and have been chosen to talk at the best themes in geometric modeling. The ensuing papers, released during this quantity, supply a cutting-edge survey of the proper difficulties and matters. the subsequent subject matters are mentioned: - tools for developing surfaces on surfaces: 4 varied recommendations to the multidimen­ sional challenge of creating an interpolant from floor information are supplied. - Surfaces in sturdy modeling: present effects at the implementation of free-fonn solids in 3 good proven strong versions are reviewed. - field splines and functions: an creation to field spline tools for the illustration of surfaces is given. easy houses of field splines are derived, and refinement and evaluate tools for field splines are offered intimately. form holding houses, the development of non-rectangular field spline surfaces, purposes to floor modeling, and imbedding difficulties, are mentioned. - complex special effects suggestions for quantity visualization: the stairs to be completed within the visualization strategy of quantity info are defined and instruments are mentioned that help in dealing with this knowledge. - Rational B-splines: an advent to the illustration of curves and surfaces utilizing rational B-splines is given, including a serious overview in their strength for commercial application.

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Endif end_procedure Fig. 10 The algorithm for generating a face octree Face octrees can be generated from a set of patches enclosing a finite region of the space. The algorithm corresponding to the generation of a classical octree can be described by the recursive algorithm (see Fig. 10) that generates the octree in preorder. 31 The two main parts of the algorithm are the clipping procedure, and the function that must detect if the portion of surface within the node is flat enough. Both algorithms are based on the use of bounding boxes of the patches in the list of faces correponding to the node.

6. 23) M = UXA + VXB + (u + 1- v)Xc + (v + 1- U)XD + (2 - V)XE + (2 - u)XP. where for any region G C IR? we have the indicator function XG (UV)_{1, , 0, (u,v)eG; otherwise. The graph of M is shaped like a hexagonal pyramid and is known as the Courant finite element. We will now take a closer look at the situation where the direction vectors of a box spline consists of repetitions of a few nonparallel directions. 19 . Suppose for an integer r ~ 2, that where E = (dI, d 2 , ... , and kl' k2' ... L = Ei k i .

Mathematical methods in computer aided geometric design, Academic Press, 1989. pp 181-194. [DoS 78) Doo, D. V. , Bebaviour of recursive subdivision surfaces near extraordinary points, Computer Aided Design 10 (1978) p 356-360. [Far 82) Farin, G. , Visually (jl cubic splines, Computer Aided Design 14(3) pp 137139. [Gol87) Goldman, R. , Tbe role of surfaces in solid modeling, in: G. ), Geometric modeling: algorithms and new trends, SIAM 1987. [Gre 74) Gregory, J. ), Computer Aided Geometric Design, Academic Press (1974), pp 71-87.

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