Tom Lyche, Larry L. Schumaker's Mathematical Methods in Computer Aided Geometric Design II PDF

Geometry Topology

By Tom Lyche, Larry L. Schumaker

This quantity relies on a global convention held in June 1991, and includes educational and unique research-level papers on mathematical tools in CAGD and photograph processing. top researchers (Barnsley, Chui, Seidell, de Casteljau) have authored invited survey papers on spline and Bezier equipment for curve and floor modeling, visualization, and information becoming in addition to connections with wavelets and fractals, and their functions in picture processing. this can be a very profitable sector with the twin laptop graphics/applied arithmetic marketplace

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5. TVansfinite Interpolation The problem of constructing a continuous surface which interpolates —filling the holes— a grid of curves appears in many applications where data are digi­ tized along lines in model surfaces [29]. Starting from a closed grid, transfinite interpolation leads to volume models of the enclosed solid volume. Standard schemes like Coons approach require grids with strong topology limitations. In any case, the main problem of transfinite interpolation is that the user is either faced with non-rectangular regions in the grid or with vertices where a number of edges other than four meet.

Because of the definition of a face node, the exact surface must lie in the band. Therefore, the whole boundary of the object is contained in the region defined by the set of bands of the face nodes in the octree [4], Figure 1. Bands of neighbor nodes must overlap at the common boundary, although not completely. The union of all face node bands defines a 'thick surface' with a width of twice the tolerance, which contains the true surface of the object. The thick surface of 5 is a connected region that can be used as a bound for S in geometric tests, and supply robust region boimds for set operations, [4].

The present paper includes a comparative study of some of these algorithms discussing shape control and fairness of the fi­ nal surface, geometric continuity, space complexity of the model and their performance in basic solid interrogations. §1. Introduction Geometric modeling has to provide efficient, interactive and powerful tools for the representation and manipulation of three-dimensional objects. However, so far there is no unified framework for modeling 3D shapes. In fact, surface models can describe either open surfaces or closed sets of patches that enclose a finite volume.

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