Intersection test and blossoming perturbation for disk parametric curves and ball parametric surfaces
Date
2006-05-02
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Abstract
Errors in curve and surface representation due to inaccuracies inthe data are considered and accounted for by introducing diskparametric curves and ball parametric surfaces. Intersection testalgorithms and interval extensions using blossoming are discussedfor each of the three cases of Bézier curves, tensor productsurfaces, and triangular patches. A stability analysis is alsoperformed for each of the three cases. It is shown that undercertain restrictions disk Bézier curves and triangular ballBézier patches are stable with respect to perturbations of thecontrol disks (balls); whereas tensor product ball Béziersurfaces are in general not.
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Qun Lin and J. G. Rokne, “Intersection test and blossoming perturbation for disk parametric curves and ball parametric surfaces,” Mathematical Problems in Engineering, vol. 2006, Article ID 29643, 28 pages, 2006. doi:10.1155/MPE/2006/29643