Robust interval algorithm for surface intersections

In this paper, we develop robust algorithms for computing interval polynomial curve-to-surface and surface-to-surface intersections. These include well-conditioned transversal intersections as well as ill-conditioned non-transversal intersections. Key components of our methods are the reduction of t...

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Veröffentlicht in:Computer aided design 1997-09, Vol.29 (9), p.617-627
Hauptverfasser: Hu, Chun-Yi, Maekawa, Takashi, Patrikalakis, Nicholas M, Ye, Xiuzi
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Sprache:eng
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Zusammenfassung:In this paper, we develop robust algorithms for computing interval polynomial curve-to-surface and surface-to-surface intersections. These include well-conditioned transversal intersections as well as ill-conditioned non-transversal intersections. Key components of our methods are the reduction of the intersection problems into solving balanced or unbalanced systems of non-linear interval polynomial equations. These systems are solved using an interval non-linear polynomial solver based on Bernstein subdivision coupled with rounded interval arithmetic, documented in a series of earlier papers. The solver provides results with numerical certainty and verifiability. Examples illustrate our techniques. We also provide a theoretical analysis of degenerate interval polynomial curve-to-surface and surface-to-surface ill-conditioned non-transversal intersections.
ISSN:0010-4485
1879-2685
DOI:10.1016/S0010-4485(96)00099-1