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Robust interval algorithm for surface intersections
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DOI：10.1016/S0010-4485(96)00099-1.png)
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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. (C) 1997 Elsevier Science Ltd.
Keyword:
CAD
CAGD
CAM
surface intersection
rounded interval arithmetic
robustness
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