Abstract
A new approach for a reliable subdivision algorithm for the intersection of parametric surfaces is presented. Bounding volumes for surface patches like axis aligned bounding boxes or parallel epipeds used in former approaches are replaced by linear interval estimations (LIE).
Two different types of LIEs are proposed, based in one case on a linear taylor approximation of the patch and an interval estimation of the Lagrange remainder and in the second case on the use of the intrinsic structure of affine arithmetic. Both approaches guarantee that a patch lies completely inside its estimation. Taking advantage of the characteristics of LIEs, the intersection test for bounding volumes is replaced by a method, that directly tests the intersection of the estimations and as a by-product, it prunes both parameter domains in a way, that only relevant parts of the domains are subdivided in the next step.
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© 2001 Springer Science+Business Media New York
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Bühler, K., Barth, W. (2001). A New Intersection Algorithm for Parametric Surfaces Based on Linear Interval Estimations. In: Krämer, W., von Gudenberg, J.W. (eds) Scientific Computing, Validated Numerics, Interval Methods. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6484-0_15
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DOI: https://doi.org/10.1007/978-1-4757-6484-0_15
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