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The computation of all plane/surface intersections for CAD/CAM applicationsThe problem of the computation and display of all intersections of a given plane with a rational bicubic surface patch for use on an interactive CAD/CAM system is examined. The general problem of calculating all intersections of a plane and a surface consisting of rational bicubic patches is reduced to the case of a single generic patch by applying a rejection algorithm which excludes all patches that do not intersect the plane. For each pertinent patch the algorithm presented computed the intersection curves by locating an initial point on each curve, and computes successive points on the curve using a tolerance step equation. A single cubic equation solver is used to compute the initial curve points lying on the boundary of a surface patch, and the method of resultants as applied to curve theory is used to determine critical points which, in turn, are used to locate initial points that lie on intersection curves which are in the interior of the patch. Examples are given to illustrate the ability of this algorithm to produce all intersection curves.
Document ID
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Hoitsma, D. H., Jr.
(Fairchild Republic Div. Farmingdale, NY, United States)
Roche, M.
(Lundy Electronics and Systems, Inc.)
Date Acquired
August 12, 2013
Publication Date
March 1, 1984
Publication Information
Publication: NASA. Langley Research Center Computer-Aided Geometry Modeling
Subject Category
Computer Programming And Software
Accession Number
Distribution Limits
Work of the US Gov. Public Use Permitted.
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