Algebraic methods for intersections of quadric surfaces in GMSOLID

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Abstract

The algebraic geometry of quadric surfaces is applied to the construction of boundary representations for computer models of solid objects. A version of this approach is currently operational in the GMSOLID system developed at General Motors. A general method is presented for finding critical points on the intersection curves of quadric surfaces and for determining whether the curves are planar. This information is needed for GMSOLID's computer representation of a designed solid. The method is also used to find intersection points of a plane and two quadrics. The method is sufficiently general to handle all quadric surfaces but has been implemented only for the quadrics of GMSOLID: cylinders, spheres, and cones. The numerical methods used in the implementation are also discussed. © 1983.

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Sarraga, R. F. (1983). Algebraic methods for intersections of quadric surfaces in GMSOLID. Computer Vision, Graphics and Image Processing, 22(2), 222–238. https://doi.org/10.1016/0734-189X(83)90066-X

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