Intersections of hyperplanes and conic sections in Rⁿ

2017/02/09 by P. M. Dearing, Dearing, P. M.
Computer Science · Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Computational Geometry and Mesh Generation #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1702.03205

openalex publication_date 2017/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Closed form expressions are given for computing the parameters and vectors that identify and define the n-1 dimensional conic section that results from the intersection of a hyperplane with an n-dimensional conic section: cone, hyperboloid of two sheets, ellipsoid or paraboloid. The conic sections are assumed to be symmetric about their major axis, but may have any orientation and center. A class of hyperboloids are identified with the property that the parameters and vectors of the intersection of all hyperboloids in a subset of the class can be computed efficiently.

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