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Extraction of cylinders and cones from minimal point sets

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Publication Date
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HAL-INRIA
Keywords
  • Cylinders
  • Interpolation
  • Mixed Set Of 3D Points
  • Cones
  • [Info.Info-Cg] Computer Science [Cs]/Computational Geometry [Cs.Cg]
  • [Info.Info-Sc] Computer Science [Cs]/Symbolic Computation [Cs.Sc]
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Abstract

We propose new algebraic methods for extracting cylinders and cones from minimal point sets, including oriented points. More precisely, we are interested in computing efficiently cylinders through a set of three points, one of them being oriented, or through a set of five simple points. We are also interested in computing efficiently cones through a set of two oriented points, through a set of four points, one of them being oriented, or through a set of six points. For these different interpolation problems, we give optimal bounds on the number of solutions. Moreover, we describe algebraic methods targeted to solve these problems efficiently.

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