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The algorithm by schwartz, sharir and collins on the piano mover's problem

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Geometry and Robotics (GeoRob 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 391))

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Abstract

A presentation of the quantifier elimination problem, and other problems connected to it, such as the "piano mover's problem", is followed by the state of the art on the question. Afterwards are explained Schwartz', Sharir's and Collins' algorithm, based on the cylindrical algebraic decomposition, and two applications to bring out its possibilities and limitations. The tracks and views of development in this research domain, which is a useful tool for algebraic geometry, are lastly indicated. Its limitation, due to a very high cost, is an actual obstacle, which is to be removed, for its use for many classes of concrete geometric and algebraic problems.

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Authors and Affiliations

  1. Laboratorie L.I.T.P. / GRECO de Calcul Formel, Université Pierre et Marie Curie Paris VI, 4 Place Jussieu, 75252, Paris Cedex 05, France

    Joël Marchand

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  1. Joël Marchand
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J. -D. Boissonnat J. -P. Laumond

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© 1989 Springer-Verlag Berlin Heidelberg

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Marchand, J. (1989). The algorithm by schwartz, sharir and collins on the piano mover's problem. In: Boissonnat, J.D., Laumond, J.P. (eds) Geometry and Robotics. GeoRob 1988. Lecture Notes in Computer Science, vol 391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51683-2_24

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  • DOI: https://doi.org/10.1007/3-540-51683-2_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51683-5

  • Online ISBN: 978-3-540-46748-9

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