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Distance Computation from an Ellipsoid to a Linear or a Quadric Surface in IRn

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Book cover Computer Algebra in Scientific Computing (CASC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4770))

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Abstract

Given the equations of the surfaces, our goal is to construct a univariate polynomial one of the zeroes of which coincides with the square of the distance between these surfaces. To achieve this goal we employ the Elimination Theory methods.

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References

  1. Schneider, P.J., Eberly, D.H.: Geometric Tools for Computer Graphics. Elsevier, San Francisco (2003)

    Google Scholar 

  2. Lin, A., Han, S.-P.: On the distance between two ellipsoids. SIAM J. on Optimization 13, 298–308 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Uteshev, A.Y., Cherkasov, T.M.: The search for maximum of a polynomial. J. Symbolic Computation 25, 587–618 (1998)

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  4. Kalinina, E.A., Uteshev, A.Y.: Elimination Theory (in Russian). St. Petersburg State University (2002)

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  5. Bikker, P., Uteshev, A.Y.: On the Bézout construction of the resultant. J. Symbolic Computation 28, 45–88 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1986)

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  7. Faddeev, D.K., Faddeeva, V.N.: Computational Methods of Linear Algebra. Freeman, San Francisco (1963)

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  8. Proskuryakov, I.V.: Problems in Linear Algebra. Mir, Moscow (1978)

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Victor G. Ganzha Ernst W. Mayr Evgenii V. Vorozhtsov

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© 2007 Springer-Verlag Berlin Heidelberg

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Uteshev, A.Y., Yashina, M.V. (2007). Distance Computation from an Ellipsoid to a Linear or a Quadric Surface in IRn . In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2007. Lecture Notes in Computer Science, vol 4770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75187-8_31

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  • DOI: https://doi.org/10.1007/978-3-540-75187-8_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75186-1

  • Online ISBN: 978-3-540-75187-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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