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Energy Minimizing Mountain Ascent

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Abstract

In this article, an optimal mountain ascent is studied as a particular problem of a human walking over a rugged terrain. First, an approximation of the terrain is constructed using particular smooth splines—macro-elements. Then a functional measuring the energy consumption along boundary curves of a macro-element is defined. Finally, the corresponding discrete problem of finding the optimal path on a mesh of curves is applied. Numerical results on real-life data indicate that computed paths are a good approximation of hiking paths in nature.

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References

  1. Helbing, D., Molnár, P.: Social force model for pedestrian dynamics. Phys. Rev. E 51, 4282–4286 (1995)

    Article  Google Scholar 

  2. Helbing, D., Keltsch, J., Molnár, P.: Modelling the evolution of human trail systems. Nature 388, 47–49 (1997)

    Article  Google Scholar 

  3. Minetti, A.E.: Optimum gradient of mountain paths. J. Appl. Physiol. 79, 1698–1703 (1995)

    Google Scholar 

  4. Minetti, A.E., Alexander, R.M.: A theory of metabolic costs for bipedal gaits. J. Theor. Biol. 186, 467–476 (1997)

    Article  Google Scholar 

  5. Minetti, A.E., Moia, G., Roi, S., Susta, D., Ferretti, G.: Energy cost of walking and running at extreme uphill and downhill slopes. J. Appl. Physiol. 93, 1039–1046 (2002)

    Google Scholar 

  6. Margaria, R.: Sulla fisiologia e specialmente sul consume energetico della marcia e della corsa a varia velocita ed inclinazione del terreno. Atti Accad. Naz. Lincei, Mem. Lincee, Mat. Appl. 7, 299–368 (1938)

    Google Scholar 

  7. De Smith, M.: GIS, distance, paths and anisotropy. In: Longley, P.A., Batty, M. (eds.) Advanced Spatial Analysis: the CASA Book of GIS, pp. 309–326. ESRI Press, Redlands (2003)

    Google Scholar 

  8. Llobera, M., Sluckin, T.: Zigzagging: Theoretical insights on climbing strategies. J. Theor. Biol. 249(2), 206–217 (2007)

    Article  Google Scholar 

  9. Lai, M.-J., Schumaker, L.L.: Spline Functions on Triangulations. Encyclopedia of Mathematics and Its Applications, vol. 110. Cambridge University Press, Cambridge (2007)

    Book  MATH  Google Scholar 

  10. Lai, M.-J., Schumaker, L.L.: Quadrilateral macro-elements. SIAM J. Math. Anal. 33, 1107–1116 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Jaklič, G., Žagar, E.: Shape preserving interpolation by cubic G 1 splines in R 3. Ann. Univ. Ferrara, Sez. 7: Sci. Mat. 54(2), 259–267 (2008)

    Article  MATH  Google Scholar 

  12. Wallner, J.: Note on curve and surface energies. Comput. Aided Geom. Des. 24(8–9), 494–498 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  13. Schröter, T., Glöckner, M.-N.: How to climb a mountain? Simulating efficient ways to the mountain top. ECMI Newsl. 46, 31–32 (2009)

    Google Scholar 

  14. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)

    MATH  Google Scholar 

  15. de Berg, M., van Kreveld, M., Overmars, M., Schwarzkopf, O.: Computational Geometry, Algorithms and Applications. Springer, Berlin (1997)

    MATH  Google Scholar 

  16. Farin, G.: Curves and Surfaces for Computer-Aided Geometric Design, 5th edn. Academic Press, New York (2002)

    Google Scholar 

  17. Wolfram Research, Inc.: Mathematica, Version 8.0. Champaign, IL (2010)

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Acknowledgements

Operation partly-financed by the European Union, European Social Fund.

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Authors and Affiliations

  1. FMF, University of Ljubljana, Ljubljana, Slovenia

    Gašper Jaklič, Tadej Kanduč & Emil Žagar

  2. IMFM, University of Ljubljana, Ljubljana, Slovenia

    Gašper Jaklič, Selena Praprotnik & Emil Žagar

  3. IAM, University of Primorska, Koper, Slovenia

    Gašper Jaklič

  4. Turboinštitut, Ljubljana, Slovenia

    Tadej Kanduč

Authors
  1. Gašper Jaklič
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  2. Tadej Kanduč
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  3. Selena Praprotnik
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  4. Emil Žagar
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Corresponding author

Correspondence to Selena Praprotnik.

Additional information

Communicated by Ilio Galligani.

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Jaklič, G., Kanduč, T., Praprotnik, S. et al. Energy Minimizing Mountain Ascent. J Optim Theory Appl 155, 680–693 (2012). https://doi.org/10.1007/s10957-012-0088-4

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  • DOI: https://doi.org/10.1007/s10957-012-0088-4

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