A note on: Spline technique for modeling roadway profile to minimize earthwork cost

Valentin R. Koch; Yves Lucet

doi:10.3934/jimo.2010.6.393

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2010, Volume 6, Issue 2: 393-400. Doi: 10.3934/jimo.2010.6.393

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A note on: Spline technique for modeling roadway profile to minimize earthwork cost

Valentin R. Koch^1, and
Yves Lucet^2,

1.
Mathematics, I. K. Barber School of Arts & Sciences Unit #5, University of British Columbia, 3333 University Way, Kelowna BC, V1V 1V7
2.
Computer Science, I. K. Barber School of Arts & Sciences Unit #4, University of British Columbia, 3333 University Way, Kelowna BC, V1V 1V7

Received: August 2009

Revised: January 2010

Published: April 2010

Abstract / Introduction Related Papers Cited by

Abstract

The gap constraint used in A. A. Moreb, Spline technique for modeling roadway profile to minimize earthwork cost, J. Ind. Man. & Opt., 5 (2) (2009), 275-283 introduces unnecessary errors, while the slope constraint may be violated for second- and higher-order splines. In this note we amend the gap constraint, while maintaining the linearity of the model. We also present an improved slope constraint for linear and quadratic splines, and show that it becomes nonlinear for cubic and higher order splines. The improvements also apply to A. Moreb, M. Aljohani, Quadratic representation for roadway profile that minimizes earthwork cost, J. Sys. Sci. & Sys. Eng., 13 (2) (2004), 245-252.

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Mathematics Subject Classification: Primary: 90C05, 90C08; Secondary: 41A15, 90B06.

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