@article{(Open Science Index):https://publications.waset.org/pdf/4572,
	  title     = {Generalized Method for Estimating Best-Fit Vertical Alignments for Profile Data},
	  author    = {Said M. Easa and  Shinya Kikuchi},
	  country	= {},
	  institution	= {},
	  abstract     = {When the profile information of an existing road is
missing or not up-to-date and the parameters of the vertical
alignment are needed for engineering analysis, the engineer has to recreate
the geometric design features of the road alignment using
collected profile data. The profile data may be collected using
traditional surveying methods, global positioning systems, or digital
imagery. This paper develops a method that estimates the parameters
of the geometric features that best characterize the existing vertical
alignments in terms of tangents and the expressions of the curve, that
may be symmetrical, asymmetrical, reverse, and complex vertical
curves. The method is implemented using an Excel-based
optimization method that minimizes the differences between the
observed profile and the profiles estimated from the equations of the
vertical curve. The method uses a 'wireframe' representation of the
profile that makes the proposed method applicable to all types of
vertical curves. A secondary contribution of this paper is to introduce
the properties of the equal-arc asymmetrical curve that has been
recently developed in the highway geometric design field.},
	    journal   = {International Journal of Civil and Environmental Engineering},
	  volume    = {3},
	  number    = {9},
	  year      = {2009},
	  pages     = {308 - 316},
	  ee        = {https://publications.waset.org/pdf/4572},
	  url   	= {https://publications.waset.org/vol/33},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 33, 2009},