Sine-Generated Curves: Theoretical and Empirical Notes

DOI: 10.4236/apm.2015.511063   PDF   HTML   XML   3,168 Downloads   4,001 Views   Citations

Abstract

Sine-generated curves belong to a class of intrinsic functions which describe a curve by specifying its “direction angle”. The curve is determined by ω, the maximum angle which the curve makes with the horizontal, and the fact that the direction angle changes in a sinusoidal fashion along the path. Sine-generated curves are shown to be excellent approximations to the path of minimal average curvature, and expressions for radius of curvature and curve sinuosity are derived.

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Hathout, D. (2015) Sine-Generated Curves: Theoretical and Empirical Notes. Advances in Pure Mathematics, 5, 689-702. doi: 10.4236/apm.2015.511063.

Conflicts of Interest

The authors declare no conflicts of interest.

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