TITLE:
Sine-Generated Curves: Theoretical and Empirical Notes
AUTHORS:
Dean Hathout
KEYWORDS:
Parametric Curves, Calculus of Variations, Optimization
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.5 No.11,
September
23,
2015
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.