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Sine-Generated Curves: Theoretical and Empirical Notes
Flintridge Preparatory School, La Canada, CA, USA
- 1 Flintridge Preparatory School, La Canada, CA, USA
Advances in Pure Mathematics·Volume 05 (2015)·Pages 689–702·Published 7 September 2015·DOI10.4236/apm.2015.511063
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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.
KeywordsParametric CurvesCalculus of VariationsOptimization
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