Sine-Generated Curves: Theoretical and Empirical Notes - Advances in Pure Mathematics

APM > Vol.5 No.11, September 2015

Advances in Pure Mathematics

Volume 5, Issue 11 (September 2015)

ISSN Print: 2160-0368 ISSN Online: 2160-0384

Google-based Impact Factor: 0.48 Citations

Sine-Generated Curves: Theoretical and Empirical Notes ()

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Download as PDF (Size: 3094KB) PP. 689-702

DOI: 10.4236/apm.2015.511063 4,911 Downloads 5,921 Views Citations

Author(s)

Dean Hathout^*

Affiliation(s)

Flintridge Preparatory School, La Canada, CA, USA.

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.

KEYWORDS

Parametric Curves, Calculus of Variations, Optimization

Share and Cite:

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

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