Accretive Darboux growth along a space curve

Gül Tuğ, Zehra Özdemir, İsmail Gök and F. Nejat Ekmekci

Applied Mathematics and Computation, 2018, vol. 316, issue C, 516-524

Abstract: In this article, we give a mathematical framework to model the kinematics of the surface growth of objects such as some crustacean creatures. For this, a growth velocity in the direction of the Darboux vector field is defined at each point on a spatial generating curve. A local orthonormal frame (alternative moving frame) is added to each point of the generating curve and a velocity is given in terms of local coordinate directions to obtain a system of differential equations. Using the analytical solutions of this system, various surface examples, including some seashells are provided and the shapes of these surfaces are illustrated.

Keywords: Alternative moving frame; Accretive growth; Darboux vector; General helix (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:316:y:2018:i:c:p:516-524

DOI: 10.1016/j.amc.2017.08.038

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