Accretive Darboux growth along a space curve

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 (al...

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Bibliographic Details
Published in:Applied mathematics and computation 2018-01, Vol.316, p.516-524
Main Authors: Tuğ, Gül, Özdemir, Zehra, Gök, İsmail, Ekmekci, F. Nejat
Format: Article
Language:English
Subjects:
Accretive growth
Alternative moving frame
Darboux vector
General helix
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Summary: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.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2017.08.038