Abstract
Relevant background material on approximating a continuous space curve using a discrete set of lines connected at vertices is assembled in this chapter. The formulation uses concepts from the nascent field of discrete differential geometry. The resulting discretized curve is a central component of the discrete elastic rod formulation. In particular, the discrete curvature vector associated with a vertex is used as a measure of bending strains and the length of the edges are used to account for stretching. For the purposes of illustration, the discretization of a helical space curve is discussed in detail.
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Jawed, M.K., Novelia, A., O’Reilly, O.M. (2018). The Discretized Curve: Vertices, Edges, and Curvature. In: A Primer on the Kinematics of Discrete Elastic Rods. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-319-76965-3_3
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DOI: https://doi.org/10.1007/978-3-319-76965-3_3
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