The discretized curve: Vertices, edges, and curvature

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.