Abstract
D iscretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is more than a century old. However, there is no general theory or methodology in the literature, despite the ubiquitous use of discrete curves in mathematics and science. There are conflicting definitions of even basic concepts such as discrete curvature j, discrete torsion s, or discrete Frenet frame. Consider, for example, j, the ‘‘discrete curvature’’ of an angle h. We will show in the first section which follows that there are three equally worthy definitions of j, to which one is led by considering the problem of approximating a regular N -gon with sides of length ‘ by a circle:
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