A Survey of the Differential Geometry of Discrete Curves
Authors:
- Daniel CarrollDCDaniel Carroll
- Eleanor HankinsEHEleanor Hankins
- Emek KöseEKEmek Köse
- Ivan SterlingISIvan Sterling
Preprint
Abstract
Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over 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 {\kappa}, discrete torsion {\tau}, or discrete Frenet frame.Keywords
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