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A Survey of the Differential Geometry of Discrete Curves

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References

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  4. A. Bobenko, A. and Pinkall, U. “Discrete surfaces with constant negative Gaussian curvature and the Hirota equation”, J. Diff. Geom. 43 (1990), 527–611.

  5. Carroll, D., Kose, E., and Sterling, I. “Improving Frenet’s Frame using Bishop’s Frame”, J. of Mathematics Research, Vol. 5, No. 4 (2013), 97–106.

  6. Doliwa, A. and Santini P. “Integrable dynamics of a discrete curve and the Ablowitz-Ladik hierarchy”, J. Math. Phys. 36 (1995), 1259–1273.

  7. Hoffman, T. “Discrete Curves and Surfaces”, Ph.D. Thesis, Technische Universität Berlin (2000).

  8. Levien, R. “From Spiral to Spline: Optimal Techniques in Interactive Curve Design”, Ph.D. Thesis, University of California, Berkeley (2009).

  9. McCrae, J. and Singh, K. “Sketching piecewise clothoid curves”, Computers & Graphics, Vol. 33, Issue 4 (Aug. 2009), 452461.

  10. Oldfather, W. A., Ellis, C. A., and Brown, Donald M. “Leonhard Euler’s elastic curves”, Isis, Vol. 20, No. 1 (Nov. 1933), 72–160.

  11. Sogo, K. “Variational discretization of Euler's Elastica problem”, J. of the Physical Society of Japan, Vol. 75, Issue 6 (2006), 064007-064007-4.

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Authors and Affiliations

  1. Mathematics and Computer Science, St Mary’s College of Maryland, 18952 East Fisher Road, Saint Marys, MD, 20686, USA

    Daniel Carroll, Eleanor Hankins, Emek Kose & Ivan Sterling

  2. Department of Mathematics, The University of Tennesee, 227 Ayres Hall, 1403 Circle Drive, Knoxville, TN, 37996, USA

    Daniel Carroll, Eleanor Hankins, Emek Kose & Ivan Sterling

Authors
  1. Daniel Carroll
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  2. Eleanor Hankins
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  3. Emek Kose
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  4. Ivan Sterling
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Correspondence to Ivan Sterling.

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Carroll, D., Hankins, E., Kose, E. et al. A Survey of the Differential Geometry of Discrete Curves. Math Intelligencer 36, 28–35 (2014). https://doi.org/10.1007/s00283-014-9472-2

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