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DISCRETE CURVATURE BASED ON AREA
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  • Journal title : Honam Mathematical Journal
  • Volume 32, Issue 1,  2010, pp.53-60
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2010.32.1.053
 Title & Authors
DISCRETE CURVATURE BASED ON AREA
Park, Kyeong-Su;
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 Abstract
The concept of discrete curvature is a discretization of the curvature. Many literatures introduce discrete curvatures derived from arc length of circular arcs. We propose a new concept of discrete curvature of a polygon at each vertex, which is derived from area of fan shapes. We estimate the error of the discrete curvature and compare the discrete curvature with old one.
 Keywords
discrete curvature;
 Language
English
 Cited by
1.
Curvature for Polygons, The American Mathematical Monthly, 2015, 122, 4, 332  crossref(new windwow)
 References
1.
T. Adamek, O. Connor, A multiscale representation method for nonrigid shapes with a single closed contour, IEEE Transactions on Circuits and Systems for Video Technology, 14(2004), 742-753. crossref(new window)

2.
V. Borrelli, F. Cazals, J-M. Morvan, On the angular defect of triangulations and the pointwise approximation of curvatures, Computer Aided Geometric Design 20 (2003), 319-341. crossref(new window)

3.
M. Jeon, D. Han, K. Park, G. Choi, Ternary univariate curvature-preserving subdivision, J. Appl. Math. & Computing 18(2005), No. 1-2, 235-246 crossref(new window)

4.
Lewiner, T., Arc-length based curvature estimator. In SIBGRAPI'04(2004), 250-257.

5.
M. M. Lipschutz, Theory and problems of differential geometry, McGraw-Hill Book Company, 1969.

6.
H. Llu, L. J. Latecki, W. Liu, A unified curvature definition for regular, polygonal, and digital planar curves, International Journal of Computer Vision 80 (2008), 104-124. crossref(new window)