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VISUAL CURVATURE FOR SPACE CURVES
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  • Journal title : Honam Mathematical Journal
  • Volume 37, Issue 4,  2015, pp.487-504
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2015.37.4.487
 Title & Authors
VISUAL CURVATURE FOR SPACE CURVES
JEON, MYUNGJIN;
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 Abstract
For a smooth plane curve, the curvature can be characterized by the rate of change of the angle between the tangent vector and a fixed vector. In this article we prove that the curvature of a space curve can also be given by the rate of change of the locally defined angle between the tangent vector at a point and the nearby point. By using height functions, we introduce turning angle of a space curve and characterize the curvature by the rate of change of the turning angle. The main advantage of the turning angle is that it can be used to characterize the curvature of discrete curves. For this purpose, we introduce a discrete turning angle and a discrete curvature called visual curvature for space curves. We can show that the visual curvature is an approximation of curvature for smooth curves.
 Keywords
curvature of space curve;discrete curvature;turning angle;discrete turning angle;
 Language
English
 Cited by
 References
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