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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.
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참고문헌 (11)
참고문헌 신청
Elena V. Anoshkina / 2002 / Asymptotic Analysis of Three-Point Approximations of Vertex Normals and Curvatures / Vi-sion, Modeling, and Visualization 2002 :211~216
Alexander G. Belyaev / 2004 / Plane and space curves. curvature, curvature-based fea-tures / Max-Planck-Institut fur Informatik
V. Borrelli / 2003 / On the angular defect of triangulations and the pointwise approximation of curvatures / Computer Aided Geometric Design 20:319~341
Manfredo P. do Carmo / 1976 / Differential Geometry of Curves and Surfaces / Prentice-Hall
D. Coeurjolly / 2001 / Discrete curvature based on osculating circles estimation / Lecture Notes in Computer Science 2059:303~312
Alexander G. Belyaev / 2004 / Plane and space curves. curvature, curvature-based fea-tures / Max-Planck-Institut fur Informatik
V. Borrelli / 2003 / On the angular defect of triangulations and the pointwise approximation of curvatures / Computer Aided Geometric Design 20:319~341
Manfredo P. do Carmo / 1976 / Differential Geometry of Curves and Surfaces / Prentice-Hall
D. Coeurjolly / 2001 / Discrete curvature based on osculating circles estimation / Lecture Notes in Computer Science 2059:303~312
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