Abstract
For a smooth plane curve, the curvature can be char- acterized by the rate of change of the angle between the tangent vector and a flxed vector. In this article we prove that the curva- ture of a space curve can also be given by the rate of change of the locally deflned 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 cur- vature 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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