Generation of Curves by Controlling Curvature Variations Based on Discrete Curves

Curvature is known as an important geometrical property for curve generation in engineering applications. Many methods have already been proposed to control the curvature distribution of curves, but most of them are for planar curves. This research proposes a new scheme for controlling curvature distribution of planar and space curves, based on discrete curves. Discrete curves, such as discrete Clothoid, have an ideal curvature distribution, because discrete geometry models have a high degree of freedom. For application to practical CAD/CAM, a parametric curve with a controlled curvature distribution can be generated based on a discrete curve with an almost ideal curvature distribution. A G2 curve consisting of quintic Bezier curve segments has been generated by the energy minimization method. The generated curve passes through the given points and has the given tangent vector, normal vector and curvature on both ends. And the curvature distribution of the generated curve by using the method of this paper shows the smooth change throughout the curve.