3D Discrete Clothoid Splines
Abstract: A clothoid spline is a planar G/sup 2/ curve with piecewise linear curvature. Its discrete analogon, planar discrete clothoid spline (PDCS for short) generated by non-linear subdivision, is also of high quality owing to piecewise linear curvature distribution. We extend the PDCS to 3D by introducing discrete curvature binormal vectors and a discrete Frenet frame. An algorithm similar to the planar case is developed for creation of 3D discrete clothoid splines, Experiments show that 3D discrete clothoid spline still retains high quality. This result makes it possible to construct discrete clothoid spline surfaces on open triangle meshes or curve nets of arbitrary topology.
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