Title: Design with smooth rational geometric spline curves based on fractional decomposition (GP. Bonneau)

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A well-known result of algebra is used to find a special parametric representation of rational curves. Some properties of this representation are given: derivatives of any order in any parameter value are written in a closed form, and an exact integration formula for non-parametric rational curves is given. These results are applied to find rational geometric spline curves which interpolate or approximate given points, and minimize an energy functional.

Reference: Proceedings ISATA, Mecatronics (1995).

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Approximation of points by a rational curve, with increasing smoothness.

(mpeg movie, 230Kb) smoothing example

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