Rational Sigma (σ )Splines

As interactive curve design is a basic need for CAD/CAM, computer graphics, vision, imaging and various other disciplines. It is desired to have a robust, visually pleasant, well-controlled, and effective scheme that can provide a useful solution to many problems of different kinds at one platform. A rational spline, with some additional shape parameters in its description as well as in the description of its piecewise stitching, may be a good choice in this regard. This chapter has been devoted to a more general rational spline, known as the sigma (σ ) spline. Although, a σ – spline is a GC1 rational spline as far as its theoretical smoothness is concerned, in most practical cases, it provides a C1, GC2 or C2 solution. It is the most generalized spline in the literature and recovers, as a special case, most of the existing methods in the literature. These methods include weighted spline, ν – spline, weighted Nu-spline, γ – spline, and so on.

Keywords

Shape Parameter Point Tension Spline Curve Control Polygon Global Tension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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