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.


Shape Parameter Point Tension Spline Curve Control Polygon Global Tension 
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