A rational cubic spline has been used with the view to its applications in computer graphics, vision, and image processing. It incorporates linear, conic and parametric cubic curve sections as special cases. The parameters (weights), in the description of the spline curve can be used to modify the shape of the curve, locally and globally. The spline attains parametric smoothness of different degrees depending on different choices of derivative settings and nature of curve segments. However, the stitching of the rational cubic segments preserves C2 smoothness and stitching of the conic segments preserves visually reasonable C1 smoothness at the neighboring knots. The curve scheme is interpolatory and can plot parabolic, hyperbolic, elliptic, and circular splines independently as well as bits and pieces of a rational cubic spline. This chapter discusses cases of elliptic arcs in space and also introduces intermediate point interpolation scheme which can force the curve to pass through given point between any segment.
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(2008). Linear, Conic and Rational Cubic Splines. In: Interactive Curve Modeling. Springer, London. https://doi.org/10.1007/978-1-84628-871-5_5
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DOI: https://doi.org/10.1007/978-1-84628-871-5_5
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