Interactive Shape Control with Rational Cubic Splines

Abstract

AbstractA rational cubic spline, with shape parameters, has been discussed with the view to its application in Computer Graphics. It incorporates both conic sections and parametric cubic curves 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 rational cubic spline attains parametric C2 smoothness whereas the stitching of the conic segments preserves visually reasonable smoothness (C1) at the neighboring knots. A very simple distance-based approximated derivative scheme is also presented to calculate control points. 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. We discuss difficult cases of elliptic arcs in space and introduce intermediate point interpolation scheme which can force the curve to pass through given point between any segment.