Interactive Shape Preserving Interpolation by T-conic Spiral Spline

A T-conic (rational cubic with a quadratic denominator) spiral spline, with shape control parameters, will be discussed with the view to its application in Computer Graphics. An efficient scheme is presented which constructs a curve interpolating a set of given data points and allows subsequent interactive alteration of the shape of the curve by changing the shape control and shape preserving parameters associated with each spiral segment. These spiral segments are either spirals taken from the conic curve or spirals created by joining circular arcs to segments of the conic. The parameters (weights), in the description of the spline curve can be used to modify the shape of the curve, locally and globally. The use of spirals gives the designer excellent control over the shape of curve that is produced because there are no internal curvature extrema, inflection points and singularities in a spiral segment.