Blended Elliptic Arc Splines

Arcs of conics are natural looking, smooth and gradual in curvature transition. The method in this paper proposes piecewise interpolating splines, which fit elliptic arcs between consecutive points in a given set of planar data points. Tangents of the curve at the data points are determined by a local procedure inspired by Akima's formulation. Elliptic arcs that suitably fit the orientation of these tangents are fit at all segments between control points, giving a G
¹
-continuous curve fit. In another option, the curve segments on both sides of the control points are made curvature continuous by blending with circular arcs; resulting in a G
²
-continuous curve. These curves avoid unwanted inflections and undulations; and are capable of recognizing and generating straight-line paths and sharp corners; and also have an option to specify tension of curve at individual segments. Moreover, this is computationally less expensive. Having these desirable properties, this method can be used as an effective curve fitting tool for multiple-valued functional approximation, motion path tracing, 2D geometric modeling (including typography), etc.