Regular algebraic curve segments (III) - applications in interactive design and data fitting

In this paper (part three of the trilogy) we use low degree G(1) and G(2) c ontinuous regular algebraic spline curves defined within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly char acterize curve families whose members have the required interpolating prope rties and possess a minimal number of inflection points. The regular algebr aic spline curves considered here have many attractive features: They are e asy to construct. There exist convenient geometric control handles to local ly modify the shape of the curve. The error of the approximation is control lable. Since the spline curve is always inside the parallelogram, the error of the fit is bounded by the size of the parallelogram. The spline curve c an be rapidly displayed, even though the algebraic curve segments are impli citly defined. (C) 2001 Elsevier Science B.V. All rights reserved.