Geometric modeling of curves using weighted linear and circular segments

Abstract

This paper presents a method for geometric modeling of curves. Linear and circular segments with weight functions are used for curve design. Similar weight functions are used for smoothing and interpolation. The curve can be composed of consecutive linear and circular segments with smoothing at knots. If an interpolating curve is necessary, then weighted linear and circular segments are used for blending.Smoothness of the designed curve depends on the chosen weight function. It is possible to design the curve of variable smoothness using different weight functions.

Interpolating Rational Bézier Spline Curves with Local Shape Control

“…The polynomials w n (u) were introduced by the author [16,17]. The representation of these polynomials w n (u) by means of Bernstein polynomials was proposed by Wiltsche [18].…”