Splines are part of the standard toolbox for the approximation of functions and curves in Rd . Still, the problem of finding the spline that best approximates an input function or curve is ill-posed, since in general this yields a “spline” with an infinite number of segments. The problem can be regularized by adding a penalty term for the number of spline segments. We show how this idea can be ...

Arc splines are G continuous curves made of circular arcs and straight-line segments. They have the advantages that the curvature of an arc spline is known and controlled at all but a finite number of points, and that the offset curve of an arc spline is another arc spline. Arc splines are used by computer-controlled machines as a natural curve along which to cut and are used by highway route p...

This paper presents a non-uniform cubic C spline framework that unifies three scenarios for incorporating data from basic curves, such as spirals and conics. In the first scenario, no parameterization of the basic curves is available, only well-spaced samples; in the second, a parameterization is available but cannot be used directly in a spline framework; only in the third scenario can pieces ...

The effect of knot modifications on the shape of B-spline and NURBS curves is discussed in this paper. Theoretical results include the description of the path of curve points, obtained by the modification of a knot value, and the examination of the one-parameter family of curves. It is shown that this family has an envelope which is a lower order B-spline or NURBS curve. Applying these results ...

An algorithm is presented that constructs a C 2-continuous B-spline quaternion curve which interpolates a given sequence of unit quaternions on the rotation group SO(3). The de Casteljau type construction method of B-spline curves can be extended to generate B-spline quaternion curves Sch92]; however, the B-spline quaternion curves do not have C 2-continuity in SO(3). The authors KKS94a] recent...