An automatic algorithm for fairing B-spline curves of general order is presented. This work was motivated by a method of Farin and Sapidis about fairing planar cubic B-spline curves by subsequently removing and reinserting knots. Instead our new algorithm is based on the idea of subsequently changing one control point of a given B-spline curve so that the new curve minimizes the integral of the...

We present an approach for representing digital image by using B-spline curve fittings to the segmented digital image. The image is first segmented to form isolated contours and regions. Each region’s boundary (contour) is thereafter approximated by a B-spline curve. A cubic B-spline curve is used instead of a far higher degree Bezier curve to approximate the boundary because it has a local con...

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 ...

Investigating the Eulerian numbers and uniform B-spline recurrence relations, a connection between Eulerian numbers and B-spline values at knot points is proved, and a relation to inner products of uniform B-splines is shown. This connection allows, with few operations, to evaluate the B-spline curve at domain knots and could be utilized to obtain an easy approximation and representation of B-s...

This paper explores numerical solutions of optimal control problems using B–Spline curves. It is aimed to give a general framework on how to use B–Splines to formulate optimal control problems and to solve them numerically using Nonlinear Trajectory Generation software package. Effects of the selection of the B–Spline parameters, such as, number of intervals, smoothness, piecewise polynomial or...

C-Bézier and C-B-spline curves, as the trigonometric extensions of cubic uniform spline curves are well-known in geometric modeling. These curves depend on a shape parameter α in a way that α → 0 yields the cubic polynomial curves. The geometric effect of the alteration of this parameter is discussed in this paper by the help of relative parametrization and linear approximation.

We study variational problems for curves approximated by B-spline curves. We show that one can obtain discrete Euler-Lagrange equations for the data describing the approximated curves. Our main application is to the occluded curve problem in 2D and 3D. In this case, the aim is to find various aesthetically pleasing solutions as opposed to a solution of a physical problem. The Lagrangians of int...