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 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...

We introduce control curves for trigonometric splines and show that they have properties similar to those for classical polynomial splines. In particular, we discuss knot insertion algorithms, and show that as more and more knots are inserted into a trigonometric spline, the associated control curves converge to the spline. In addition, we establish a convex-hull property and a variation-dimini...

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 paper presents a technique for construction of C interpolating rational Bézier spline curves by means of blending rational quadric Bézier curves. A class of polynomials which satisfy special boundary conditions is used for blending. Properties of the polynomials are considered. The constructed spline curves have local shape control that make them useful in such geometric applications as rea...

For planar spline curves and bivariate box-spline functions, the cone of normals of a polynomial spline piece is enclosed by the cone of normals of its spline control polyhedron. This note collects some concrete examples to show that this is not true for subdivision surfaces, both at extraordinary points and in the regular, box-spline setting. A larger set, the cross products of families of con...

We address the problem of how to perform prescribed shape modification of NURBS curves merely by the modification of the weight of some of their control points. As is known, NURBS curves can be considered as central projections of nonrational B-spline curves. Making use of the property that there is an infinite number of nonrational B-spline curves the central projection of which is a given NUR...

Given a planar spline curve and local tolerances, a matched pair of polygons is computed that encloses the curve and whose width (distance between corresponding break points) is below the tolerances. This is the simplest instance of a subdividable linear efficient variety enclosure, short sleve. We develop general criteria, that certify correctness of a global, polygonal enclosure built from a ...

As much powerful tools in sounding and computer science appear for the construction of charts, new processing methods are to be used. We present a model for locating intersections in a set of B-spline curves. This method is applied for the generalization of isobathymetric lines which are designed with B-spline curves. The interest of our method is that it processes with large sets of data and m...