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...

The objective of the paper is to continue the study of an interesting class of rational splines in polar coordinates, introduced by SS anchez-Reyes 17] and independently by de Casteljau 6]. We refer to these curves as p-splines. They are a generalization of certain analogous of B ezier curves in polar coordinates which we call p-B ezier. We present an alternative way to have an exact representa...

The modification of a knot of a B-spline curve of order k generates a family of B-spline curves. We show that an envelope of this family is a B-spline curve defined by the same control polygon, and its order is k −m, where m is the multiplicity of the modified knot. Moreover, their arbitrary order derivatives differ only in a multiplier.  2003 Elsevier Science B.V. All rights reserved.

The use of developable surfaces in ship design is of engineering importance because they can be easily manufactured without stretching or tearing, or without the use of heat treatment. In some cases, a ship hull can be entirely designed with the use of developable surfaces. In this paper, a method to create a quasi-developable B-spline surface between two limit curves is presented. The centreli...

A method of generating cubic blending spline curves based on weighted trigonometric and hyperbolic polynomial is presented in this paper. The curves inherit nearly all properties of cubic B-splines and enjoy some other advantageous properties for modeling. They can represent some conics and some transcendental curves exactly. Here weight coefficients are also shape parameters, which are called ...

This paper presents an algorithm for estimating the control points of the B-spline and curve matching which are achieved by using the dissimilarity measure based on the knot associated with the B-spline curves. The B-splines stand as one of the most efficient curve representations and possess very attractive properties such as spatial uniqueness, boundedness and continuity, local shape controll...

This paper proposes a methodology to change the shape of a B-Spline curve locally. Present algorithm modifies the existing B-Spline curve and makes it pass through a given point P, constrained to lie in region R, with limited deviation from the original curve. Proposed methodology splits the curve into atmost three segments based on the curvature of the curve and then modifies only one segment ...

Both the four-point and the uniform cubic B-spline refinement (i.e. subdivision) schemes double the number of vertices of a closed-loop polygonal curve P and produce sequences of vertices fj and bj respectively. We proposed to analyze a subdivision scheme Js that blends the rules of these two refinement methods to produce vertices of the form vj=(1–s)fj+sbj. Iterative applications of Js yield a...

Most shapes are simply too complicated to define using a single Bézier curve. A spline curve is a sequence of curve segments that are connected together to form a single continuous curve. For example, a piecewise collection of Bézier curves, connected end to end, can be called a spline curve. Overhauser curves are another example of splines. The word “spline” can also be used as a verb, as in “...

This paper describes the development of a regular hull meshing code using cubic B-Spline curves. The discretization procedure begins by definition curves over stations, bow and stern contours plan lines. Thus, new knots are created applying an equal spaced subdivision on defined B-spline Then, these transversal space knots, longitudinal subdivided into equally too. Subsequently, knots. Finally,...