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 ...

Although curves can be generally described by using concepts such as NURBS, we will introduce subdivision curves as a lead-in to the more general concept of subdivision surfaces. Suppose we wanted to perform knot-insertion in the middle of a B-spline curve defined by four control points, p0 through p3. Using the blossoming technique, we would determine the control point to be as in Figure 1. Th...

In this note a recurrence relation for rational B-splines is presented. Using this formula, it is possible to write a rational spline in terms of normalized rational B-splines of lower order, with certain rational coeecients; these coincide with that generated by the well-known "rational version of the de Boor algorithm" based on knot-insertion Farin '88], Farin '89]. A modiied relation is pres...

We present a simple and efficient method for computing zeros of spline functions. The method exploits the close relationship between a spline and its control polygon and is based on repeated knot insertion. Like Newton’s method it is quadratically convergent, but the new method overcomes the principal problem with Newton’s method in that it always converges and no starting value needs to be sup...

A new method using the cubic B-spline curves with nominal uniform knot set to parameterize the geometry is proposed to deal with shape optimization problems. In the method, the control points of the B-spline curves are set to be the design variables in the optimization scheme. A knot insertion algorithm has been introduced in order to keep the geometry unchanged whilst increasing the number of ...

We describe the case of a 52-year-old man with end-stage emphysema who underwent a right-sided lung transplantation. During preoperative monitoring an apparently non-functioning Swan-Ganz catheter could not be removed through the insertion site - right internal jugular vein. Another Swan-Ganz catheter was successfully installed through the left internal jugular vein, pulmonary artery pressures ...

This report deals with approximation of a given scattered univariate or bivariate data set that possesses certain shape properties, such as convexity, monotonicity, and/or range restrictions. The data are approximated for instance by tensor-product B-splines preserving the shape characteristics present in the data. Shape preservation of the spline approximant is obtained by additional linear co...

The application of collocation methods using spline basis functions to solve differential model equations has been in use for a few decades. However, the application of spline collocation to the solution of the nonlinear, coupled, partial differential equations (in primitive variables) that define the motion of fluids has only recently received much attention. The issues that affect the effecti...

Variable degree polynomial (VDP) splines have recently proved themselves as a valuable tool in obtaining shape preserving approximations. However, some usual properties which one would expect of a spline space in order to be useful in geometric modeling, do not follow easily from their definition. This includes total positivity (TP) and variation diminishing, but also constructive algorithms ba...