Weight-based shape modification of NURBS curves

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 NURBS curve, we provide a weight-based shape modification method by means of which one can prescribe not only the new position of an arbitrary chosen point of a plane NURBS curve but the tangent direction as well.  1999 Elsevier Science B.V. All rights reserved.