B-splines

B-splines are a family of smooth curves that can be constructed to interpolate or approximate a set of control points. They are used extensively for curve and surface design in engineering and media applications. Their popularity comes from the fact that they offer a simple and intuitive means of adjusting the shape of a curve or surface interactively. Any point on a B-spline curve or surface is defined as a local blend of the control points. The most widely used blending functions are cubic. Higher order blending makes the surface smoother and consequently less detailled. The normal formulation of the B-spline blend is in a parametric space where the control points are equally distributed. Non uniform splines use an irregular distribution of the control points to create special effects, such as discontinuities in the curve or surface. Rational splines provide a further means of user interaction by weighting each point such that the curve is pulled more strongly towards the higher weights. (C) 2010 John Wiley & Sons, Inc.