Difference Between Bezier Curve and B-Spline Curve

Bezier Curve vs B-Spline Curve

In numerical analysis in mathematics and in drawing computer graphics, many types of curves are taken help of. Bezier Curve and B-Spline Curve are two of the popular models for such analysis. There are many similarities in these two types of curves and experts call B-Spline curve to be a variation of Bezier curve. However, there are many differences also that will be discussed in this article for the benefit of the readers.

What is Bezier Curve?

Bezier curves are parametric curves used frequently in modeling smooth surfaces in computer graphics and many other related fields. These curves can be scaled indefinitely. Linked Bezier curves contain paths that are combinations that are intuitive and can be modified. This tool is also made use of in controlling motions in animation videos. When programmers of these animations talk about the physics involved, they are in essence talking about these Bezier curves. Bezier curves were first developed by Paul de Castlejau using Castlejau’s algorithm, which is considered a stable method to develop such curves. However, these curves became famous in 1962 when French designer Pierre Bezier used them to design automobiles.

The most popular Bezier curves are quadratic and cubic in nature as higher degree curves are expensive to draw and evaluate. An example of the equation of Bezier curve involving two points (linear curve) is as follows

B(t) = P0 + t(P1 – P0) = (1 – t)P0 + tP1, tε[0,1]

What is B-Spline Curve?

B-Spline curves are considered as a generalization of Bezier curves and as such share many similarities with it. However, they have more desired properties than Bezier curves. B-Spline curves require more information such as degree of the curve and a knot vector, and in general involve a more complex theory than Bezier curves. They however possess many advantages that off set this shortcoming. Firstly, a B-Spline curve can be a Bezier curve whenever the programmer so desires. Further B-Spline curve offers more control and flexibility than Bezier curve. It is possible to use lower degree curves and still maintain a large number of control points. B-Spline, despite being more useful are still polynomial curves and cannot represent simple curves like circles and ellipses. For these shapes, a further generalization of B-Spline curves known as NURBS are used.

Bezier vs B-Spline curves

• Both Bezier and B-Spline curves are used for drawing and evaluating smooth curves, especially in computer graphics and animations.

• B-Spline are considered a special case of Bezier curves

• B-Spline offer more control and flexibility than Bezier curves