Difference between Spline, B-Spline and Bezier Curves

1. Spline :
A spline curve is a mathematical representation for which it is easy to build an interface that will allow a user to design and control the shape of complex curves and surfaces.

2. B-Spline :
B-Spline is a basis function that contains a set of control points. The B-Spline curves are specified by Bernstein basis function that has limited flexibility.

3. Bezier :
These curves are specified with boundary conditions, with a characterizing matrix or with blending function. A Bezier curve section can be filled by any number of control points. The number of control points to be approximated and their relative position determine the degree of Bezier polynomial.



Difference between Spline, B-Spline and Bezier Curves :

Spline B-Spline Bezier
A spline curve can be specified by giving a specified set of coordinate positions, called control points which indicate the general shape of the curve. The B-Spline curves are specified by Bernstein basis function that has limited flexibiity. The Bezier curves can be specified with boundary conditions, with a characterizing matrix or with blending function.
It follows the general shape of the curve. These curves are a result of the use of open uniform basis function. The curve generally follows the shape of a defining polygon.
Typical CAD application for spline include the design of automobile bodies, aircraft and spacecraft surfaces and ship hulls. These curves can be used to construct blending curves. These are found in painting and drawing packages as well as in CAD applications.
It possess a high degree of smoothness at the places where the polynomial pieces connect. The B-Spline allows the order of the basis function and hence the degree of the resulting curve is independent of number of vertices. The degree of the polynomial defining the curve segment is one less than the number of defining polygon point.
A spline curve is a mathematical representation for which it is easy to build
an interface that will allow a user to design and control the shape of complex
curves and surfaces.
In B-Spline, there is local control over the curve surface and the shape of the curve is affected by every vertex. It is a parametric curve used in related fields.

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