**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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