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**Properties of Bezier Curve**

They generally follow the shape of the control polygon, which consists of the segments

joining the control points.

They always pass through the first and last control points.

They are contained in the convex hull of their defining control points.

The degree of the polynomial defining the curve segment is one less that the number of

defining polygon point. Therefore, for 4 control points, the degree of the polynomial is 3.

A Bezier curve generally follows the shape of the defining polygon.

The direction of the tangent vector at the end points is same as that of the vector

determined by first and last segments.

The convex hull property for a Bezier curve ensures that the polynomial smoothly

follows the control points.

No straight line intersects a Bezier curve more times than it intersects its control polygon.

They are invariant under an affine transformation.

Bezier curves exhibit global control means moving a control point alters the shape of the

whole curve.

A given Bezier curve can be subdivided at a point t=t0 into two Bezier segments which

join together at the point corresponding to the parameter value t=t0.