# Explain properties of Bezier Curve.

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Explain properties of Bezier Curve.

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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.