Properties of Bezier Curve:

The Bezier curve contain the following properties :

1. As Bezier curves are polynomial functions, they are simply computed, and infinitely differentiable (so tangents & curvatures are simply computed).

2. The curve starts at the first control point, P₀, and ends at the last control point, P_n. this does not pass through any of the intermediate control points.

3. The tangent at the beginning point (u = 0) lies along the vector from P₀ to P₁; the tangent at the ending point (u = 1) lies along with the vector from P_{n -1} to P_n.

4. The whole curve lies in the interior of the convex hull of the control points. It is known the convex hull property, and is very useful for several CAD/CAM routines.

5. Bezier curves are invariant over affine transformations of the control points. In other terms, if the control points are translated, or rotated, the curve moves to the equivalent new coordinate frame without altering its shape.