Properties of Bezier Curves:

The Bezier curve contain the following properties :

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

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

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

4. The overall curve lies in the interior of the convex hull of the control points. It is called as the convex hull property, and is very useful for many CAD/CAM routines.

5. Bezier curves are invariant over affine transformations of control points. In other terms, if the control points are translated, or rotated, the curve moves to the equivalent new coordinate frame exclusive of altering its shape.