Some of the desirable properties of a bezier curve include the following:
- Bezier curves 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.