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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.

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