The Bézier curve is one of the most commonly used parametric curves in CAGD and Computer Graphics and has many

good properties for shape design. Developing more convenient techniques for designing and modifying Bézier curve is an im-

portant problem, and is also an important research issue in CAD/CAM and NC technology fields. This work investigates the

optimal shape modification of Bézier curves by geometric constraints. This paper presents a new method by constrained optimi-

zation based on changing the control points of the curves. By this method, the authors modify control points of the original Bézier

curves to satisfy the given constraints and modify the shape of the curves optimally. Practical examples are also given.