Shape Modification of Bézier Curves by Constrained Optimization of Position and Tangent Vector

This paper investigates geometric constrained optimization for shape modification of Bézier curves. For the tangent vector constraint of a single parameter, precise formula is obtained for shape modification of Bézier curve. The shape modification problem with both position vector and tangent vector constraints of a single parameter and multiple parameters are also considered. Practical examples are given to show the efficiency of this proposed method.