Construction of Bézier Curves by Energy Constraints

Bézier curve is a widely used modeling tool in Computer Aided Geometric Design.Construction of Bézier curves with energy constraints is one of the important topics in curve design.For design of Bézier curve with given ending control points and initial tangent vector,the remaining control points can be determined by known conditions and a parameterαwith minimal jerk energy.The parameterαcan be uniquely determined by bending energy constraints.For the ordered set of points,a combined Bézier curve with G^1 continuity can be constructed by minimal jerk energy and bending energy constraints.Finally,the combined Bézier curves of given ordered set of points and satisfying energy constraints are constructed by several examples,verifying the effectiveness and feasibility of the proposed method when compared with other methods.