Design Of Interpolation Curve Based On Curvature Variation

The construction of fair curves that satisfies the geometric constraints is an impor-tant issue in computer aided geometric design.Designers hope to define a curve via giving some control points and parameters and modify the curves freely.Bezier curves consist of control points,and have many good properties in shape design.In practice,the shape modification can be transformed as optimization problem in mathematics.However,a single Bezier curve has great limitations in the complicated product design which requires extremely fairness.According to the issue,this paper presents a design method for matching arbitrary G1 and G2 Hermite data.We construct a Bezier curve model which satisfies the geo-metric constraints.Curvature variation energy is used for measuring fair curves.Then,using Simpson formula to approximate the curvature variation energy.We last solve this constrained minimization problem via the Block Coordinate Descent Method.Several comparative examples are provided to demonstrate the effectiveness of the proposed method and applications to shape design are also shown.