中文摘要：

建立曲面上曲线的离散表达模型，并提出一种基于力密度方法的曲线形状调整和光顺算法．基于曲线控制网格与索网结构的耦合关系，建立外载荷变化最小、外载荷最小、杆长度最小和节点位移最小等优化模型，在统一求解框架下实现曲线的约束变形．由外载荷最小和节点位移最小的线性组合建立曲线的光顺模型，可以对曲面上离散曲线的形状和光顺性进行有效的控制，用于曲线的局部和全局光顺．通过以约束的形式限定点的位置，可使曲线在光顺过程中插值目标点．应用实例验证了算法的有效性．

英文摘要：

Using an analogy between the control polygon and the bar network, four minimization models as deformation engines, i.e. minimization of the force variations, minimization of the forces, minimization of the bar length were, minimization of the node displacements, were investigated. These minimization problems were formulated as a unified mathematical form by using the nodes perturbation. So it is convenient to obtain a multiple combination of the minimization models which are used to satisfy the various shape requirements. The combination of minimization of the forces and minimization of the node displacements is used for the global and local smoothness. Experimental cases show that the proposed method can be widely applied to curve editing.