虚拟环境下变形线性体实时建模算法研究

研究提出一套虚拟环境下线绳和缆索两类变形线性体的几何变形数学建模算法。首先将变形线性体的物理和几何特性,对它们建模的共同之处进行研究,采用微分几何方法在正交直角坐标系下描述其变形,选择样条函数描述线性体的中心线,提出描述扭转变形的一种简单方法,结合广义弹簧理论建立它们的变形能数学模型,应用材料力学理论设计参数,并采用能量极小化方法求解;其次分别针对线绳和缆索的特性修改共性模型,形成各自的建模算法;第三通过仿真模型与实际变形线性体的对比实验验证仿真算法的正确性。实验结果表明,该算法能够正确描绘线绳和缆索变形,并能够满足虚拟环境的实时交互帧频率。

Research on Real-time Modeling Algorithm of Deformable Linear Objects in Virtual Environment

A new algorithm for the mathematical modeling of deformable linear objects including ropes and cables in virtual environment was proposed according to their physical and geometrical characteristics.Firstly,a research on the general modeling technologies of them was taken.Their deformation was described in a right-handed orthonormal basis with the theory of differential geometry,and their centerline was presented proposed by B-spline.Torsion around the centerline was simply described as well.With the method of generalized spring system,the mathematical model of their deformation energy was built.The physical parameters in the model were calculated by mechanics of material,and the model was solved by an energy minimizing algorithm.Secondly,the modeling methods of ropes and cables were studied respectively based on the general model.Thirdly,the contrast experiments were done between the real bodies and the simulation results to verify the efficiency of the algorithm.The results show the deformation of the ropes and cables are correctly described,and the whole system can be solved at interactive frame rates.