基于能量约束及高斯曲率的薄壳弹性膨胀变形

Thin shells elastic inflation based on constraint of energy and Gauss curvature

三维薄壳膨胀变形是VR/AR/MR关键技术之一,自碰撞和自相交是膨胀变形的主要问题。基于离散高斯曲率和弹性形变能量函数,提出无碰撞、无自交的薄壳弹性膨胀变形算法。在三维薄壳的离散网格上定义弹性形变能量函数的膜能和弯曲能,构造离散高斯曲率约束以避免膨胀过程产生自碰撞和自相交问题,通过Newmark-beta运动控制方程求解变形运动下一时刻薄壳顶点的位置和速度。实验结果表明,该算法能够有效避免自碰撞和自相交问题产生。

Inflation of 3D thin shell is the key technology in VR/AR/MR. Self-penetration and self-collision are the bottlenecks of deformation simulation. A method based on discrete Gauss curvature and elastic deformation energy function to simulate the inflation of thin shells was presented. The elastic deformation energy function included membrane energy and bending energy on discrete mesh of 3D thin shells was constructed, and constrained conditions based on Gauss curvature were added to avoid self-penetration and self-collision phenomenon in the process of inflation. The position and velocity of the next frame were obtained by solving the equations of motion through Newmark-beta method. Experimental results show that the proposed method is more in accordance with the inflation phenomenon in the real world.