论文标题
使用可塑性对表面进行建模的旋转应变方法
A Rotation-Strain Method to Model Surfaces using Plasticity
论文作者
论文摘要
对表面的任意较大变形进行建模平滑地嵌入三维空间很具有挑战性。困难来自两个方面：现有的几何处理或正向仿真方法惩罚了当前状态和休息配置之间的差异以保持初始形状，这将导致尖峰或摇摆的大变形；问题的共同性质使其更加复杂，因为变形的表面必须在局部满足基本形式的兼容条件，以确保存在可行的解决方案。为了应对这两个挑战，我们提出了一种旋转 - 应变方法，以兼容的方式修改基本形式，并使用可塑性平稳地对表面网格的大变形进行建模。用户规定了几个顶点的位置，我们的方法找到了一个平稳的应变和旋转场，在该场合符合目标位置。我们演示了几个示例，在满足用户约束时，将三角形网格平滑地变形为较大的应变。
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference between the current status and the rest configuration to maintain the initial shape, which will lead to sharp spikes or wiggles for large deformations; the co-dimensional nature of the problem makes it more complicated because the deformed surface has to locally satisfy compatibility conditions on fundamental forms to guarantee a feasible solution exists. To address these two challenges, we propose a rotation-strain method to modify the fundamental forms in a compatible way, and model the large deformation of surface meshes smoothly using plasticity. The user prescribes the positions of a few vertices, and our method finds a smooth strain and rotation field under which the surface meets the target positions. We demonstrate several examples whereby triangle meshes are smoothly deformed to large strains while meeting user constraints.
