Physics-based skin deformation methods can greatly improve the realism of character animation, but require non-trivial training, intensive manual intervention, and heavy numerical calculations. Due to these limitations, it is generally time-consuming to implement them, and difficult to achieve a high runtime efficiency. In order to tackle the above limitations caused by numerical calculations of physics-based skin deformation, we propose a simple and efficient analytical approach for physics-based skin deformations. Specifically, we (1) employ Fourier series to convert 3D mesh models into continuous parametric representations through a conversion algorithm, which largely reduces data size and computing time but still keeps high realism, (2) introduce a partial differential equation (PDE)-based skin deformation model and successfully obtain the first analytical solution to physics-based skin deformations which overcomes the limitations of numerical calculations. Our approach is easy to use, highly efficient, and capable to create physically realistic skin deformations.

基于物理的皮肤变形方法可以极大地改善角色动画的逼真度，但是需要不平凡的训练，密集的人工干预和大量的数值计算。由于这些限制，实现它们通常很耗时，并且难以实现较高的运行时效率。为了解决由基于物理的皮肤变形的数值计算引起的上述限制，我们提出了一种简单有效的基于物理的皮肤变形的分析方法。具体来说，我们（1）使用傅里叶级数通过转换算​​法将3D网格模型转换为连续的参数表示形式，这在很大程度上减少了数据大小和计算时间，但仍然保持了较高的真实性，（2）引入了基于偏微分方程（PDE）的皮肤变形模型，并成功获得了基于物理的皮肤变形的第一个解析解，从而克服了数值计算的局限性。我们的方法易于使用，高效且能够产生逼真的皮肤变形。