Modeling contact between deformable solids is a fundamental problem in computer animation, mechanical design, and robotics. Existing methods based on $C^0$-discretizations -- piece-wise linear or polynomial surfaces -- suffer from discontinuities and irregularities in tangential contact forces, which can significantly affect simulation outcomes and even prevent convergence. To overcome this limitation, we employ smooth surface representations for both contacting bodies. Through a series of test cases, we show that our approach offers advantages over existing methods in terms of accuracy and robustness for both forward and inverse problems. The contributions of our work include identifying the limitations of existing methods, examining the advantages of smooth surface representation, and proposing forward and inverse problems to analyze contact force irregularities.

翻译：可变形固体间的接触建模是计算机动画、机械设计与机器人领域的核心问题。基于$C^0$离散化方法（分段线性或多项式表面）的现有方法在切向接触力中存在不连续性与不规则性，这严重影响仿真结果甚至阻碍收敛。为克服这一局限性，我们采用光滑表面表征接触双方。通过系列测试案例表明，我们的方法在正问题与逆问题的精度与鲁棒性上均优于现有方法。本工作贡献包括：识别现有方法的局限性、验证光滑表面表征的优势，并提出用于分析接触力不规则性的正问题与逆问题框架。