We propose a system for differentiating through solutions to geometry processing problems. Our system differentiates a broad class of geometric algorithms, exploiting existing fast problem-specific schemes common to geometry processing, including local-global and ADMM solvers. It is compatible with machine learning frameworks, opening doors to new classes of inverse geometry processing applications. We marry the scatter-gather approach to mesh processing with tensor-based workflows and rely on the adjoint method applied to user-specified imperative code to generate an efficient backward pass behind the scenes. We demonstrate our approach by differentiating through mean curvature flow, spectral conformal parameterization, geodesic distance computation, and as-rigid-as-possible deformation, examining usability and performance on these applications. Our system allows practitioners to differentiate through existing geometry processing algorithms without needing to reformulate them, resulting in low implementation effort, fast runtimes, and lower memory requirements than differentiable optimization tools not tailored to geometry processing.

翻译：我们提出了一种对几何处理问题解进行微分计算的系统。该系统能够对广泛类别的几何算法进行微分，充分利用了几何处理中常见的现有快速问题专用方案，包括局部-全局求解器和交替方向乘子法求解器。本系统与机器学习框架兼容，为新型逆向几何处理应用开启了大门。我们将网格处理的散射-聚集方法与基于张量的工作流相结合，并依托应用于用户指定命令式代码的伴随方法，在后台生成高效的反向传播过程。我们通过对平均曲率流、谱共形参数化、测地距离计算以及尽可能刚性变形进行微分计算来验证本方法，并考察了这些应用场景下的可用性与性能。本系统使实践者能够对现有几何处理算法直接进行微分，无需重新构建算法框架，相较于非针对几何处理定制的可微分优化工具，实现了更低的实现成本、更快的运行速度以及更少的内存需求。