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求解过程进行微分的系统。该系统能够对广泛的几何算法进行微分，利用几何处理中常见的现有快速问题特定方案，包括局部-全局和ADMM求解器。它与机器学习框架兼容，为逆几何处理应用的新类别打开了大门。我们将网格处理中的分散-聚集方法与基于张量的工作流相结合，并依赖于应用于用户指定命令式代码的伴随方法，在幕后生成高效的反向传播。通过微分平均曲率流、谱共形参数化、测地距离计算以及尽可能刚性变形，我们展示了该方法的可用性和性能。我们的系统允许从业者直接对现有几何处理算法进行微分，而无需重新制定它们，从而相比非针对几何处理的可微优化工具，实现了更低的实现成本、更快的运行时间和更低的内存需求。