TinyAD: Automatic Differentiation in Geometry Processing Made Simple

Non-linear optimization is essential to many areas of geometry processing research. However, when experimenting with different problem formulations or prototyping new algorithms, a major practical obstacle the need figure out derivatives objective functions, especially second-order are required. Deriving and manually implementing gradients Hessians both time-consuming error-prone. Automatic differentiation techniques address this problem, but can introduce diverse set obstacles themselves, e.g. limiting supported language features, imposing restrictions on program's control flow, incurring significant run time overhead, making it hard exploit sparsity patterns common in processing. We show that for geometric problems, particular meshes, simplest form forward-mode automatic not only most flexible, also actually efficient choice. TinyAD: lightweight C++ library automatically computes Hessians, sparse by differentiating small (tiny) sub-problems. Its simplicity enables easy integration; no on, e.g., looping branching imposed. TinyAD provides basic ingredients quickly implement first second order Newton-style solvers, allowing flexible adjustment solver details. By showcasing compact implementations methods from parametrization, deformation, direction field design, we demonstrate how lowers barrier exploring non-linear techniques. This fast research ideas, improves replicability existing algorithms available community as an open source library.