Differentiable Rendering of Parametric Geometry

We propose an efficient method for differentiable rendering of parametric surfaces and curves, which enables their use in inverse graphics problems. Our central observation is that a representative triangle mesh can be extracted from a continuous parametric object in a differentiable and efficient way. We derive differentiable meshing operators for surfaces and curves that provide varying levels of approximation granularity. With triangle mesh approximations, we can readily leverage existing machinery for differentiable mesh rendering to handle parametric geometry. Naively combining differentiable tessellation with inverse graphics settings lacks robustness and is prone to reaching undesirable local minima. To this end, we draw a connection between our setting and the optimization of triangle meshes in inverse graphics and present a set of optimization techniques, including regularizations and coarse-to-fine schemes. We show the viability and efficiency of our method in a set of image-based computer-aided design applications.