NVIDIA researchers introduces a new technique called FlexiCubes, which aims to address the limitations of existing isosurface extraction methods for gradient-based mesh optimization. FlexiCubes adapts a Dual Marching Cubes formulation by introducing additional degrees of freedom to flexibly position each extracted vertex within its dual cell. The formulation is carefully constrained to produce manifold and watertight meshes that are intersection-free in the majority of cases, enabling well-behaved differentiation with respect to the underlying mesh. The key feature of FlexiCubes is its ability to consistently optimize meshes using gradient-based methods.

FlexiCubes offers significant benefits for various mesh generation applications, including inverse rendering, optimizing physical and geometric energies, and generative 3D modeling. The resulting meshes capture desired geometry at low element counts and are easily optimized via gradient descent. The technique also includes extensions such as adaptively adjusting mesh resolution via hierarchical refinement and automatically tetrahedralizing the interior of the domain.

The implementation leverages a scalar signed-distance function defined in space to extract its 0-isosurface as a triangle mesh. The method involves extracting mesh vertices within cells and evaluating objective functions on the resulting mesh. The researchers discuss the challenges of gradient-based optimization in the context of isosurface extraction from unknown scalar fields, highlighting the need for a specialized approach like FlexiCubes. The technique is designed to be used iteratively during gradient-based optimization, offering a new perspective on differentiable mesh optimization.