  Surface parameterization plays an essential role in numerous computer
graphics and geometry processing applications. Traditional parameterization
approaches are designed for high-quality meshes laboriously created by
specialized 3D modelers, thus unable to meet the processing demand for the
current explosion of ordinary 3D data. Moreover, their working mechanisms are
typically restricted to certain simple topologies, thus relying on cumbersome
manual efforts (e.g., surface cutting, part segmentation) for pre-processing.
In this paper, we introduce the Flatten Anything Model (FAM), an unsupervised
neural architecture to achieve global free-boundary surface parameterization
via learning point-wise mappings between 3D points on the target geometric
surface and adaptively-deformed UV coordinates within the 2D parameter domain.
To mimic the actual physical procedures, we ingeniously construct
geometrically-interpretable sub-networks with specific functionalities of
surface cutting, UV deforming, unwrapping, and wrapping, which are assembled
into a bi-directional cycle mapping framework. Compared with previous methods,
our FAM directly operates on discrete surface points without utilizing
connectivity information, thus significantly reducing the strict requirements
for mesh quality and even applicable to unstructured point cloud data. More
importantly, our FAM is fully-automated without the need for pre-cutting and
can deal with highly-complex topologies, since its learning process adaptively
finds reasonable cutting seams and UV boundaries. Extensive experiments
demonstrate the universality, superiority, and inspiring potential of our
proposed neural surface parameterization paradigm. The code will be publicly
available.
