Blended Chart Surfaces: A Seamless Explicit Representation for Smooth Surface Fitting

Blended Chart Surfaces is a new explicit surface representation built for smooth fitting and differentiable geometry processing. Instead of relying on an implicit field or a neural map with chart seams, it starts from a coarse proxy mesh that defines topology and approximate shape, then optimizes a polynomial patch at each proxy vertex to match a target surface.

The key trick is a smooth one-ring blending scheme that fuses neighboring patches, so the final surface stays globally smooth across patch boundaries. That matters for workflows that need stable normals, curvature, or energy terms, since those quantities can be evaluated directly rather than reconstructed after iso-surfacing or patched together from a canonical domain.

For developers, the practical appeal is control: topology and coarse geometry stay anchored to the proxy, while local patches absorb the fine detail. The construction is also rigid-motion and scale equivariant with respect to the proxy mesh, which should make it easier to reason about fitting behavior across differently sized or positioned inputs.

The method was evaluated on a range of topologies and geometric complexity, and compared with interpolating-function baselines and mesh-displacement MLPs. The result is a tradeoff that favors compactness, simplicity, and access to differential quantities while avoiding the seam issues that often show up in explicit neural surface methods.