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

Blended Chart Surfaces present a compact, network‑free, explicit surface representation that is smooth by construction and anchored to user‑provided topology. The method jointly optimizes polynomial maps at proxy mesh vertices to fit an implicit target shape, then fuses neighboring maps with a smooth one‑ring coordinate blending scheme, decoupling coarse geometry from fine details. The resulting surface is globally smooth, fully differentiable, and equivariant to rigid motions and scaling, enabling reliable access to differential quantities and surface energies while avoiding seam artifacts common in other explicit neural maps.

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