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

arXiv: https://arxiv.org/abs/2606.18069 · HTML: https://mlsanity.com/paper/2606.18069/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 55 references that are in the map.
- First posted on arXiv 16 Jun 2026.

## Builds on (most cited first, 20 of 20)

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- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [ReLU Fields: The Little Non-linearity That Could](https://mlsanity.com/paper/2205.10824/) (2022)
- [Neural Subdivision](https://mlsanity.com/paper/2005.01819/) (2020)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [Better Patch Stitching for Parametric Surface Reconstruction](https://mlsanity.com/paper/2010.07021/) (2020)
- [Neural Geometry Processing via Spherical Neural Surfaces](https://mlsanity.com/paper/2407.07755/) (2024)
- [Neural Parametric Surfaces for Shape Modeling](https://mlsanity.com/paper/2309.09911/) (2023)
- [MASH: Masked Anchored SpHerical Distances for 3D Shape Representation and Generation](https://mlsanity.com/paper/2504.09149/) (2025)
- [Algebraic Smooth Occluding Contours](https://mlsanity.com/paper/2306.01973/) (2023)
- [Polyhedral design with blended n-sided interpolants](https://mlsanity.com/paper/2601.19322/) (2026)

## Abstract (arXiv)

A surface representation suitable for geometry processing should be compact and explicit, provide global smoothness guarantees, support a wide range of surface topologies, and offer reliable access to differential quantities such as normals and surface energies, while remaining compatible with modern differentiable optimization. Existing neural representations typically sacrifice one or more of these properties: implicit fields typically require iso-surfacing for downstream use, while explicit neural maps are constrained by canonical-domain parametrizations or exhibit seam artifacts between local charts. We introduce Blended Chart Surfaces, a compact, network-free, explicit representation that is smooth by construction and anchored to user-provided topology. Given a coarse proxy mesh encoding the intended surface topology and approximate geometry, Blended Chart Surfaces jointly optimize for a polynomial map at each proxy vertex using an off-the-shelf optimizer to fit to an implicit target shape, avoiding the need for an input parametrization. Neighboring maps are fused using a smooth 'one-ring coordinate' blending scheme, decoupling topology and coarse geometry (carried by the proxy) from geometric details (carried by the local patches). The surface is globally smooth, fully differentiable, and enables stable evaluation of derivatives, making differential quantities and surface energies directly accessible. Additionally, our construction is equivariant to rigid motions and scaling of the proxy mesh. We evaluate Blended Chart Surfaces on various topologies and geometric complexity, and compare against explicit alternatives including interpolating-function baselines and mesh-displacement MLPs. Across these, Blended Chart Surfaces achieve a favorable trade-off among compactness, simplicity, access to differential quantities, and expressivity while remaining smooth across patch boundaries.