# SHARC: Reference point driven Spherical Harmonic Representation for Complex Shapes

arXiv: https://arxiv.org/abs/2604.01894 · HTML: https://mlsanity.com/paper/2604.01894/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 45 references that are in the map.
- First posted on arXiv 2 Apr 2026.

## Builds on (most cited first, 26 of 26)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [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)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [3DILG: Irregular Latent Grids for 3D Generative Modeling](https://mlsanity.com/paper/2205.13914/) (2022)
- [Neural Fields as Learnable Kernels for 3D Reconstruction](https://mlsanity.com/paper/2111.13674/) (2021)
- [GIFS: Neural Implicit Function for General Shape Representation](https://mlsanity.com/paper/2204.07126/) (2022)
- [Point2Skeleton: Learning Skeletal Representations from Point Clouds](https://mlsanity.com/paper/2012.00230/) (2020)
- [3PSDF: Three-Pole Signed Distance Function for Learning Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2205.15572/) (2022)
- [Coverage Axis: Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2110.00965/) (2021)
- [Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram](https://mlsanity.com/paper/2210.13676/) (2022)
- [Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization](https://mlsanity.com/paper/2401.12946/) (2024)
- [Top-Down Shape Abstraction Based on Greedy Pole Selection](https://mlsanity.com/paper/1910.08954/) (2019)
- [Medial Skeletal Diagram: A Generalized Medial Axis Approach for 3D Shape Representation](https://mlsanity.com/paper/2310.09395/) (2023)
- [LSMAT Least Squares Medial Axis Transform](https://mlsanity.com/paper/2010.05066/) (2020)
- [MATTopo: Topology-preserving Medial Axis Transform with Restricted Power Diagram](https://mlsanity.com/paper/2403.18761/) (2024)
- [MASH: Masked Anchored SpHerical Distances for 3D Shape Representation and Generation](https://mlsanity.com/paper/2504.09149/) (2025)
- [FSH3D: 3D Representation via Fibonacci Spherical Harmonics](https://mlsanity.com/paper/2406.08308/) (2024)
- [Shape Representation using Gaussian Process mixture models](https://mlsanity.com/paper/2604.00862/) (2026)

## Abstract (arXiv)

We propose SHARC, a novel framework that synthesizes arbitrary, genus-agnostic shapes by means of a collection of Spherical Harmonic (SH) representations of distance fields. These distance fields are anchored at optimally placed reference points in the interior volume of the surface in a way that maximizes learning of the finer details of the surface. To achieve this, we employ a cost function that jointly maximizes sparsity and centrality in terms of positioning, as well as visibility of the surface from their location. For each selected reference point, we sample the visible distance field to the surface geometry via ray-casting and compute the SH coefficients using the Fast Spherical Harmonic Transform (FSHT). To enhance geometric fidelity, we apply a configurable low-pass filter to the coefficients and refine the output using a local consistency constraint based on proximity. Evaluation of SHARC against state-of-the-art methods demonstrates that the proposed method outperforms existing approaches in both reconstruction accuracy and time efficiency without sacrificing model parsimony. The source code is available at https://github.com/POSE-Lab/SHARC.