SHARC: Reference point driven Spherical Harmonic Representation for Complex Shapes

Abstract

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.

Figures (11)

• Figure 1: Overview of the SHARC pipeline. From a dense pool of interior candidates, we select a sparse set of reference points that maximize surface visibility. For each point, the local radial distance field is encoded into Spherical Harmonic (SH) coefficients. To reconstruct the shape, we decode these fields and recover the surface points, using a local consistency constraint to filter noisy reconstructed points.
• Figure 2: Qualitative comparison of reconstruction quality. We compare SHARC against CoverageAxis++ wang2024coverage and MASH Li-2025-MASH, demonstrating our method's ability to preserve fine geometric detail using significantly fewer geometric primitives.
• Figure 3: Runtime analysis. Mean execution time (in seconds) for CoverageAxis++ (CA++), Raw Medial Axis (RMA), MASH, and our method across four datasets. The total time is decomposed into Preprocessing (gray), Encoding (blue), and Decoding/Reconstruction (orange).
• Figure 4: Visual Impact of Proximity Threshold ($\tau_{prox}$). We evaluate reconstruction quality on the Multi-Face Bust and Armadillo models. Without a threshold ($\tau_{prox}=\text{None}$), the selection is driven purely by visibility, resulting in a sparse representation ($|\mathcal{C}|=31$ for Armadillo) that fails to capture fine details like the scales on the leg or facial creases. Our default setting ($\tau_{prox}=0.2$) enforces locality, recovering these high-frequency features with a compact set of anchors ($|\mathcal{C}|=60$). A strict threshold ($\tau_{prox}=0.05$) results in an excessive number of reference points ($|\mathcal{C}|=830$) without significant visual improvement.
• Figure 5: Visual Impact of Spherical Harmonic Bandwidth ($L$). We compare reconstructions of the Stanford Dragon, Thai Statue, Earth, and City models at varying bandwidths. Lower bandwidths ($L=16, 32$) result in overly smoothed geometry, failing to capture high-frequency features. Our default setting ($L=64$) successfully recovers fine details such as the dragon's scales and the sharp corners of the skyscrapers. Doubling the bandwidth to $L=128$ offers minor visual improvement while increasing the storage footprint (see Sec.4.2 of main paper).