Spherical Hermite Maps

TL;DR

Spherical Hermite Maps provide an efficient, high-quality method for evaluating spherical functions with continuous derivatives, enabling real-time rendering and improved normal estimation in graphics applications.

Contribution

The paper introduces Spherical Hermite Maps, a novel derivative-augmented LUT that achieves bicubic quality with fewer samples and enables continuous gradients, improving performance and quality in spherical function evaluation.

Findings

Significantly improve PSNR over bilinear interpolation

Match bicubic quality at one-quarter the computational cost

Reduce normal estimation error and enhance visual stability

Abstract

Spherical functions appear throughout computer graphics, from spherical harmonic lighting and precomputed radiance transfer to neural radiance fields and procedural planet rendering. Efficient evaluation is critical for real-time applications, yet existing approaches face a quality-performance trade-off: bilinear LUT sampling is fast but produces faceting, while bicubic filtering requires 16 texture samples. Most implementations use finite differences for normals, requiring extra samples and introducing noise. This paper presents Spherical Hermite Maps, a derivative-augmented LUT representation that resolves this trade-off. By storing function values alongside scaled partial derivatives at each texel of a padded cubemap, bicubic-Hermite reconstruction is enabled from only four texture samples (a 2x2 footprint) while providing continuous gradients from the same samples. The key insight is that Hermite interpolation reconstructs smooth derivatives as a byproduct of value reconstruction, making surface normals effectively free. In controlled experiments, Spherical Hermite Maps improve PSNR by 8-41 dB over bilinear interpolation and match 16-tap bicubic quality at one-quarter the cost. Analytic normals reduce mean angular error by 9-13% on complex surfaces while yielding stable specular highlights. Three applications demonstrate versatility: spherical harmonic glyph visualization, radial depth-map impostors for mesh level-of-detail, and procedural planet/asteroid rendering with spherical heightfields.