Spherical Hermite Maps
Mohamed Abouagour, Eleftherios Garyfallidis

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…
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Taxonomy
TopicsComputer Graphics and Visualization Techniques · 3D Shape Modeling and Analysis · Advanced Vision and Imaging
