球面赫尔米特映射
Spherical Hermite Maps
AI总结：
本文提出球面赫尔米特映射，通过存储函数值和偏导数，实现高效的球面函数评估，提升PSNR并减少法线计算噪声，适用于多种图形应用。
摘要：
球面函数在计算机图形学中广泛出现，从球谐分析照明和预计算辐射传输到神经辐射场和程序性行星渲染。高效的评估对于实时应用至关重要，但现有方法面临质量与性能之间的权衡：双线性LUT采样速度快但会产生面状效应，而双三次滤波需要16个纹理样本。大多数实现使用有限差分法计算法线，需要额外样本并引入噪声。本文提出了球面赫尔米特映射，一种带有导数的LUT表示方法，解决了这一权衡。通过在每个填充立方体贴图的每个texel中存储函数值和缩放后的偏导数，仅需四个纹理样本（2x2的足迹）即可通过双三次-赫尔米特重建实现连续梯度。关键思想是赫尔米特插值在值重建过程中自然产生平滑的导数，使法线计算几乎免费。在受控实验中，球面赫尔米特映射在双线性插值基础上将PSNR提高8-41 dB，并在成本降低四分之一的情况下达到16 taps双三次滤波的质量。解析法线在复杂表面上将平均角误差降低9-13%，同时产生稳定的镜面高光。三个应用展示了其多功能性：球谐分析Glyph可视化、径向深度图impostors用于网格细节层次、以及使用球面高程场的程序性行星/小行星渲染。
英文摘要：
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.
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