A basis of discrete harmonic functions for efficient representation and analysis of crystallographic texture is presented. Discrete harmonics are a numerical representation of the harmonics on the sphere. A finite element formulation is utilized to calculate these orthonormal basis functions, which provides several advantageous features for quantitative texture analysis. These include high‐precision numerical integration, a simple implementation of the non‐negativity constraint and computational efficiency. Simple examples of pole figure and texture interpolation and of Fourier filtering using these basis sets are presented.

中文翻译：

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离散球谐函数用于纹理表示和分析

提出了用于有效表示和分析晶体织构的离散谐波函数的基础。离散谐波是球上谐波的数字表示。利用有限元公式来计算这些正交基函数，这为定量纹理分析提供了几个有利的功能。其中包括高精度数值积分，非负约束的简单实现和计算效率。给出了极图和纹理插值以及使用这些基集进行傅立叶滤波的简单示例。