Abstract In dimensional metrology the straightness, flatness or cylindricity of surfaces is commonly measured at a limited number of equidistant points on the surface. This paper describes some opportunities and characteristics of discrete Legendre polynomials to describe and analyze such measurements. The reference surface can be adequately described using a few lower order polynomials while the higher order polynomials describe the form deviations and these are independent of different reference surface definitions. Cylindricity can be described by combining Fourier coefficients for the circumference with discrete Legendre polynomials for measurements taken along the axis. Some application examples are given.

中文翻译：

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使用离散勒让德多项式表征直线度、平面度和圆柱度

摘要 在尺寸计量中，表面的直线度、平面度或圆柱度通常在表面上有限数量的等距点上进行测量。本文描述了离散勒让德多项式的一些机会和特征来描述和分析此类测量。参考表面可以使用一些低阶多项式来充分描述，而高阶多项式描述形状偏差，并且这些独立于不同的参考表面定义。圆柱度可以通过将圆周的傅立叶系数与用于沿轴测量的离散勒让德多项式相结合来描述。给出了一些应用实例。