中文摘要：

曲面测量面对复杂化和高精度化的挑战，除不断优化测量方法和测量仪器外，被测曲面内禀性对测量结果的影响也应给予重视。从曲面被测点微分邻域分析出发，全面阐述曲面测量中由被测对象自身特征引起的测量误差各向异性问题，提出曲面测量各向异性概念，定义各向异性误差，并详细分析其与各影响因素的关系。概括各向异性在曲面测量中的仪器综合定位误差与测量误差关系、确定工件安置方位、仪器设计和加工误差对测量误差影响四个方面的应用，提出测量仪器最大允许定位误差计算方法。以渐开螺旋面测量为例分析验证各向异性及其测量误差计算方法。研究表明曲面测量各向异性对测量仪器设计、测量方法确定和测量结果不确定度分析等方面既有理论价值又有实际意义。

英文摘要：

Curved surface measurement faces the challenges of complexity and high precision now, the impact of the surface intrinsic features on the measurement results should be taken into consideration seriously, in addition to constantly develop measurement methods and instruments. From the analysis of the measured surface point differential neighborhood, the measurement error anisotropy problem caused by measured object itself is comprehensively expounded. The concept of anisotropy of surface measurement and the definition of anisotropy error are proposed, and its relationship with the influencing factors is clarified. The applications of anisotropy of surface measurement in four aspects of curved surface measurement technology are outlined, and the maximum allowable positioning error calculation method of measurement instrument is proposed. As an application example, the anisotropy of involute tooth surface measurement is analyzed, and the anisotropic measurement error and maximum allowable positioning error calculation method are verified. The research conclusions have not only theoretical meaning but also far-reaching practical value on precision instruments design, measuring method design, uncertainty analysis of measurement results, and etc.