Abstract: Surface measurement plays a key role in reverse engineering of free-form surfaces. Considering measurement precision and efficiency of geometry with the freeform feature from the point of view of measurement and reconstruction, adaptive measurement of plane curves based on non-uniform B-splines is presented, which is able to remove noise and point with big error in the measurement process through adjusting the span. The coordinate measuring machine can measure whole free surface automatically and continuously with improvement in precision and efficiency. Last, the method is illustrated with examples. Curve fitting accuracy has achieved the 100 nm level and measurement accuracy of μm level. It has active guidance meaning and applied value to the engineering practice.

Key words: free-form surface, adaptive measurement, non-uniform B-splines, adaptive adjustment of span

摘要： 曲面测量是自由曲面逆向工程中的关键步骤。从测量和重构的角度，综合考虑具有自由曲面特征的几何体测量效率及精度，提出基于非均匀B样条的平面曲线自适应测量算法，通过跨距的自适应调整去除测量过程中的噪点及误点，指导接触式三坐标测量机（Coordinate Measuring Machine，CMM）自动连续测量整张自由曲面，提高了测量效率和测量精度。最后实例验证了该方法，曲线拟合精度达到100 nm级，测量精度达到μm级，具有较强的工程应用价值。

关键词: 自由曲面, 自适应测量, 非均匀Ｂ样条, 跨距自适应调整