The on-machine inspection occupies certain manufacturing time, so it is important to improve the inspection accuracy as much as possible on the premise of an acceptable sampling scale. We proposed efficient adaptive sampling methods for NURBS curve and surface based on deviation analysis. The deviation is defined as the difference between the theoretical and reconstructed curves. For curve sampling, the less significant points are removed iteratively from initial dense on-curve points. In addition, we derived a closed solution for curve deviation, thus it is superior to existing methods in terms of reconstruction accuracy and time consumption. The curve sampling algorithm is further extended to surface sampling by simplifying it into curve sampling in two directions. Our methods are compared with classic sampling strategies and the results show that the curve and surface reconstruction errors of our method are reduced by 62% and 71% respectively.
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