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In dimensional inspection using coordinate measuring machines (CMMs), the following issues are critical to achieve accurate inspection while minimizing the cost and time: 1) How can we select the sampling positions of the measurements so that we can get as much information from a limited number of samples as possible and 2) given the limited number of measurements, how can we assess the form error so that one can reliably decide whether the product is acceptable? To address these problems, we propose a wavelet-based model that takes advantage of the fact that the Lipschitz regularity holds for the CMM data. Under the framework of the proposed model, we derive the optimal sampling positions and propose a systematic procedure to estimate the form error given the limited number of sampled points. The proposed method is validated using both synthetic and real CMM data sets for straightness measurements. The comparison with other existing methods demonstrates the effectiveness of our method.