Modeling geometric errors in computerized measuring microscopes (CMMs) is a critical step in ensuring measurement accuracy and reliability. This study proposes a method utilizing differential geometry to model geometric errors in CMMs. The approach focuses on identifying errors, modeling them through generalized coordinates, and applying transformations from Cartesian to curvilinear coordinates to minimize discrepancies between measured and actual coordinates. Experiments conducted on a two-dimensional error model reveal that the distribution of absolute errors predominantly falls within small value ranges, providing a foundation for targeted error mitigation strategies. By minimizing deviations, it ensures reliable operation in precision measurement systems. Its flexibility and robustness make it suitable for broad applications, offering a foundation for further optimization in complex measurement scenarios.