Telescope mirrors determine the imaging quality and the observation ability of the telescopes. Unfortunately, manufacturing highly accurate mirrors remains a bottleneck problem in space optics. One primary cause is the lack of a technique to robustly measure the three-dimensional (3-D) shapes of mirrors for inverse engineering. After centuries of study, researchers developed different techniques for testing the quality of telescope mirrors and proposed different methods for measuring the 3-D shapes of mirrors. Among them, interferometers become popular in evaluating the surface errors of the manufactured mirrors. However, interferometers could not measure some important mirror parameters, e.g., paraxial radius, geometry dimension, and eccentric errors, directly and accurately although these parameters are essential for mirror manufacturing. For those methods that could measure these parameters, their measurement accuracies are far beyond satisfactory. We present a technique for robust measurement of the 3-D shapes of mirrors with single-shot projection. Experimental results show that this technique is significantly more robust than state-of-The-Art techniques, which makes it feasible for commercial devices to measure the shapes of mirrors quantitatively and robustly.