<p>The refinement of industrial technology and market demands has driven an increase in precision requirements for components and parts. Accurate control and evaluation of roundness errors are crucial to the performance and quality of products in high-end equipment, precision instruments, aerospace, and other critical sectors. This paper proposes an optimized roundness error extraction method based on data transformation and the Quickhull convex hull algorithm. This method preprocesses the extraction point sets used in roundness error evaluation through extreme values transformation and mean value transformation. Subsequently, it utilizes the Quickhull convex hull algorithm to extract valid calculation points that significantly impact the roundness error calculation, thereby enhancing the efficiency of roundness error evaluation. Experimental results show that when applying the Extreme values transformation method and Mean value transformation method to process 120 uniformly extraction points per revolution, the number of valid calculation points can be optimized to 23 and 14 points respectively. And as the number of extraction points increases, the optimization efficiency becomes higher. Furthermore, it is applicable to different numbers of extraction points and fitting calculation methods. This method is of great significance in improving processing efficiency, ensuring product quality, and providing new insights for the development of roundness error evaluation technologies.</p>