Improvement of piecewise developable surface approximation algorithm based on Gauss image

Developable surfaces play a crucial role in industrial product design. Approximating three-dimensional surfaces using piecewise developable surfaces is a significant research area. In this paper, we propose an improved algorithm for piecewise developable surface approximation based on Gauss image features. Firstly, we employ a density-based spherical clustering method rather than the traditional greedy approach, ensuring better alignment with the Gauss image, and enabling effective shape deformation to improve developability. We also focus on the first principal component to enhance the one-dimensional feature of the Gauss image. Next, shape deformation is incorporated into the Gauss image optimization process to preserve a higher degree of similarity between the output developable surface and the original input mesh. Finally, a segmentation algorithm is integrated to facilitate the manufacturing process of the resulting developable surfaces. To evaluate the performance of our method, we compare it with existing developable surface approximation algorithms using metrics such as maximum Gauss curvature, the number of developable patches, and Hausdorff distance. Experimental results demonstrate that our proposed algorithm outperforms current methods.