Peel and Pool: The Path to Mandala Perfection
摘要
Mandalas are renowned for their sacred symmetry, a principle that resonates deeply with human consciousness. This symmetry is manifested in the circular arrangement of their motifs. However, the circular layers derived from mandala images are often error-prone and unreliable for structural analysis. In contrast, using convex-hull layers and partitioning them into regular layers proves to be more reliable. We demonstrate this interesting fact through various illustrations and novel theoretical results. These findings, grounded in discrete geometry, facilitate the exploration of mandala structures using a novel peel-and-pool technique based on iterative convex-hull layers (‘peeling’) and regular layers (‘pooling’). Our technique can rectify handcrafted or distorted mandalas, restoring their overall symmetry and enhancing their geometric harmony. These concepts offer fresh insights into the mathematical beauty of mandalas, with applications in art analysis, pattern recognition, and cultural studies. We validate the efficacy of our approach through experiments and visualizations.