A novel algorithm for finding convex hull of a generic polygon with simulation of progressively supporting elastic lines

Convex hull computation is a critical problem in computational geometry with a wide range of applications. Existing approaches focus on separate algorithms for calculating the convex hull of polygons and curvilinear polygons, leaving room for improvement in terms of efficiency and accuracy. To address these limitations, we propose the “Simulation of Progressively Supporting Elastic lines” (SPSEL) algorithm, which leverages the physical properties of elastic lines and their progressive support process. The SPSEL algorithm efficiently computes the convex hull of generic polygons that contain both straight and curved edges. This paper provides a comprehensive overview of the SPSEL algorithm, including its terminology, overall process, and specific methods used in key algorithmic steps. Comparative tests are conducted to assess its performance, and the experimental results demonstrate the superior performance of the SPSEL algorithm compared to the Johnstone’s algorithm, specifically designed for curved convex hulls. The SPSEL algorithm exhibits efficiency and effectiveness in handling various types of generic polygons, showcasing its potential for achieving linear-time operations. Furthermore, the paper discusses the possibilities of extending the SPSEL algorithm to address the computation of convex envelopes for 3D shapes, a challenging research area with theoretical and practical implications. Overall, the SPSEL algorithm offers an advanced solution for computing convex hulls of polygons with both straight and curved edges, demonstrating improved efficiency and accuracy compared to existing methods. These findings contribute to the field of computational geometry and have broad implications for applications requiring convex hull computation in diverse domains.