Mathematical Modeling and Optimization of Bench Dragon Motion Paths

"Bench dragon" is a traditional folk culture activity in Zhejiang and Fujian provinces from China, which has the value of viewing and sports. Participants' benches are connected end to end, forming a dragon shape. To optimize the performance, this paper establishes a mathematical model covering collision detection, pitch optimization, and turning path design. The collision detection adopts the separation axis theorem (SAT algorithm) to calculate the normal vector and projection of the bench-frame to judge whether the intersection and ensure the safety in the dynamic environment. The pitch is optimized using the iterative method to make the bench dragon turn around smoothly without collision, and the optimal pitch is 0.43 meters. The turning path design solves the cut point by combining the circle equation, and optimizes the path by plane geometry to obtain the shortest turning path. The model is accurate and efficient, describing positions and velocities per second from -100 to 100 seconds. Future studies could further consider the complicated situations such as deformation of the bench to accommodate the varied scenes. This manuscript provides theoretical support for the design and optimization of the bench-dragon performance and demonstrates the application value of mathematical modeling in traditional culture.