3d cup modeling using bessel–gamma functions and octopus machine learning

In this research, an innovative method is presented for three-dimensional modeling of artistic, cup-like shapes, where bessel and gamma functions are used to generate the base form. to determine the optimal function parameters (n, a, b) and to optimize the height range and surface smoothness, the octopus machine learning metaheuristic algorithm is employed. the final output is displayed with appealing coloring, three-dimensional effects, and soft lighting, demonstrating that the combination of analytical mathematics and artificial intelligence enables the creation of complex and visually captivating artistic forms.