Morphological dynamics analysis on 3D surface using the Gray-Scott model

This paper proposes a 3D surface morphology dynamics analysis method based on an improved Gray-Scott model, designed to achieve rapid transformation and deformation of complex geometric shapes. By replacing the traditional Laplace operator with the Laplace-Beltrami operator, this model can directly handle shape transformations on triangular mesh surfaces without the need for geometric simplification. The method employs an explicit numerical scheme and operator splitting techniques to enhance computational efficiency and stability. Numerical experiments on both 2D and 3D models demonstrate the effectiveness of the method, including smooth transitions between simple and complex shapes, as well as transformations of surfaces such as spheres and bunny models. These results highlight the potential applications of this method in fields such as computer vision, virtual reality, medical imaging, and smart material design, particularly in scenarios requiring high-precision and efficient 3D shape transformations.