A simple method of shape transformation using the modified Gray–Scott model

Abstract

In this paper, based on the original Gray–Scott model, we propose a modified Gray–Scott model by introducing a target term into the reaction–diffusion equations. We apply this modified model in the context of shape transformation problems. To expedite the process from the source shape to the target shape, we utilize the explicit Euler method to solve our proposed modified Gray–Scott model, making our approach simpler and more efficient. To validate the feasibility of our method, we conduct simulation experiments in both two-dimensional (2D) and three-dimensional (3D) spaces. By progressing through experiments of increasing complexity, we demonstrate the natural effectiveness of our simulation method as a viable approach for shape transformation. To demonstrate the efficiency of the method, we provide the runtime consumed by the simulated shape transformation experiment. Additionally, to assess the correspondence between the ground truth values of the target shape and the simulated results, we calculate the corresponding area change rate and volume change rate in 2D and 3D spaces to prove that our proposed method can effectively transform into the target shape.