Unveiling the secrets of resist development with a groundbreaking approach. This paper introduces a novel concept: each development path follows the trajectory of least resistance to developer penetration. This innovative idea posits that the development of the final line profile requires minimal dissolution time. The authors achieve this by using a variational calculation of the path integral along each local development trajectory. This calculation uniquely determines the dissolution profile as a solution to a nonlinear partial differential equation (PDE). The photoactive compound (PAC) concentration is derived from the standard Dill’s equations for exposure-bleaching, accommodating both monotonic and standing waves. The implementation and testing of this procedure demonstrate remarkable accuracy, eliminating path crossings inherent in traditional string algorithms. This method also avoids the arbitrary elimination of unfavorable points across all developing times, offering a significant advancement in resist development modeling and prediction.