It is a difficult problem how to smoothly visualize the binary finite differential data during the post processing of casting CAE system. A mathematical model is proposed to reconstruct these data to be a continuous implicit function based on the Hamilton-Jacobi equations

which is independent of information of the original STL geometry and numerical simulation while it is only related to the underlying geometry represented by the finite differential data. Meanwhile

an efficient fast sweeping method is presented to solve the model. The solving process is parallelized with OpenMP language. The results reveal that the presented method can be used to effectively reconstruct arbitrary complex binary finite differential data and then realize smooth visualization. In addition

the model can be also used to reconstruct the continuous finite differential data.