In the process of designing animation characters and background elements, there may be a high degree of visual blur, resulting in a strong sense of picture distortion, and it is easy to expose the incomplete picture. Accordingly, this paper proposes to use directional derivatives to deal with animation-like visual problems. This method is based on the theoretical basis of directional derivatives, combined with the current mathematical methods of animation character and background element design, and defines the important role of directional derivatives in animation and background design, and more effectively enhances the visual results of animation characters. In the research of clarity and distortion, this paper uses directional derivative derivation as the cutting-in method to test the algorithm for visual simulation and restoration of animated characters and background elements so that the algorithm can be used for each animation character and background element. The defect point is calculated, and the clarity and self-healing ability of the video itself are improved by the influence of the mathematical parameters of the surrounding known points on itself and the key variable of the directional derivative in the field. The results show that the directional derivative can play a role in promoting sublimation in the design of animated characters and background elements.