At present, the development of animation-based works for human–computer interaction applications has increased. To generate animations, actions are pre-recorded and animation flows are configured. In this research, from two images of letters of the sign language alphabet, intermediate frames were generated using a numerical traced algorithm based on homotopy. The parameters of a homotopy curve were optimized with a genetic algorithm to generate intermediate frames. In the experiments performed, sequences where a person executes pairs of letters in sign language were recorded and animations of the same pairs of letters were generated with the proposed method. Subsequently, the similarity of the real sequences to the animations was measured using Dynamic Time Wrapping. The results obtained show that the images obtained are consistent with their execution by a person. Animation files between sign pairs were created from sign images, with each file weighing an average of 18.3 KB. By having sequences between pairs of letters it is possible to animate words and sentences. The animations generated by this homotopy-based animation method optimized with a genetic algorithm can be used in various deaf interaction applications to provide assistance. From several pairs of letters a file base was generated using the animations between pairs of letters; with these files you can create animations of words and sentences.