Suppose I have two functions which I know are homotopic to one another. Is there software I can use to find a homotopy between them?

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Ideally, this would be something working on a numerical level, rather than symbolic. For more context, I have two sound samples: One of a standard English speaker pronouncing a phoneme (a basic unit of speech), and one of a person with a speech impediment pronouncing a phoneme. Both of these samples can be modeled with continuous functions, and those functions approximated by polynomials, so the goal is to find an approximation of a homotopy between those functions.