Relation function between surfaces, what to read?

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Suppose I have two continuous surfaces A and B. I want to define the function f which will link the surfaces like A = f(B), i.e. when B changing then A also will changes in the way defined by f and vice versa. Especially interesting case that look like A = f(B,Θ) where parameter Θ define how exactly surfaces A and B linked.

Where/what can I read about this and stuff around? If you faced similar problem please share something about.

Thanks!