I need a general equation that I can use to model the nonlinear or exponential relationship between a variable Y and two predictor variables X1 and X2. My sketch below shows the type of relationship I am looking for. Note that all three variables range between 0 and 1.
What about $y = x_1^{\frac{1}{2}x_2 + 2(1-x_2)}$. The exponent needs some reparametrization though, in case you want to have a $y = x_1$ when $x_2=1/2$...