Bidimensional splines, strictly increasing in one argument

I am working in R. I want to specify flexibly a function q(X,Y) where q is strictly increasing with respect to X (but not necessarily with respect to Y).
I want to use bidimensional splines but I don't know how to do (how to impose the monotonicity constraint in 2D).
So far, my method is to select several values of Y, and for each values of Y, I compute a monotone splines with respect to X. And then I interpolate to create the whole function q. But I wonder if it was possible to do all this in 1 step?