Suppose we had the equation y=x^3 , and then represented our data points as vectors.
Let the unit vectors of our axes be u=1+0i and v=0+1i, then our data point vectors have the form d[n]=x[n]u+y[n]v, for the nth data point.
We then produce a pair of affine vectors, g and h.
g = ucos(theta)+vsin(theta); h=ucos(phi)+isin(phi)
We then restate our d[n] coordinates in terms of g and h instead of u and v.
For for theta = 32 degrees and phi = 58 degrees, we get the following image:
d[n] = xu+yv = xu + (x^3)v = x[2]g+y[2]h
