Comment by wholinator2

There's an equal sign in the equation. That means it is true when y = x + 1. There's no filter we're applying, that's literally what the equation says. What you plot is f(x,y) = (y-x-1)/(x^2+y^2). The line plot is when that equals zero, the fuzzinss of it is when it doesnt. But notice that f(x,y)=0 is exactly equivalent to y=x+1. They're exactly the same. Thus, when you're plotting the fuzzy graph it is definitively _not_ a plot of y=x+1, it's a plot of z=(y-x-1)/(x^2+y^2) and those are not the same thing.

We'd only need to "apply a filter" to get the line graph if we started with z(x,y), but that's not what you wrote