Properly fading out grids

Question

I'm working on an illustration of a particular multiscale analysis method.

\begin{tikzpicture}[
    scale=1.5,
    circ/.style = {
        circle,
        draw,
        black!75,
        outer sep=0pt,
        inner sep=1pt
    }
]

    \begin{scope}[step=0.5, very thin, black!30]
        \draw [xshift=-2.5cm] (-0.9, -1) grid (1, 1);
        \draw [] (-1, -1) grid (1, 1);
        \draw [xshift=2.5cm] (-1, -1) grid (0.9, 1);
    \end{scope}

    \filldraw[fill=blue!40!white, fill opacity=0.5, draw=blue!50!white, very thin] (-0.5, -1) rectangle (0.5, 1);

    \foreach \y in {-1, -0.5, 0, 0.5, 1} {
        \foreach \x in {-0.5, 0, 0.5} {
            \node [circ, fill=black!75] (enode) at (\x, \y) {};
        }
        \foreach \x in {-1.5, -1, 1, 1.5} {
            \node [circ, fill=white] (bnode) at (\x, \y) {};
        }
    }
\end{tikzpicture}

The above code produces the following result:

I'm now, out of general interest and in an attempt to become better at TikZ, trying to put the finishing touches to the figure and try and fade the five hanging horizontal line segments of the left and right subdomains to white without affecting the rest of the subdomain.

My attempt to reproduce the answer by Ilhan Polat leads to an error that the counter variable \x is undefined. Another answer, by Jean-Christophe Dubacq, to a similar question does not work as expected — I assume this is because the grid is not centered and transform-ing the fade doesn't work either.

Could someone please lend a hand and explain how to do this in an elegant way, or, at all? Thanks in advance.

Answer 1

Not, sure if this is what you are looks for, but with the \usetikzlibrary{fadings} you can use path fading=west on the lines on the left and path fading=east on the right hand side

    \begin{scope}[step=0.5, very thin, black!30]
        \draw [xshift=-2.5cm, path fading=west] (-0.9, -1) grid (1, 1);
        \draw [] (-1, -1) grid (1, 1);
        \draw [xshift=2.5cm, path fading=east] (-1, -1) grid (0.9, 1);
    \end{scope}

to achieve:

If you just want the hanging parts to fade, not the squares, then draw them separately using:

\begin{scope}[step=0.5, very thin, black!30]
    \draw [xshift=-2.5cm] (-0.5, -1) grid (1, 1);
    \draw [xshift=-2.5cm, path fading=west] (-0.9, -1) grid (-0.5, 1);
    \draw [] (-1, -1) grid (1, 1);
    \draw [xshift=2.5cm] (-1, -1) grid (0.5, 1);
    \draw [xshift=2.5cm, , path fading=east] (0.5, -1) grid (0.9, 1);
\end{scope}

which yields:

Code:

\documentclass[border=2pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{fadings}

\begin{document}
\begin{tikzpicture}[
    scale=1.5,
    circ/.style = {
        circle,
        draw,
        black!75,
        outer sep=0pt,
        inner sep=1pt
    }
]

    \begin{scope}[step=0.5, very thin, black!30]
        \draw [xshift=-2.5cm, path fading=west] (-0.9, -1) grid (1, 1);
        \draw [] (-1, -1) grid (1, 1);
        \draw [xshift=2.5cm, path fading=east] (-1, -1) grid (0.9, 1);
    \end{scope}

    \filldraw[fill=blue!40!white, fill opacity=0.5, draw=blue!50!white, very thin] 
        (-0.5, -1) rectangle (0.5, 1);

    \foreach \y in {-1, -0.5, 0, 0.5, 1} {
        \foreach \x in {-0.5, 0, 0.5} {
            \node [circ, fill=black!75] (enode) at (\x, \y) {};
        }
        \foreach \x in {-1.5, -1, 1, 1.5} {
            \node [circ, fill=white] (bnode) at (\x, \y) {};
        }
    }
\end{tikzpicture}
\end{document}

Answer 2

I figured out how to do this on my own but prefer the look of the answer by Peter Grill. Simply create another column and apply the fade to them:

The artifact on the right does not appear in the PDF. Here's the MWE:

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{fadings}

    \begin{document}
        \begin{tikzpicture}[
             scale=1.5,
             circ/.style = {
                 circle,
                 draw,
                 black!75,
                 outer sep=0pt,
                 inner sep=1pt
             }
        ]

        \begin{scope}[step=0.5, very thin, black!30]
            \draw [xshift=-3.5cm, path fading=west] (-0.5, -1) grid (0, 1);
            \draw [xshift=-2.5cm] (-1, -1) grid (1, 1);
            \draw [] (-1, -1) grid (1, 1);
            \draw [xshift=2.5cm] (-1, -1) grid (1, 1);
            \draw [xshift=3.5cm, path fading=east] (0, -1) grid (0.5, 1);
        \end{scope}

        \filldraw[fill=blue!40!white, fill opacity=0.5, draw=blue!50!white, very thin] (-0.5, -1) rectangle (0.5, 1);

        \foreach \y in {-1, -0.5, 0, 0.5, 1} {
            \foreach \x in {-0.5, 0, 0.5} {
                \node [circ, fill=black!75] (enode) at (\x, \y) {};
            }
            \foreach \x in {-1.5, -1, 1, 1.5} {
                \node [circ, fill=white] (bnode) at (\x, \y) {};
            }
        }
    \end{tikzpicture}
\end{document}

It should also be possible to create custom shadings and clip them to accomplish an analogous effect when working on more complex shapes where such tricks do not apply.

Edit: Upon further review, this is the same as employed here by Dubacq. I misread.