TikZ not drawing some lines in grid

Question

When I use \draw to create a grid, several lines are missing. See the attached code and images, where, for example, the dashed red grid is missing the bottom and left boundaries. Actually the solid green and solid red gird are missing it as well. I'm not sure if I am getting graphical bugs or if this is intended behavior:

\documentclass{article}
\usepackage{tikz}
\pagestyle{empty}

\pgfdeclarelayer{level0}
\pgfdeclarelayer{level1}
\pgfdeclarelayer{level2}
\pgfsetlayers{main,level0,level1,level2}

\begin{document}

\begin{figure}[h]
  \centering
    \begin{tikzpicture}[scale=2]
      \begin{pgfonlayer}{level0} % Level 0
        \draw[help lines] (0,0) grid (5,5); % Base grid
        \draw[very thick, scale=5] (0,0) grid (1,1); % Darker lines to mark e.g. box boundaries
      \end{pgfonlayer}

      \begin{pgfonlayer}{level1} % Level 1
        \draw[green, dashed] (.5,.5) grid[step=.5] (4.5,4.5); % Ghost cells
        \draw[green] (1,1) grid[step=.5] (4,4);
      \end{pgfonlayer}

      \begin{pgfonlayer}{level2} % Level 2
        \draw[red, dashed] (1.75,1.75) grid[step=.25] (3.25,3.25); % Ghost cells
        \draw[red] (2,2) grid[step=.25] (3,3);
      \end{pgfonlayer}

    \end{tikzpicture}
    \caption{Standard isotropic refinement.}
\end{figure}

\end{document}

Thank you!

Answer 1

The PGF manual section on the grid operation (14.9 in my version) says:

It is important to note that the grid is always “phased” such that it contains the point (0,0) if that point happens to be inside the rectangle. Thus, the grid does not always have an intersection at the corner points; this occurs only if the corner points are multiples of the stepping. Note that due to rounding errors, the “last” lines of a grid may be omitted. In this case, you have to add an epsilon to the corner points. [emphasis added]

Not sure why you're missing the lines at the start of the grid instead of the end, but in any case the analogous workaround works.

\documentclass{article}
\usepackage{tikz}
\pagestyle{empty}

\pgfdeclarelayer{level0}
\pgfdeclarelayer{level1}
\pgfdeclarelayer{level2}
\pgfsetlayers{main,level0,level1,level2}

\begin{document}

\begin{figure}[h]
  \centering
    \begin{tikzpicture}[scale=2]
      \begin{pgfonlayer}{level0} % Level 0
        \draw[help lines] (0,0) grid (5,5); % Base grid
        \draw[very thick, scale=5] (0,0) grid (1,1); % Darker lines to mark e.g. box boundaries
      \end{pgfonlayer}

      \begin{pgfonlayer}{level1} % Level 1
        \draw[green, dashed] (.4999,.4999) grid[step=.5] (4.5,4.5); % Ghost cells
        \draw[green] (0.999,0.999) grid[step=.5] (4,4);
      \end{pgfonlayer}

      \begin{pgfonlayer}{level2} % Level 2
        \draw[red, dashed] (1.74999,1.74999) grid[step=.25] (3.25,3.25); % Ghost cells
        \draw[red] (2,2) grid[step=.25] (3,3);
      \end{pgfonlayer}

    \end{tikzpicture}
    \caption{Standard isotropic refinement.}
\end{figure}

\end{document}