How to put node in an accurate place? How to use different style of font in TikZ?

Question

I want to draw something like this:

This is my code:

\documentclass{article}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz}
%\usepackage[active,tightpage,floats]{preview}
%\setlength\PreviewBorder{30pt}%
\usetikzlibrary{calc, fit, shapes.geometric}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

%\colorlet{MAROON}{Maroon}

\begin{document}

\begin{figure}[ht]
  \centering
  \begin{tikzpicture}
    \coordinate (Origin)   at (0,0);

    \coordinate (XAxisMax) at (5.5,0);
    \coordinate (YAxisMax) at (0,4.5);

    \coordinate (Ylow) at (-0.5,0);
    \coordinate (Xlow) at (0,-0.5);
    \coordinate (XMax) at (5.5,-0.5);
    \coordinate (YMax) at (-0.5,4.5);

    \draw [thick, darkgray] (Origin) -- (XAxisMax);% Draw x axis
    \draw [thick, darkgray] (Origin) -- (YAxisMax);% Draw y axis

    \draw [thick, darkgray!40, -latex] (Xlow) -- (XMax);% Draw x axis
    \draw [thick, darkgray!40, -latex] (Ylow) -- (YMax);% Draw y axis

    \foreach \x in {1,2,...,10}{% Two indices running over each
      \foreach \y in {1,2,...,8}{% node on the grid we have drawn 
        \node[thick,draw,circle,inner sep=2pt,fill=gray!60, name=circle-\x-\y] at (0.5*\x,0.5*\y) {};
            % Places a dot at those points
      }
    }


    \begin{pgfonlayer}{background}
    \node (B) [draw, color=BrickRed, fill=red!30, rectangle, rounded corners, fit={(circle-1-1) (circle-10-1)}] {};
    \end{pgfonlayer}

    \begin{pgfonlayer}{background}
    \node (A) [draw, color=BrickRed, fill=red!30, rectangle, rounded corners, fit={(circle-1-5) (circle-10-8)}] {};
    \end{pgfonlayer}

    \node[align=center, below] at (2.75,0) {$i$};
    \node[align=center, left]  at (0,2.25) {$j$};
    \node[align=center, left]  at (-0.5,2.25) {Data\\domain};
    \node [above] at (A.north) {$k = N -1$};
    \coordinate (bb1) at (circle-10-1);
    \node [above right of = 5pt] at (bb1) {$BB1$};
  \end{tikzpicture}
  \caption{Bounding boxes for convex union of data regions}
  \label{figure:single}
\end{figure}
\end{document}

I am not put right side content properly. (for example, I have tried putting BB1, but it is not coming at proper location). And how to use different size and style of code like used here for path[k][j]?

This is my output:

Answer 1

This is a possible solution:

• all nodes are located starting from the existent circles (however I'm almost sure this answer will not locate them in the proper [mysterious] location ;-))
• the fonts of nodes on the right side of the circles are set in teletype by means of a style

    \tikzset{my tt/.style={
      font=\ttfamily#1},
    }

let's say customizable, with the argument (in the code will be use to set the size of the font).

The code:

\documentclass{article}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{tikz}
%\usepackage[active,tightpage,floats]{preview}
%\setlength\PreviewBorder{30pt}%
\usetikzlibrary{calc, fit, shapes.geometric}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}


\tikzset{my tt/.style={
  font=\ttfamily#1},
}

%\colorlet{MAROON}{Maroon}

\begin{document}

\begin{figure}[ht]
  \centering
  \begin{tikzpicture}
    \coordinate (Origin)   at (0,0);

    \coordinate (XAxisMax) at (5.5,0);
    \coordinate (YAxisMax) at (0,4.5);

    \coordinate (Ylow) at (-0.5,0);
    \coordinate (Xlow) at (0,-0.5);
    \coordinate (XMax) at (5.5,-0.5);
    \coordinate (YMax) at (-0.5,4.5);

    \draw [thick, darkgray] (Origin) -- (XAxisMax);% Draw x axis
    \draw [thick, darkgray] (Origin) -- (YAxisMax);% Draw y axis

    \draw [thick, darkgray!40, -latex] (Xlow) -- (XMax);% Draw x axis
    \draw [thick, darkgray!40, -latex] (Ylow) -- (YMax);% Draw y axis

    \foreach \x in {1,2,...,10}{% Two indices running over each
      \foreach \y in {1,2,...,8}{% node on the grid we have drawn 
        \node[thick,draw,circle,inner sep=2pt,fill=gray!60, name=\x-\y] at (0.5*\x,0.5*\y) {};
            % Places a dot at those points
      }
    }


    \begin{pgfonlayer}{background}
    \node (B) [draw, color=BrickRed, fill=red!30, rectangle, rounded corners, fit={(1-1) (10-1)}] {};
    \end{pgfonlayer}

    \begin{pgfonlayer}{background}
    \node (A) [draw, color=BrickRed, fill=red!30, rectangle, rounded corners, fit={(1-5) (10-8)}] {};
    \end{pgfonlayer}

    \node[align=center, below] at (2.75,0) {$i$};
    \node[align=center, left]  at (0,2.25) {$j$};
    \node[align=center, left]  at (-0.5,2.25) {Data\\domain};
    \node[above] at (A.north) {$k = N -1$};

    \node[right=5pt,my tt=\large] at (10-2) {BB1};
    \node[right=5pt,my tt=\scriptsize] at (10-1) {path[k][j]};

    \node[right=5pt,my tt=\scriptsize, text width=1cm] at (10-7) {path[i][j] and path[i][k]};
    \node[right=5pt,my tt=\large, anchor=south west] at (10-8) {BB0};
  \end{tikzpicture}
  \caption{Bounding boxes for convex union of data regions}
  \label{figure:single}
\end{figure}
\end{document}

The result:

Notice that to locate more precisely the nodes, you can play with their relative position (with the positioning library) and also with the node's anchor.

Here is a simple example:

\documentclass[tikz,border=2pt,png]{standalone}
\usetikzlibrary{positioning,shapes.misc}
\pgfdeclarelayer{back}
\pgfsetlayers{back,main}
\begin{document}
\begin{tikzpicture}
\node[draw] at (0,0) (x) {Start};
\begin{pgfonlayer}{back}
 \node[draw,cross out, blue] at (x){};
\end{pgfonlayer}

% Simple usage of <position> of=<name>
\node[right of =x] {x};
\node[right of =x, anchor=north,red] {n};
\node[right of =x, anchor=north west,red!20] {nw};
\node[right of =x, anchor=north east,red!70] {ne};
\node[right of =x, anchor=south,blue] {s};
\node[right of =x, anchor=south west,blue!20] {sw};
\node[right of =x, anchor=south east,blue!70] {se};

% Usage of <position> = <distance> of <name>
\node[left=1.5cm of x, anchor=center] {x};
\node[left=1.5cm of x, anchor=north,red] {n};
\node[left=1.5cm of x, anchor=north west,red!20] {nw};
\node[left=1.5cm of x, anchor=north east,red!70] {ne};
\node[left=1.5cm of x, anchor=south,blue] {s};
\node[left=1.5cm of x, anchor=south west,blue!20] {sw};
\node[left=1.5cm of x, anchor=south east,blue!70] {se};
\end{tikzpicture}
\end{document}

The result:

Refer to the pgfmanual for a complete list of anchors.