TikZ: Differences in relative positioning

Question

I would like to find out why TikZ doesn't behave like I would expect. I made small example:

\node[dot_label_se={$y_3$}, below=1.5cm of point_y2] (point_y3) {};
\node[dot_label_se={$z_3$}, below right=1.5cm and 2cm of point_y2] (point_z3) {};
\node[dot_label_se={$v_3$}, below=3cm of point_v1] (point_v3) {};

The problem is with points z3 and v3. First of all look at z3 positioning it is the same as y3 but shifted right by 2cm, so why height is slightly different?

In case of v3 I tried to put it relative to v1 by 3cm (2 x 1,5cm) and result is different than having v2 1.5cm below v1 and then v3 1.5cm below v2. Isn't node positioning relative to node center?

Edit: (full working example - just points)

\documentclass[10pt,a4paper]{book}
\usepackage[utf8]{inputenc}
\usepackage{arevtext, arevmath}

\usepackage{tikz}
\usetikzlibrary{arrows,positioning}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{arrows.meta,calc}

\tikzset{
dot_label_se/.style={circle, inner sep=2pt, fill, label={[text depth=0pt,    text height=0.5ex, xshift=-0.07cm]-35:#1}, name=#1},
dot_label_sw/.style={circle, inner sep=2pt, fill, label={[text depth=0pt, text height=0.5ex, xshift=0.14cm]215:#1}, name=#1},
}

\begin{document}
\begin{figure}
\begin{tikzpicture}[font=\sffamily\small\em]

\node[dot_label_se={$y_1$}, left=1cm] (point_y1) {};
\node[dot_label_se={$z_1$}, right=1cm] (point_z1) {};
\node[dot_label_se={$x_1$}, left=2cm of point_y1] (point_x1) {};
\node[dot_label_sw={$v_1$}, right=2cm of point_z1] (point_v1) {};

\node[dot_label_se={$x_2$}, below=1.5cm of point_x1] (point_x2) {};
\node[dot_label_sw={$y_2$}, below=1.5cm of point_y1] (point_y2) {};

\node[dot_label_se={$x_3$}, below=1.5cm of point_x2] (point_x3) {};
\node[dot_label_se={$y_3$}, below=1.5cm of point_y2] (point_y3) {};
\node[dot_label_se={$z_3$}, below right=1.5cm and 2cm of point_y2] (point_z3) {};
\node[dot_label_se={$v_3$}, below=3cm of point_v1] (point_v3) {};

\end{tikzpicture}
\end{figure}
\end{document}

Answer 1

EDIT: As I mentioned in my comment, the problem is considering node size in determining of distances between nodes. It seems that the best solution is add option on grid and use your MWE as is.

However, I took liberty and rewrite your MWE. See if the my MWE is acceptable to you:

\documentclass[tikz,
               border=3mm,
               ]{standalone}
\usetikzlibrary{arrows.meta,
                decorations,decorations.markings,
                positioning
                }

\begin{document}
    \begin{tikzpicture}[on grid,
    node distance = 15mm and 15mm,
  dot/.style args = {#1/#2}{circle, fill=black, 
                            inner sep=0pt, outer sep=0pt, minimum size=5pt,
                            label={[node distance=2pt, inner sep=1pt]#1:{#2}},
                            node contents={}},
       DL/.style = {postaction={decorate},
                    decoration = {markings,
                                  mark=at position 0.6 with {\arrow{Stealth[length=3mm]}}
                                  }
                    },
                        ]
\node (n11) [dot=-45/$x_1$];
\node (n12) [dot=-45/$y_1$,right=of n11];
\node (n13) [dot=-45/$z_1$,right=of n12];
\node (n14) [dot=-45/$v_1$,right=of n13];
    \foreach \i [count=\j from 1] in {2,3,4}{\draw[DL] (n1\j) -- (n1\i);}
\node (n21) [dot=-45/$x_2$,below=of n11];
\node (n22) [dot=225/$y_2$,right=of n21];
    \draw[DL] (n21) -- (n22);
\node (n31) [dot=-45/$x_3$,below=of n21];
\node (n32) [dot=-45/$y_3$,below=of n22];
\node (n33) [dot=-45/$z_3$,below=30mm of n13];
\node (n34) [dot=-45/$v_3$,below=30mm of n14];
    \foreach \i [count=\j from 1] in {2,3,4}{\draw[DL] (n3\j) -- (n3\i);}
    \draw[DL] (n22) -- (n33);
    \end{tikzpicture}
\end{document}

Note: in positioning of nodes is used syntax determined in TikZ library positioning. Used in your MWE is deprecated.

Answer 2

You're assuming your nodes to behave like points, but in reality they are assigned a width and a height. When using relative positioning, your calculations are thus slightly off.

Try aligning them on an edge — for example, on the left side — and using relative positioning from there. Reconstructed from your example (which is not an MWE, otherwise a more comprehensive answer would be possible), it would probably look like this:

\node[dot_label_se={$x_1$}] (point_x1) {};
\node[dot_label_se={$y_1$}, right=2cm of point_x1] (point_y1) {};
\node[dot_label_se={$z_1$}, right=2cm of point_y1] (point_z1) {};
\node[dot_label_se={$x_2$}, below=1.5cm of point_x1] (point_x2) {};
\node[dot_label_se={$y_2$}, right=2cm of point_x2] (point_y2) {};
\node[dot_label_se={$x_3$}, below=1.5cm of point_x2] (point_x3) {};
\node[dot_label_se={$y_3$}, right=2cm of point_x1] (point_y3) {};
\node[dot_label_se={$z_3$}, right=2cm of point_y3] (point_z3) {};

By expanding only in one direction, you're minimizing the possibility of problems arising. If you still have problems aligning them, you can add a key definining the minimum width for all nodes to the same, high enough value.

Answer 3

To avoid taking the node shapes into account when positioning other nodes, consider adding .center to node names and anchor=center. For example:

\node[dot_label_se={$y_3$}, below=1.5cm of point_y2.center,anchor=center] (point_y3) {};
\node[dot_label_se={$z_3$}, below right=1.5cm and 2cm of point_y2.center,anchor=center] (point_z3) {};
\node[dot_label_se={$v_3$}, below=3cm of point_v1.center,anchor=center] (point_v3) {};

Consider the following example:

\documentclass[tikz]{standalone}
\usetikzlibrary{positioning}

\begin{document}
\begin{tikzpicture}[bul/.style = {fill,circle,inner sep=3pt}]
\node [bul](1) {};
\node [bul,below=1.5 of 1](2) {};
\node [bul,below=1.5 of 2](3) {};
\node [bul,right=2 of 1](4) {};
\node [bul,below right=1.5 and 2 of 2](5) {};
\draw (4)--(1)--(2)--(3)--(5);
\end{tikzpicture}

\end{document}

And now this:

\begin{tikzpicture}[bul/.style = {fill,circle,inner sep=3pt}]
\node [bul](1) {};
\node [bul,below=1.5 of 1.center,anchor=center](2) {};
\node [bul,below=1.5 of 2.center,anchor=center](3) {};
\node [bul,right=2 of 1.center,anchor=center](4) {};
\node [bul,below right=1.5 and 2 of 2.center,anchor=center](5) {};
\draw (4)--(1)--(2)--(3)--(5);
\end{tikzpicture}