Points in 3D coordinate system with tikz

Question

i would like to set points into a 3D coordinate system but I have a problem with the axis. Now I must use (-1.1,2.0,1.1) but the data points are in (-110,200,110) format. How can I change the axis, that I can set the points without divide/100 (about 200 points)?

The range of the coordinates is: x = 0 ... 250, y = -110 ... 110, z = 0 ... 250

In this MWE, there are only eight points:

\documentclass[ngerman]{standalone}   
\usepackage{tikz}

\begin{document}
    \begin{tikzpicture}[scale=2,x={(0.7cm,0.7cm)},y={(3cm,0cm)}, z={(0cm,1cm)}]
        \draw[->, >=latex] (-1.10,0,0) -- (1.10,0,0) node[above]{$y$};
        \draw[->, >=latex] (0,0,0) -- (0,2.00,0) node[below]{$x$};
        \draw[->, >=latex] (0,0,0) -- (0,0,2.50) node[left]{$z$};
        \shadedraw  plot [only marks, mark=*, mark size=1.5pt, mark options={fill=gray}] coordinates{
            (-1.10,2.00,1.10)
            (-1.10,2.00,1.30)
            (-1.10,2.00,1.50)
            (-1.10,2.00,1.70)
            (-1.10,2.00,1.90)
            (-1.10,2.00,2.10)
            (-1.10,2.00,2.30)
            (-1.10,2.00,2.50)
        };  
    \end{tikzpicture}
\end{document}

Answer 1

First of all, I do not see a reason why not to use pgfplots here, for which this problem is basically nonexistent. But let's assume that there is such a reason. In that case, you easily introduce dimension too large errors. This is one way to avoid them in the current setting, but I do not think that this will work generally (which it would in pgfplots.) You can introduce scaled basis vectors.

\documentclass[ngerman]{standalone}   
\usepackage{tikz}
\tikzset{scaled unit vectors/.code={
\path (#1,0,0) coordinate (ex) (0,#1,0) coordinate (ey) 
            (0,0,#1) coordinate (ez);},scaled cs/.style={x={(ex)},y={(ey)},z={(ez)}}}
\begin{document}
    \begin{tikzpicture}[scale=2,x={(0.7cm,0.7cm)},y={(3cm,0cm)}, z={(0cm,1cm)}]
        \draw[->, >=latex] (-1.10,0,0) -- (1.10,0,0) node[above]{$y$};
        \draw[->, >=latex] (0,0,0) -- (0,2.00,0) node[below]{$x$};
        \draw[->, >=latex] (0,0,0) -- (0,0,2.50) node[left]{$z$};
        \tikzset{scaled unit vectors=0.01}
        \shadedraw[scaled cs] 
             plot [only marks, mark=*, mark size=1.5pt, mark options={fill=gray}] coordinates{
            (-110,200,110)
            (-110,200,130)
            (-110,200,150)
            (-110,200,170)
            (-110,200,190)
            (-110,200,210)
            (-110,200,230)
            (-110,200,250)
        };  
    \end{tikzpicture}
\end{document}