How to add grid and define z domain for 3D plotting

Question

I'm trying to reproduce the following graph.

I didn't find a way to:

add a horizontal grid
stop drawing the line at (n,n,0) to draw a dashed line below
(Bonus) change the ticks' mark by a circle

Do you have any idea how to do so?

Current situation:

%%%%%%%%%%%%%%%%%% INTRODUCTION %%%%%%%%%%%%%%%%%%
\documentclass[]{standalone}
%%%%%%%%%%%%%%%%%% INPUT %%%%%%%%%%%%%%%%%%
%\input{preamble.tex}
%\input{parameters.tex}
%%%%%%%%%%%%%%%%%% PACKAGE %%%%%%%%%%%%%%%%%%
\usepackage{tgadventor}
\usepackage{sansmath}
\usepackage[usenames, dvipsnames]{xcolor}
\usepackage{tikz} % permet l'intégration des dessins TikZ (les graphiques Geogebra peuvent être exportés au format TikZ)
\usetikzlibrary{%
    matrix,
    arrows,
    arrows.meta,
    bending,
    calc,
    math,
    shapes,
    backgrounds,
    decorations.markings,
    }
\tikzset{%
    graphpgf/.style={%
        font={\sansmath\sffamily\Large}, 
        line cap=round, line join=round, 
        >={Latex[length=3mm]}, 
        x=1.0cm, y=1.0cm, 
        background rectangle/.style={fill=white, shift={(-5pt,-5pt)}},
        show background rectangle,
        inner frame sep=10pt
    }
}
\usepackage{pgfplots} % Permet de tracer de graphiques
\pgfplotsset{compat=1.16}
\pgfplotsset{%
    /pgfplots/3Dxyz/.style={%
        %%%%%%%%%%  Dimensionnement de l'image  %%%%%%%%%%
        width=15cm,
        height=15cm,
        unit vector ratio=1 1 1.1,
        %%%%%%%%%%  esthétique des axes  %%%%%%%%%%
        xlabel=$\mathrm{x}$,

        ylabel=$\mathrm{y}$,
        zlabel=$\mathrm{z}$,
        axis lines = center,
        scaled ticks=false, 
        tick label style={/pgf/number format/fixed},
        enlargelimits=false,
        line width=0.4mm,
        every major grid/.append style={black!20, line width=0.35mm,},
        every minor grid/.append style={black!15, line width=0.15mm,},
        every major tick/.append style={
            line width=0.4 mm, 
            %major tick length=7pt, 
            black,
            },
        every minor tick/.append style={line width=0.15mm, minor tick length=4pt, black},
        axis line style = {shorten >=-12.5pt, shorten <=-12.5pt, -{Latex[length=3mm]}},
        grid=major,
    }
}
%%%%%%%%%%%%%%%%%% DOCUMENT %%%%%%%%%%%%%%%%%%
\begin{document}
\begin{tikzpicture}[graphpgf]
%%%%%%%%%%%%%%%%%% Data Table %%%%%%%%%%%%%%%%%%
\begin{axis}[%
    3Dxyz,
    view={145}{25},
    %minor tick num=4,
    %%%     Axe x
    xmin=-4-.3, xmax=4+.3,
    xtick={-10,-9,...,10},
    %minor xtick={-10,...,8},
    domain=-5:5,
    %%%     Axe y
    ymin=-4-.3,ymax=4+.3,
    ytick={-10,-9,...,10},
    %minor ytick={-8,...,8},
    %minor y tick num=4,
    y domain=-5:5,
    %%%     Axe z
    zmin=-1,    zmax=4,
    ztick={-10,-9,...,10},
]%
    \addplot3[%
        color=orange,
        opacity=0.8,
        line width=0.4mm,
        smooth,
        %samples y=1,
        %samples=199,
        ]%
        (1,2,x)
        node[right, pos=0.8] {f}
    ;
    \addplot3[%
        color=blue,
        opacity=0.8,
        line width=0.4mm,
        smooth,
        %samples y=1,
        %samples=199,
        ]%
        (x,x,x)
        node[left, pos=0.8] {g}
    ;
\end{axis}
\end{tikzpicture}
\end{document}

You can use the tricks from this post to turn change the lifestyle for negative z. — , Dec 18 '20 at 18:52

score 3 · Accepted Answer · answered Dec 19 '20 at 04:13

This uses the tricks from this post. It also adds a plane and has the z axis dashed below 0. Many parameters here are in the code that gets executed at the end of the axis, but could be stored in pgf keys. But it may be a start.

\documentclass[]{standalone}
%%%%%%%%%%%%%%%%%% INPUT %%%%%%%%%%%%%%%%%%
%\input{preamble.tex}
%\input{parameters.tex}
%%%%%%%%%%%%%%%%%% PACKAGE %%%%%%%%%%%%%%%%%%
\usepackage{tgadventor}
\usepackage{sansmath}
\usepackage[usenames, dvipsnames]{xcolor}
%\usepackage{tikz} % permet l'intégration des dessins TikZ (les graphiques Geogebra peuvent être exportés au format TikZ)
\usepackage{pgfplots} % Permet de tracer de graphiques
\pgfplotsset{compat=1.16} 
\usetikzlibrary{3d,arrows.meta,backgrounds,calc,shadows.blur}
\tikzset{%
    graphpgf/.style={%
        font={\sansmath\sffamily\Large}, 
        line cap=round, line join=round, 
        >={Latex[length=3mm]}, 
        x=1.0cm, y=1.0cm, 
        background rectangle/.style={fill=white, shift={(-5pt,-5pt)}},
        show background rectangle,
        inner frame sep=10pt
    }
}
\makeatletter
\pgfplotsset{%
    /pgfplots/3Dxyz/.style={%
        %%%%%%%%%%  Dimensionnement de l'image  %%%%%%%%%%
        width=15cm,
        height=15cm,
        unit vector ratio=1 1 1.1,
        %%%%%%%%%%  esthétique des axes  %%%%%%%%%%
        xlabel=$\mathrm{x}$,

        ylabel=$\mathrm{y}$,
        zlabel=$\mathrm{z}$,
        %axis lines = center,
        hide axis,
        scaled ticks=false, 
        %tick label style={/pgf/number format/fixed},
        enlargelimits=false,
        line width=0.4mm,
        every major grid/.append style={black!20, line width=0.35mm,},
        every minor grid/.append style={black!15, line width=0.15mm,},
        every major tick/.append style={
            line width=0.4 mm, 
            %major tick length=7pt, 
            black,
            },
        every minor tick/.append style={line width=0.15mm, minor tick length=4pt, black},
        axis line style = {shorten >=-12.5pt, shorten <=-12.5pt, 
            -{Latex[length=3mm]},thick},
        every inner x axis line/.append style={red},
        every inner y axis line/.append style={green!60!black},
        every inner z axis line/.append style={blue},
        grid=major,
        set layers=standard,
        execute at end plot visualization={%
        \path (\pgfplots@data@xmax,\pgfplots@data@ymax,0) coordinate(XYpp)
        (\pgfplots@data@xmax,\pgfplots@data@ymin,0) coordinate(XYpm)
        --(\pgfplots@data@xmin,\pgfplots@data@ymin,0) coordinate(XYmm)
        --(\pgfplots@data@xmin,\pgfplots@data@ymax,0) coordinate(XYmp);
        \path (0.5\pgfplots@data@xmin+0.5\pgfplots@data@xmax,%
            0.5\pgfplots@data@ymin+0.5\pgfplots@data@ymax,0) coordinate
            (XY-O);
        \begin{pgfonlayer}{axis background}
         \draw[dashed,/pgfplots/every inner z axis line,-]
          (0,0,\pgfplots@data@zmin) -- (0,0,0);
        \end{pgfonlayer}

        \begin{scope}[canvas is xy plane at z=0]
         \begin{pgfonlayer}{axis background}
         \pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
         \path let \p1=($(XYpp)-(XYmp)$),\p2=($(XYpp)-(XYmp)$),
            \n1={0.9veclen(\x1,\y1)},\n2={0.9veclen(\x2,\y2)},
            \n3={0.025\n1+0.025\n2} in
           (XY-O)
            node[transform shape,opacity=0.2,
                minimum width=\n1,
                minimum height=\n2,
                blur shadow={shadow xshift=0pt,shadow yshift=0pt,
                shadow blur radius=\n3,
                shadow blur steps=25}]{};
         \end{pgfonlayer}

        \end{scope}
        \begin{pgfonlayer}{axis lines}
         \pgfkeys{/pgf/fpu,/pgf/fpu/output format=fixed}%
         \pgfmathsetmacro{\myxmax}{\pgfplots@data@xmax}
         \pgfmathsetmacro{\myxmin}{\pgfplots@data@xmin}
         \pgfmathsetmacro{\myymax}{\pgfplots@data@ymax}
         \pgfmathsetmacro{\myymin}{\pgfplots@data@ymin}
         \pgfmathsetmacro{\myzmax}{\pgfplots@data@zmax}
         \pgfmathtruncatemacro{\intxmax}{int(\pgfplots@data@xmax-0.1)}
         \pgfmathtruncatemacro{\intxmin}{int(\pgfplots@data@xmin+0.1)}
         \pgfmathtruncatemacro{\intymax}{int(\pgfplots@data@ymax-0.1)}
         \pgfmathtruncatemacro{\intymin}{int(\pgfplots@data@ymin+0.1)}
         \pgfmathtruncatemacro{\intzmax}{int(\pgfplots@data@zmax-0.1)}
         \pgfkeys{/pgf/fpu=false}%
         \draw[->,/pgfplots/.cd,every inner x axis line]
          (\myxmin,0,0) --  (\myxmax,0,0);
         \foreach \x in {\intxmin,...,\intxmax}
          {\edef\temp{\noexpand\path (\x,\myymin,0) edge[dotted] (\x,\myymax,0)
          (\x,0,0) node[label={[/pgfplots/every inner x axis line]above left:{$\x$}},
            circle,inner sep=1.2pt,fill,/pgfplots/every inner x axis line]{};}
          \temp}
         \draw[->,/pgfplots/.cd,every inner y axis line]
          (0,\myymin,0) --  (0,\myymax,0);
         \foreach \y in {\intymin,...,\intymax}
          {\edef\temp{\noexpand\path (\myxmin,\y,0) edge[dotted] (\myxmax,\y,0)
          (0,\y,0) node[label={[/pgfplots/every inner y axis line]above right:{$\y$}},
            circle,inner sep=1.2pt,fill,/pgfplots/every inner y axis line]{};}
          \temp}
         \draw[->,/pgfplots/.cd,every inner z axis line]
          (0,0,0) --  (0,0,\myzmax);
         \foreach \z in {0,...,\intzmax}
          {\edef\temp{\noexpand\path 
          (0,0,\z) node[label={[/pgfplots/every inner z axis line]above left:{$\z$}},
            circle,inner sep=1.2pt,fill,/pgfplots/every inner z axis line]{};}
          \temp}
        \end{pgfonlayer}
        }
    }
}
\makeatother
\def\addFGBGplot[#1]#2;{
    \begin{pgfonlayer}{axis background}
      \addplot3[#1,only background] #2;
    \end{pgfonlayer} 
    \begin{pgfonlayer}{main}
      \addplot3[#1,only foreground] #2;
    \end{pgfonlayer} 
}
% Styles to plot only points that are before or behind the sphere.
\pgfplotsset{only foreground/.style={%
    restrict expr to domain={rawz}{-0.05:100},
}}
\pgfplotsset{only background/.style={dashed,%
    restrict expr to domain={rawz}{-100:0.05}
}}
%%%%%%%%%%%%%%%%%% DOCUMENT %%%%%%%%%%%%%%%%%%
\begin{document}
\begin{tikzpicture}%[graphpgf]
%%%%%%%%%%%%%%%%%% Data Table %%%%%%%%%%%%%%%%%%
\begin{axis}[%
    3Dxyz,
    view={145}{25},
    %minor tick num=4,
    %%%     Axe x
    xmin=-4-.3, xmax=4+.3,
    xtick={-10,-9,...,10},
    %minor xtick={-10,...,8},
    domain=-5:5,
    %%%     Axe y
    ymin=-4-.3,ymax=4+.3,
    ytick={-10,-9,...,10},
    %minor ytick={-8,...,8},
    %minor y tick num=4,
    y domain=-5:5,
    %%%     Axe z
    zmin=-1,    zmax=4,
    ztick={-10,-9,...,10},
]%
\addFGBGplot[%
    color=orange,
    line width=0.4mm,
    samples y=1,
    samples=201,
    ]%
    (1,2,x);
\addFGBGplot[%
    color=cyan,
    line width=0.4mm,
    samples y=1,
    samples=201,
    ]%
    (x,x,x);

\end{axis}
\end{tikzpicture}
\end{document}

TikZ, pgfplots are all fake 3D. It's better to use real 3D Asymptote — Black Mild, Dec 19 '20 at 09:48
@BlackMild Yes, asymptote has many 3d features. But does it also one to draw the hidden parts dashed automatically? — , Dec 19 '20 at 12:42

How to add grid and define z domain for 3D plotting

1 Answers1