How can I give this perspective with Tikz?












3















I am trying to complete the image of the figure: I know how to perform the dashed circle and the legs of the table. The problem is to draw the upper part of the table. Can you give me a hint of how to do it?



Thank you!



image of a table viewed head on in perspective










share|improve this question

























  • Can you show us the code you already have?

    – Sigur
    7 hours ago











  • As far as I know, the most straightforward way will be to employ this great answer.

    – marmot
    7 hours ago











  • I am just starting... marmot, that seems really difficult!!

    – Eduardo
    7 hours ago






  • 1





    Yes, unfortunately these cool macros are not yet part of a package or library. So for the time being you would still copy the preamble. Notice that once you copied it, the rest will not be difficult.

    – marmot
    6 hours ago
















3















I am trying to complete the image of the figure: I know how to perform the dashed circle and the legs of the table. The problem is to draw the upper part of the table. Can you give me a hint of how to do it?



Thank you!



image of a table viewed head on in perspective










share|improve this question

























  • Can you show us the code you already have?

    – Sigur
    7 hours ago











  • As far as I know, the most straightforward way will be to employ this great answer.

    – marmot
    7 hours ago











  • I am just starting... marmot, that seems really difficult!!

    – Eduardo
    7 hours ago






  • 1





    Yes, unfortunately these cool macros are not yet part of a package or library. So for the time being you would still copy the preamble. Notice that once you copied it, the rest will not be difficult.

    – marmot
    6 hours ago














3












3








3


2






I am trying to complete the image of the figure: I know how to perform the dashed circle and the legs of the table. The problem is to draw the upper part of the table. Can you give me a hint of how to do it?



Thank you!



image of a table viewed head on in perspective










share|improve this question
















I am trying to complete the image of the figure: I know how to perform the dashed circle and the legs of the table. The problem is to draw the upper part of the table. Can you give me a hint of how to do it?



Thank you!



image of a table viewed head on in perspective







tikz-pgf






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited 7 hours ago









Paul Stanley

14.4k42848




14.4k42848










asked 7 hours ago









EduardoEduardo

725




725













  • Can you show us the code you already have?

    – Sigur
    7 hours ago











  • As far as I know, the most straightforward way will be to employ this great answer.

    – marmot
    7 hours ago











  • I am just starting... marmot, that seems really difficult!!

    – Eduardo
    7 hours ago






  • 1





    Yes, unfortunately these cool macros are not yet part of a package or library. So for the time being you would still copy the preamble. Notice that once you copied it, the rest will not be difficult.

    – marmot
    6 hours ago



















  • Can you show us the code you already have?

    – Sigur
    7 hours ago











  • As far as I know, the most straightforward way will be to employ this great answer.

    – marmot
    7 hours ago











  • I am just starting... marmot, that seems really difficult!!

    – Eduardo
    7 hours ago






  • 1





    Yes, unfortunately these cool macros are not yet part of a package or library. So for the time being you would still copy the preamble. Notice that once you copied it, the rest will not be difficult.

    – marmot
    6 hours ago

















Can you show us the code you already have?

– Sigur
7 hours ago





Can you show us the code you already have?

– Sigur
7 hours ago













As far as I know, the most straightforward way will be to employ this great answer.

– marmot
7 hours ago





As far as I know, the most straightforward way will be to employ this great answer.

– marmot
7 hours ago













I am just starting... marmot, that seems really difficult!!

– Eduardo
7 hours ago





I am just starting... marmot, that seems really difficult!!

– Eduardo
7 hours ago




1




1





Yes, unfortunately these cool macros are not yet part of a package or library. So for the time being you would still copy the preamble. Notice that once you copied it, the rest will not be difficult.

– marmot
6 hours ago





Yes, unfortunately these cool macros are not yet part of a package or library. So for the time being you would still copy the preamble. Notice that once you copied it, the rest will not be difficult.

– marmot
6 hours ago










1 Answer
1






active

oldest

votes


















5














All credits go to Max' answer. All I do is to truncate his general projection to a simpler case, which may help to understand better what's going on here. Max' picture shows very nicely what his code does: it transforms the objects in such a way that the edges that are parallel to the x axis meet in p, the ones parallel to the y axis in q and the ones parallel to the z axis in r. (Yes, that's just a sloppy definition of "vanishing points".) However, in order to reproduce something like your screenshot, we only need to play with q, which is what the following animation does.



documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{shapes.geometric,intersections}
usepgfmodule{nonlineartransformations}
% Max magic
makeatletter
% the first part is not in use here
deftikz@scan@transform@one@point#1{%
tikz@scan@one@pointpgf@process#1%
pgf@pos@transform{pgf@x}{pgf@y}}
tikzset{%
grid source opposite corners/.code args={#1and#2}{%
pgfextract@processtikz@transform@source@southwest{%
tikz@scan@transform@one@point{#1}}%
pgfextract@processtikz@transform@source@northeast{%
tikz@scan@transform@one@point{#2}}%
},
grid target corners/.code args={#1--#2--#3--#4}{%
pgfextract@processtikz@transform@target@southwest{%
tikz@scan@transform@one@point{#1}}%
pgfextract@processtikz@transform@target@southeast{%
tikz@scan@transform@one@point{#2}}%
pgfextract@processtikz@transform@target@northeast{%
tikz@scan@transform@one@point{#3}}%
pgfextract@processtikz@transform@target@northwest{%
tikz@scan@transform@one@point{#4}}%
}
}

deftikzgridtransform{%
pgfextract@processtikz@current@point{}%
pgf@process{%
pgfpointdiff{tikz@transform@source@southwest}%
{tikz@transform@source@northeast}%
}%
pgf@xc=pgf@xpgf@yc=pgf@y%
pgf@process{%
pgfpointdiff{tikz@transform@source@southwest}{tikz@current@point}%
}%
pgfmathparse{pgf@x/pgf@xc}lettikz@tx=pgfmathresult%
pgfmathparse{pgf@y/pgf@yc}lettikz@ty=pgfmathresult%
%
pgfpointlineattime{tikz@ty}{%
pgfpointlineattime{tikz@tx}{tikz@transform@target@southwest}%
{tikz@transform@target@southeast}}{%
pgfpointlineattime{tikz@tx}{tikz@transform@target@northwest}%
{tikz@transform@target@northeast}}%
}

% Initialize H matrix for perspective view
pgfmathsetmacroH@tpp@aa{1}pgfmathsetmacroH@tpp@ab{0}pgfmathsetmacroH@tpp@ac{0}%pgfmathsetmacroH@tpp@ad{0}
pgfmathsetmacroH@tpp@ba{0}pgfmathsetmacroH@tpp@bb{1}pgfmathsetmacroH@tpp@bc{0}%pgfmathsetmacroH@tpp@bd{0}
pgfmathsetmacroH@tpp@ca{0}pgfmathsetmacroH@tpp@cb{0}pgfmathsetmacroH@tpp@cc{1}%pgfmathsetmacroH@tpp@cd{0}
pgfmathsetmacroH@tpp@da{0}pgfmathsetmacroH@tpp@db{0}pgfmathsetmacroH@tpp@dc{0}%pgfmathsetmacroH@tpp@dd{1}

%Initialize H matrix for main rotation
pgfmathsetmacroH@rot@aa{1}pgfmathsetmacroH@rot@ab{0}pgfmathsetmacroH@rot@ac{0}%pgfmathsetmacroH@rot@ad{0}
pgfmathsetmacroH@rot@ba{0}pgfmathsetmacroH@rot@bb{1}pgfmathsetmacroH@rot@bc{0}%pgfmathsetmacroH@rot@bd{0}
pgfmathsetmacroH@rot@ca{0}pgfmathsetmacroH@rot@cb{0}pgfmathsetmacroH@rot@cc{1}%pgfmathsetmacroH@rot@cd{0}
%pgfmathsetmacroH@rot@da{0}pgfmathsetmacroH@rot@db{0}pgfmathsetmacroH@rot@dc{0}pgfmathsetmacroH@rot@dd{1}

pgfkeys{
/three point perspective/.cd,
p/.code args={(#1,#2,#3)}{
pgfmathparse{int(round(#1))}
ifnumpgfmathresult=0else
pgfmathsetmacroH@tpp@ba{#2/#1}
pgfmathsetmacroH@tpp@ca{#3/#1}
pgfmathsetmacroH@tpp@da{ 1/#1}
coordinate (vp-p) at (#1,#2,#3);
fi
},
q/.code args={(#1,#2,#3)}{
pgfmathparse{int(round(#2))}
ifnumpgfmathresult=0else
pgfmathsetmacroH@tpp@ab{#1/#2}
pgfmathsetmacroH@tpp@cb{#3/#2}
pgfmathsetmacroH@tpp@db{ 1/#2}
coordinate (vp-q) at (#1,#2,#3);
fi
},
r/.code args={(#1,#2,#3)}{
pgfmathparse{int(round(#3))}
ifnumpgfmathresult=0else
pgfmathsetmacroH@tpp@ac{#1/#3}
pgfmathsetmacroH@tpp@bc{#2/#3}
pgfmathsetmacroH@tpp@dc{ 1/#3}
coordinate (vp-r) at (#1,#2,#3);
fi
},
coordinate/.code args={#1,#2,#3}{
pgfmathsetmacrotpp@x{#1} %<- Max' fix
pgfmathsetmacrotpp@y{#2}
pgfmathsetmacrotpp@z{#3}
},
}

tikzset{
view/.code 2 args={
pgfmathsetmacrorot@main@theta{#1}
pgfmathsetmacrorot@main@phi{#2}
% Row 1
pgfmathsetmacroH@rot@aa{cos(rot@main@phi)}
pgfmathsetmacroH@rot@ab{sin(rot@main@phi)}
pgfmathsetmacroH@rot@ac{0}
% Row 2
pgfmathsetmacroH@rot@ba{-cos(rot@main@theta)*sin(rot@main@phi)}
pgfmathsetmacroH@rot@bb{cos(rot@main@phi)*cos(rot@main@theta)}
pgfmathsetmacroH@rot@bc{sin(rot@main@theta)}
% Row 3
pgfmathsetmacroH@m@ca{sin(rot@main@phi)*sin(rot@main@theta)}
pgfmathsetmacroH@m@cb{-cos(rot@main@phi)*sin(rot@main@theta)}
pgfmathsetmacroH@m@cc{cos(rot@main@theta)}
% Set vector values
pgfmathsetmacrovec@x@x{H@rot@aa}
pgfmathsetmacrovec@y@x{H@rot@ab}
pgfmathsetmacrovec@z@x{H@rot@ac}
pgfmathsetmacrovec@x@y{H@rot@ba}
pgfmathsetmacrovec@y@y{H@rot@bb}
pgfmathsetmacrovec@z@y{H@rot@bc}
% Set pgf vectors
pgfsetxvec{pgfpoint{vec@x@x cm}{vec@x@y cm}}
pgfsetyvec{pgfpoint{vec@y@x cm}{vec@y@y cm}}
pgfsetzvec{pgfpoint{vec@z@x cm}{vec@z@y cm}}
},
}

tikzset{
perspective/.code={pgfkeys{/three point perspective/.cd,#1}},
perspective/.default={p={(15,0,0)},q={(0,15,0)},r={(0,0,50)}},
}

tikzdeclarecoordinatesystem{three point perspective}{
pgfkeys{/three point perspective/.cd,coordinate={#1}}
pgfmathsetmacrotemp@p@w{H@tpp@da*tpp@x + H@tpp@db*tpp@y + H@tpp@dc*tpp@z + 1}
pgfmathsetmacrotemp@p@x{(H@tpp@aa*tpp@x + H@tpp@ab*tpp@y + H@tpp@ac*tpp@z)/temp@p@w}
pgfmathsetmacrotemp@p@y{(H@tpp@ba*tpp@x + H@tpp@bb*tpp@y + H@tpp@bc*tpp@z)/temp@p@w}
pgfmathsetmacrotemp@p@z{(H@tpp@ca*tpp@x + H@tpp@cb*tpp@y + H@tpp@cc*tpp@z)/temp@p@w}
pgfpointxyz{temp@p@x}{temp@p@y}{temp@p@z}
}
tikzaliascoordinatesystem{tpp}{three point perspective}

makeatother

begin{document}
tdplotsetmaincoords{70}{0}
foreach X [evaluate=X as vq using {X*X}]in {2,2.1,...,4,3.9,3.8,...,2.1}{
begin{tikzpicture}[scale=pi,%tdplot_main_coords
view={tdplotmaintheta}{tdplotmainphi},
perspective={
p = {(0,0,10)},
q = {(0,vq,1.25)},
}
]
path[tdplot_screen_coords] (-2,-1) rectangle (2,2);
foreach Y in {-1,1}
{foreach X in {1,-1}
{shade[top color=gray!50,bottom color=gray!60,middle color=gray!20,
shading angle=90] (tpp cs:X*0.9,Y*0.9,1) -- (tpp cs:X*0.89,Y*0.9,0)
to[bend left=X*12]
(tpp cs:X*0.81,Y*0.9,0) -- (tpp cs:X*0.8,Y*0.8,1);}}
node[cylinder,draw,minimum width=4mm,minimum height=5mm,aspect=0.5,inner
sep=3pt,rotate=90,cylinder uses custom fill,cylinder end fill=gray!50!black,
cylinder body fill=black,label={[font=sffamily]below left:2}] (c2) at
(tpp cs:0,0,0.1){};
draw[name path=line] (c2.top|-c2.before top) -- (tpp cs:0,0,1);
draw[gray!50,fill=gray!50]
(tpp cs:-1,-1,1) -- (tpp cs:1,-1,1) -- (tpp cs:1,1,1) -- (tpp cs:-1,1,1) -- cycle;
draw[gray!50,fill=white,thick]
(tpp cs:-1,-1,1) -- (tpp cs:1,-1,1)
-- (tpp cs:1,-1,0.9) -- (tpp cs:-1,-1,0.9) -- cycle;

draw[dashed,fill=gray!25,name path=circle] plot[variable=x,smooth,domain=0:360]
(tpp cs:{0.8*cos(x)},{0.8*sin(x)},1);
node[cylinder,draw,minimum width=4mm,minimum height=2mm,aspect=0.5,inner
sep=3pt,rotate=85,cylinder uses custom fill,cylinder end fill=gray!50!black,
cylinder body fill=black] (c1) at
(tpp cs:0.4,0.1,1.2){};
node[anchor=north,font=sffamily] at ([yshift=-1mm]c1){1};
draw[dashed,name intersections={of=circle and line}] (intersection-1)
-- (tpp cs:0,0,1);
draw (tpp cs:0,0,1) -- (c1.west);
end{tikzpicture}}
end{document}


enter image description here



And if you replace the loop by



 foreach X [evaluate=X as vq using {X*X}]in {3.5}{


say, you'll get.



enter image description here



Of course, you may find that another choice of parameters reproduces your screen shot more closely. Apart from the entries of q you can also play with the view angles.






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    1 Answer
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    active

    oldest

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    5














    All credits go to Max' answer. All I do is to truncate his general projection to a simpler case, which may help to understand better what's going on here. Max' picture shows very nicely what his code does: it transforms the objects in such a way that the edges that are parallel to the x axis meet in p, the ones parallel to the y axis in q and the ones parallel to the z axis in r. (Yes, that's just a sloppy definition of "vanishing points".) However, in order to reproduce something like your screenshot, we only need to play with q, which is what the following animation does.



    documentclass[tikz,border=3.14mm]{standalone}
    usepackage{tikz-3dplot}
    usetikzlibrary{shapes.geometric,intersections}
    usepgfmodule{nonlineartransformations}
    % Max magic
    makeatletter
    % the first part is not in use here
    deftikz@scan@transform@one@point#1{%
    tikz@scan@one@pointpgf@process#1%
    pgf@pos@transform{pgf@x}{pgf@y}}
    tikzset{%
    grid source opposite corners/.code args={#1and#2}{%
    pgfextract@processtikz@transform@source@southwest{%
    tikz@scan@transform@one@point{#1}}%
    pgfextract@processtikz@transform@source@northeast{%
    tikz@scan@transform@one@point{#2}}%
    },
    grid target corners/.code args={#1--#2--#3--#4}{%
    pgfextract@processtikz@transform@target@southwest{%
    tikz@scan@transform@one@point{#1}}%
    pgfextract@processtikz@transform@target@southeast{%
    tikz@scan@transform@one@point{#2}}%
    pgfextract@processtikz@transform@target@northeast{%
    tikz@scan@transform@one@point{#3}}%
    pgfextract@processtikz@transform@target@northwest{%
    tikz@scan@transform@one@point{#4}}%
    }
    }

    deftikzgridtransform{%
    pgfextract@processtikz@current@point{}%
    pgf@process{%
    pgfpointdiff{tikz@transform@source@southwest}%
    {tikz@transform@source@northeast}%
    }%
    pgf@xc=pgf@xpgf@yc=pgf@y%
    pgf@process{%
    pgfpointdiff{tikz@transform@source@southwest}{tikz@current@point}%
    }%
    pgfmathparse{pgf@x/pgf@xc}lettikz@tx=pgfmathresult%
    pgfmathparse{pgf@y/pgf@yc}lettikz@ty=pgfmathresult%
    %
    pgfpointlineattime{tikz@ty}{%
    pgfpointlineattime{tikz@tx}{tikz@transform@target@southwest}%
    {tikz@transform@target@southeast}}{%
    pgfpointlineattime{tikz@tx}{tikz@transform@target@northwest}%
    {tikz@transform@target@northeast}}%
    }

    % Initialize H matrix for perspective view
    pgfmathsetmacroH@tpp@aa{1}pgfmathsetmacroH@tpp@ab{0}pgfmathsetmacroH@tpp@ac{0}%pgfmathsetmacroH@tpp@ad{0}
    pgfmathsetmacroH@tpp@ba{0}pgfmathsetmacroH@tpp@bb{1}pgfmathsetmacroH@tpp@bc{0}%pgfmathsetmacroH@tpp@bd{0}
    pgfmathsetmacroH@tpp@ca{0}pgfmathsetmacroH@tpp@cb{0}pgfmathsetmacroH@tpp@cc{1}%pgfmathsetmacroH@tpp@cd{0}
    pgfmathsetmacroH@tpp@da{0}pgfmathsetmacroH@tpp@db{0}pgfmathsetmacroH@tpp@dc{0}%pgfmathsetmacroH@tpp@dd{1}

    %Initialize H matrix for main rotation
    pgfmathsetmacroH@rot@aa{1}pgfmathsetmacroH@rot@ab{0}pgfmathsetmacroH@rot@ac{0}%pgfmathsetmacroH@rot@ad{0}
    pgfmathsetmacroH@rot@ba{0}pgfmathsetmacroH@rot@bb{1}pgfmathsetmacroH@rot@bc{0}%pgfmathsetmacroH@rot@bd{0}
    pgfmathsetmacroH@rot@ca{0}pgfmathsetmacroH@rot@cb{0}pgfmathsetmacroH@rot@cc{1}%pgfmathsetmacroH@rot@cd{0}
    %pgfmathsetmacroH@rot@da{0}pgfmathsetmacroH@rot@db{0}pgfmathsetmacroH@rot@dc{0}pgfmathsetmacroH@rot@dd{1}

    pgfkeys{
    /three point perspective/.cd,
    p/.code args={(#1,#2,#3)}{
    pgfmathparse{int(round(#1))}
    ifnumpgfmathresult=0else
    pgfmathsetmacroH@tpp@ba{#2/#1}
    pgfmathsetmacroH@tpp@ca{#3/#1}
    pgfmathsetmacroH@tpp@da{ 1/#1}
    coordinate (vp-p) at (#1,#2,#3);
    fi
    },
    q/.code args={(#1,#2,#3)}{
    pgfmathparse{int(round(#2))}
    ifnumpgfmathresult=0else
    pgfmathsetmacroH@tpp@ab{#1/#2}
    pgfmathsetmacroH@tpp@cb{#3/#2}
    pgfmathsetmacroH@tpp@db{ 1/#2}
    coordinate (vp-q) at (#1,#2,#3);
    fi
    },
    r/.code args={(#1,#2,#3)}{
    pgfmathparse{int(round(#3))}
    ifnumpgfmathresult=0else
    pgfmathsetmacroH@tpp@ac{#1/#3}
    pgfmathsetmacroH@tpp@bc{#2/#3}
    pgfmathsetmacroH@tpp@dc{ 1/#3}
    coordinate (vp-r) at (#1,#2,#3);
    fi
    },
    coordinate/.code args={#1,#2,#3}{
    pgfmathsetmacrotpp@x{#1} %<- Max' fix
    pgfmathsetmacrotpp@y{#2}
    pgfmathsetmacrotpp@z{#3}
    },
    }

    tikzset{
    view/.code 2 args={
    pgfmathsetmacrorot@main@theta{#1}
    pgfmathsetmacrorot@main@phi{#2}
    % Row 1
    pgfmathsetmacroH@rot@aa{cos(rot@main@phi)}
    pgfmathsetmacroH@rot@ab{sin(rot@main@phi)}
    pgfmathsetmacroH@rot@ac{0}
    % Row 2
    pgfmathsetmacroH@rot@ba{-cos(rot@main@theta)*sin(rot@main@phi)}
    pgfmathsetmacroH@rot@bb{cos(rot@main@phi)*cos(rot@main@theta)}
    pgfmathsetmacroH@rot@bc{sin(rot@main@theta)}
    % Row 3
    pgfmathsetmacroH@m@ca{sin(rot@main@phi)*sin(rot@main@theta)}
    pgfmathsetmacroH@m@cb{-cos(rot@main@phi)*sin(rot@main@theta)}
    pgfmathsetmacroH@m@cc{cos(rot@main@theta)}
    % Set vector values
    pgfmathsetmacrovec@x@x{H@rot@aa}
    pgfmathsetmacrovec@y@x{H@rot@ab}
    pgfmathsetmacrovec@z@x{H@rot@ac}
    pgfmathsetmacrovec@x@y{H@rot@ba}
    pgfmathsetmacrovec@y@y{H@rot@bb}
    pgfmathsetmacrovec@z@y{H@rot@bc}
    % Set pgf vectors
    pgfsetxvec{pgfpoint{vec@x@x cm}{vec@x@y cm}}
    pgfsetyvec{pgfpoint{vec@y@x cm}{vec@y@y cm}}
    pgfsetzvec{pgfpoint{vec@z@x cm}{vec@z@y cm}}
    },
    }

    tikzset{
    perspective/.code={pgfkeys{/three point perspective/.cd,#1}},
    perspective/.default={p={(15,0,0)},q={(0,15,0)},r={(0,0,50)}},
    }

    tikzdeclarecoordinatesystem{three point perspective}{
    pgfkeys{/three point perspective/.cd,coordinate={#1}}
    pgfmathsetmacrotemp@p@w{H@tpp@da*tpp@x + H@tpp@db*tpp@y + H@tpp@dc*tpp@z + 1}
    pgfmathsetmacrotemp@p@x{(H@tpp@aa*tpp@x + H@tpp@ab*tpp@y + H@tpp@ac*tpp@z)/temp@p@w}
    pgfmathsetmacrotemp@p@y{(H@tpp@ba*tpp@x + H@tpp@bb*tpp@y + H@tpp@bc*tpp@z)/temp@p@w}
    pgfmathsetmacrotemp@p@z{(H@tpp@ca*tpp@x + H@tpp@cb*tpp@y + H@tpp@cc*tpp@z)/temp@p@w}
    pgfpointxyz{temp@p@x}{temp@p@y}{temp@p@z}
    }
    tikzaliascoordinatesystem{tpp}{three point perspective}

    makeatother

    begin{document}
    tdplotsetmaincoords{70}{0}
    foreach X [evaluate=X as vq using {X*X}]in {2,2.1,...,4,3.9,3.8,...,2.1}{
    begin{tikzpicture}[scale=pi,%tdplot_main_coords
    view={tdplotmaintheta}{tdplotmainphi},
    perspective={
    p = {(0,0,10)},
    q = {(0,vq,1.25)},
    }
    ]
    path[tdplot_screen_coords] (-2,-1) rectangle (2,2);
    foreach Y in {-1,1}
    {foreach X in {1,-1}
    {shade[top color=gray!50,bottom color=gray!60,middle color=gray!20,
    shading angle=90] (tpp cs:X*0.9,Y*0.9,1) -- (tpp cs:X*0.89,Y*0.9,0)
    to[bend left=X*12]
    (tpp cs:X*0.81,Y*0.9,0) -- (tpp cs:X*0.8,Y*0.8,1);}}
    node[cylinder,draw,minimum width=4mm,minimum height=5mm,aspect=0.5,inner
    sep=3pt,rotate=90,cylinder uses custom fill,cylinder end fill=gray!50!black,
    cylinder body fill=black,label={[font=sffamily]below left:2}] (c2) at
    (tpp cs:0,0,0.1){};
    draw[name path=line] (c2.top|-c2.before top) -- (tpp cs:0,0,1);
    draw[gray!50,fill=gray!50]
    (tpp cs:-1,-1,1) -- (tpp cs:1,-1,1) -- (tpp cs:1,1,1) -- (tpp cs:-1,1,1) -- cycle;
    draw[gray!50,fill=white,thick]
    (tpp cs:-1,-1,1) -- (tpp cs:1,-1,1)
    -- (tpp cs:1,-1,0.9) -- (tpp cs:-1,-1,0.9) -- cycle;

    draw[dashed,fill=gray!25,name path=circle] plot[variable=x,smooth,domain=0:360]
    (tpp cs:{0.8*cos(x)},{0.8*sin(x)},1);
    node[cylinder,draw,minimum width=4mm,minimum height=2mm,aspect=0.5,inner
    sep=3pt,rotate=85,cylinder uses custom fill,cylinder end fill=gray!50!black,
    cylinder body fill=black] (c1) at
    (tpp cs:0.4,0.1,1.2){};
    node[anchor=north,font=sffamily] at ([yshift=-1mm]c1){1};
    draw[dashed,name intersections={of=circle and line}] (intersection-1)
    -- (tpp cs:0,0,1);
    draw (tpp cs:0,0,1) -- (c1.west);
    end{tikzpicture}}
    end{document}


    enter image description here



    And if you replace the loop by



     foreach X [evaluate=X as vq using {X*X}]in {3.5}{


    say, you'll get.



    enter image description here



    Of course, you may find that another choice of parameters reproduces your screen shot more closely. Apart from the entries of q you can also play with the view angles.






    share|improve this answer






























      5














      All credits go to Max' answer. All I do is to truncate his general projection to a simpler case, which may help to understand better what's going on here. Max' picture shows very nicely what his code does: it transforms the objects in such a way that the edges that are parallel to the x axis meet in p, the ones parallel to the y axis in q and the ones parallel to the z axis in r. (Yes, that's just a sloppy definition of "vanishing points".) However, in order to reproduce something like your screenshot, we only need to play with q, which is what the following animation does.



      documentclass[tikz,border=3.14mm]{standalone}
      usepackage{tikz-3dplot}
      usetikzlibrary{shapes.geometric,intersections}
      usepgfmodule{nonlineartransformations}
      % Max magic
      makeatletter
      % the first part is not in use here
      deftikz@scan@transform@one@point#1{%
      tikz@scan@one@pointpgf@process#1%
      pgf@pos@transform{pgf@x}{pgf@y}}
      tikzset{%
      grid source opposite corners/.code args={#1and#2}{%
      pgfextract@processtikz@transform@source@southwest{%
      tikz@scan@transform@one@point{#1}}%
      pgfextract@processtikz@transform@source@northeast{%
      tikz@scan@transform@one@point{#2}}%
      },
      grid target corners/.code args={#1--#2--#3--#4}{%
      pgfextract@processtikz@transform@target@southwest{%
      tikz@scan@transform@one@point{#1}}%
      pgfextract@processtikz@transform@target@southeast{%
      tikz@scan@transform@one@point{#2}}%
      pgfextract@processtikz@transform@target@northeast{%
      tikz@scan@transform@one@point{#3}}%
      pgfextract@processtikz@transform@target@northwest{%
      tikz@scan@transform@one@point{#4}}%
      }
      }

      deftikzgridtransform{%
      pgfextract@processtikz@current@point{}%
      pgf@process{%
      pgfpointdiff{tikz@transform@source@southwest}%
      {tikz@transform@source@northeast}%
      }%
      pgf@xc=pgf@xpgf@yc=pgf@y%
      pgf@process{%
      pgfpointdiff{tikz@transform@source@southwest}{tikz@current@point}%
      }%
      pgfmathparse{pgf@x/pgf@xc}lettikz@tx=pgfmathresult%
      pgfmathparse{pgf@y/pgf@yc}lettikz@ty=pgfmathresult%
      %
      pgfpointlineattime{tikz@ty}{%
      pgfpointlineattime{tikz@tx}{tikz@transform@target@southwest}%
      {tikz@transform@target@southeast}}{%
      pgfpointlineattime{tikz@tx}{tikz@transform@target@northwest}%
      {tikz@transform@target@northeast}}%
      }

      % Initialize H matrix for perspective view
      pgfmathsetmacroH@tpp@aa{1}pgfmathsetmacroH@tpp@ab{0}pgfmathsetmacroH@tpp@ac{0}%pgfmathsetmacroH@tpp@ad{0}
      pgfmathsetmacroH@tpp@ba{0}pgfmathsetmacroH@tpp@bb{1}pgfmathsetmacroH@tpp@bc{0}%pgfmathsetmacroH@tpp@bd{0}
      pgfmathsetmacroH@tpp@ca{0}pgfmathsetmacroH@tpp@cb{0}pgfmathsetmacroH@tpp@cc{1}%pgfmathsetmacroH@tpp@cd{0}
      pgfmathsetmacroH@tpp@da{0}pgfmathsetmacroH@tpp@db{0}pgfmathsetmacroH@tpp@dc{0}%pgfmathsetmacroH@tpp@dd{1}

      %Initialize H matrix for main rotation
      pgfmathsetmacroH@rot@aa{1}pgfmathsetmacroH@rot@ab{0}pgfmathsetmacroH@rot@ac{0}%pgfmathsetmacroH@rot@ad{0}
      pgfmathsetmacroH@rot@ba{0}pgfmathsetmacroH@rot@bb{1}pgfmathsetmacroH@rot@bc{0}%pgfmathsetmacroH@rot@bd{0}
      pgfmathsetmacroH@rot@ca{0}pgfmathsetmacroH@rot@cb{0}pgfmathsetmacroH@rot@cc{1}%pgfmathsetmacroH@rot@cd{0}
      %pgfmathsetmacroH@rot@da{0}pgfmathsetmacroH@rot@db{0}pgfmathsetmacroH@rot@dc{0}pgfmathsetmacroH@rot@dd{1}

      pgfkeys{
      /three point perspective/.cd,
      p/.code args={(#1,#2,#3)}{
      pgfmathparse{int(round(#1))}
      ifnumpgfmathresult=0else
      pgfmathsetmacroH@tpp@ba{#2/#1}
      pgfmathsetmacroH@tpp@ca{#3/#1}
      pgfmathsetmacroH@tpp@da{ 1/#1}
      coordinate (vp-p) at (#1,#2,#3);
      fi
      },
      q/.code args={(#1,#2,#3)}{
      pgfmathparse{int(round(#2))}
      ifnumpgfmathresult=0else
      pgfmathsetmacroH@tpp@ab{#1/#2}
      pgfmathsetmacroH@tpp@cb{#3/#2}
      pgfmathsetmacroH@tpp@db{ 1/#2}
      coordinate (vp-q) at (#1,#2,#3);
      fi
      },
      r/.code args={(#1,#2,#3)}{
      pgfmathparse{int(round(#3))}
      ifnumpgfmathresult=0else
      pgfmathsetmacroH@tpp@ac{#1/#3}
      pgfmathsetmacroH@tpp@bc{#2/#3}
      pgfmathsetmacroH@tpp@dc{ 1/#3}
      coordinate (vp-r) at (#1,#2,#3);
      fi
      },
      coordinate/.code args={#1,#2,#3}{
      pgfmathsetmacrotpp@x{#1} %<- Max' fix
      pgfmathsetmacrotpp@y{#2}
      pgfmathsetmacrotpp@z{#3}
      },
      }

      tikzset{
      view/.code 2 args={
      pgfmathsetmacrorot@main@theta{#1}
      pgfmathsetmacrorot@main@phi{#2}
      % Row 1
      pgfmathsetmacroH@rot@aa{cos(rot@main@phi)}
      pgfmathsetmacroH@rot@ab{sin(rot@main@phi)}
      pgfmathsetmacroH@rot@ac{0}
      % Row 2
      pgfmathsetmacroH@rot@ba{-cos(rot@main@theta)*sin(rot@main@phi)}
      pgfmathsetmacroH@rot@bb{cos(rot@main@phi)*cos(rot@main@theta)}
      pgfmathsetmacroH@rot@bc{sin(rot@main@theta)}
      % Row 3
      pgfmathsetmacroH@m@ca{sin(rot@main@phi)*sin(rot@main@theta)}
      pgfmathsetmacroH@m@cb{-cos(rot@main@phi)*sin(rot@main@theta)}
      pgfmathsetmacroH@m@cc{cos(rot@main@theta)}
      % Set vector values
      pgfmathsetmacrovec@x@x{H@rot@aa}
      pgfmathsetmacrovec@y@x{H@rot@ab}
      pgfmathsetmacrovec@z@x{H@rot@ac}
      pgfmathsetmacrovec@x@y{H@rot@ba}
      pgfmathsetmacrovec@y@y{H@rot@bb}
      pgfmathsetmacrovec@z@y{H@rot@bc}
      % Set pgf vectors
      pgfsetxvec{pgfpoint{vec@x@x cm}{vec@x@y cm}}
      pgfsetyvec{pgfpoint{vec@y@x cm}{vec@y@y cm}}
      pgfsetzvec{pgfpoint{vec@z@x cm}{vec@z@y cm}}
      },
      }

      tikzset{
      perspective/.code={pgfkeys{/three point perspective/.cd,#1}},
      perspective/.default={p={(15,0,0)},q={(0,15,0)},r={(0,0,50)}},
      }

      tikzdeclarecoordinatesystem{three point perspective}{
      pgfkeys{/three point perspective/.cd,coordinate={#1}}
      pgfmathsetmacrotemp@p@w{H@tpp@da*tpp@x + H@tpp@db*tpp@y + H@tpp@dc*tpp@z + 1}
      pgfmathsetmacrotemp@p@x{(H@tpp@aa*tpp@x + H@tpp@ab*tpp@y + H@tpp@ac*tpp@z)/temp@p@w}
      pgfmathsetmacrotemp@p@y{(H@tpp@ba*tpp@x + H@tpp@bb*tpp@y + H@tpp@bc*tpp@z)/temp@p@w}
      pgfmathsetmacrotemp@p@z{(H@tpp@ca*tpp@x + H@tpp@cb*tpp@y + H@tpp@cc*tpp@z)/temp@p@w}
      pgfpointxyz{temp@p@x}{temp@p@y}{temp@p@z}
      }
      tikzaliascoordinatesystem{tpp}{three point perspective}

      makeatother

      begin{document}
      tdplotsetmaincoords{70}{0}
      foreach X [evaluate=X as vq using {X*X}]in {2,2.1,...,4,3.9,3.8,...,2.1}{
      begin{tikzpicture}[scale=pi,%tdplot_main_coords
      view={tdplotmaintheta}{tdplotmainphi},
      perspective={
      p = {(0,0,10)},
      q = {(0,vq,1.25)},
      }
      ]
      path[tdplot_screen_coords] (-2,-1) rectangle (2,2);
      foreach Y in {-1,1}
      {foreach X in {1,-1}
      {shade[top color=gray!50,bottom color=gray!60,middle color=gray!20,
      shading angle=90] (tpp cs:X*0.9,Y*0.9,1) -- (tpp cs:X*0.89,Y*0.9,0)
      to[bend left=X*12]
      (tpp cs:X*0.81,Y*0.9,0) -- (tpp cs:X*0.8,Y*0.8,1);}}
      node[cylinder,draw,minimum width=4mm,minimum height=5mm,aspect=0.5,inner
      sep=3pt,rotate=90,cylinder uses custom fill,cylinder end fill=gray!50!black,
      cylinder body fill=black,label={[font=sffamily]below left:2}] (c2) at
      (tpp cs:0,0,0.1){};
      draw[name path=line] (c2.top|-c2.before top) -- (tpp cs:0,0,1);
      draw[gray!50,fill=gray!50]
      (tpp cs:-1,-1,1) -- (tpp cs:1,-1,1) -- (tpp cs:1,1,1) -- (tpp cs:-1,1,1) -- cycle;
      draw[gray!50,fill=white,thick]
      (tpp cs:-1,-1,1) -- (tpp cs:1,-1,1)
      -- (tpp cs:1,-1,0.9) -- (tpp cs:-1,-1,0.9) -- cycle;

      draw[dashed,fill=gray!25,name path=circle] plot[variable=x,smooth,domain=0:360]
      (tpp cs:{0.8*cos(x)},{0.8*sin(x)},1);
      node[cylinder,draw,minimum width=4mm,minimum height=2mm,aspect=0.5,inner
      sep=3pt,rotate=85,cylinder uses custom fill,cylinder end fill=gray!50!black,
      cylinder body fill=black] (c1) at
      (tpp cs:0.4,0.1,1.2){};
      node[anchor=north,font=sffamily] at ([yshift=-1mm]c1){1};
      draw[dashed,name intersections={of=circle and line}] (intersection-1)
      -- (tpp cs:0,0,1);
      draw (tpp cs:0,0,1) -- (c1.west);
      end{tikzpicture}}
      end{document}


      enter image description here



      And if you replace the loop by



       foreach X [evaluate=X as vq using {X*X}]in {3.5}{


      say, you'll get.



      enter image description here



      Of course, you may find that another choice of parameters reproduces your screen shot more closely. Apart from the entries of q you can also play with the view angles.






      share|improve this answer




























        5












        5








        5







        All credits go to Max' answer. All I do is to truncate his general projection to a simpler case, which may help to understand better what's going on here. Max' picture shows very nicely what his code does: it transforms the objects in such a way that the edges that are parallel to the x axis meet in p, the ones parallel to the y axis in q and the ones parallel to the z axis in r. (Yes, that's just a sloppy definition of "vanishing points".) However, in order to reproduce something like your screenshot, we only need to play with q, which is what the following animation does.



        documentclass[tikz,border=3.14mm]{standalone}
        usepackage{tikz-3dplot}
        usetikzlibrary{shapes.geometric,intersections}
        usepgfmodule{nonlineartransformations}
        % Max magic
        makeatletter
        % the first part is not in use here
        deftikz@scan@transform@one@point#1{%
        tikz@scan@one@pointpgf@process#1%
        pgf@pos@transform{pgf@x}{pgf@y}}
        tikzset{%
        grid source opposite corners/.code args={#1and#2}{%
        pgfextract@processtikz@transform@source@southwest{%
        tikz@scan@transform@one@point{#1}}%
        pgfextract@processtikz@transform@source@northeast{%
        tikz@scan@transform@one@point{#2}}%
        },
        grid target corners/.code args={#1--#2--#3--#4}{%
        pgfextract@processtikz@transform@target@southwest{%
        tikz@scan@transform@one@point{#1}}%
        pgfextract@processtikz@transform@target@southeast{%
        tikz@scan@transform@one@point{#2}}%
        pgfextract@processtikz@transform@target@northeast{%
        tikz@scan@transform@one@point{#3}}%
        pgfextract@processtikz@transform@target@northwest{%
        tikz@scan@transform@one@point{#4}}%
        }
        }

        deftikzgridtransform{%
        pgfextract@processtikz@current@point{}%
        pgf@process{%
        pgfpointdiff{tikz@transform@source@southwest}%
        {tikz@transform@source@northeast}%
        }%
        pgf@xc=pgf@xpgf@yc=pgf@y%
        pgf@process{%
        pgfpointdiff{tikz@transform@source@southwest}{tikz@current@point}%
        }%
        pgfmathparse{pgf@x/pgf@xc}lettikz@tx=pgfmathresult%
        pgfmathparse{pgf@y/pgf@yc}lettikz@ty=pgfmathresult%
        %
        pgfpointlineattime{tikz@ty}{%
        pgfpointlineattime{tikz@tx}{tikz@transform@target@southwest}%
        {tikz@transform@target@southeast}}{%
        pgfpointlineattime{tikz@tx}{tikz@transform@target@northwest}%
        {tikz@transform@target@northeast}}%
        }

        % Initialize H matrix for perspective view
        pgfmathsetmacroH@tpp@aa{1}pgfmathsetmacroH@tpp@ab{0}pgfmathsetmacroH@tpp@ac{0}%pgfmathsetmacroH@tpp@ad{0}
        pgfmathsetmacroH@tpp@ba{0}pgfmathsetmacroH@tpp@bb{1}pgfmathsetmacroH@tpp@bc{0}%pgfmathsetmacroH@tpp@bd{0}
        pgfmathsetmacroH@tpp@ca{0}pgfmathsetmacroH@tpp@cb{0}pgfmathsetmacroH@tpp@cc{1}%pgfmathsetmacroH@tpp@cd{0}
        pgfmathsetmacroH@tpp@da{0}pgfmathsetmacroH@tpp@db{0}pgfmathsetmacroH@tpp@dc{0}%pgfmathsetmacroH@tpp@dd{1}

        %Initialize H matrix for main rotation
        pgfmathsetmacroH@rot@aa{1}pgfmathsetmacroH@rot@ab{0}pgfmathsetmacroH@rot@ac{0}%pgfmathsetmacroH@rot@ad{0}
        pgfmathsetmacroH@rot@ba{0}pgfmathsetmacroH@rot@bb{1}pgfmathsetmacroH@rot@bc{0}%pgfmathsetmacroH@rot@bd{0}
        pgfmathsetmacroH@rot@ca{0}pgfmathsetmacroH@rot@cb{0}pgfmathsetmacroH@rot@cc{1}%pgfmathsetmacroH@rot@cd{0}
        %pgfmathsetmacroH@rot@da{0}pgfmathsetmacroH@rot@db{0}pgfmathsetmacroH@rot@dc{0}pgfmathsetmacroH@rot@dd{1}

        pgfkeys{
        /three point perspective/.cd,
        p/.code args={(#1,#2,#3)}{
        pgfmathparse{int(round(#1))}
        ifnumpgfmathresult=0else
        pgfmathsetmacroH@tpp@ba{#2/#1}
        pgfmathsetmacroH@tpp@ca{#3/#1}
        pgfmathsetmacroH@tpp@da{ 1/#1}
        coordinate (vp-p) at (#1,#2,#3);
        fi
        },
        q/.code args={(#1,#2,#3)}{
        pgfmathparse{int(round(#2))}
        ifnumpgfmathresult=0else
        pgfmathsetmacroH@tpp@ab{#1/#2}
        pgfmathsetmacroH@tpp@cb{#3/#2}
        pgfmathsetmacroH@tpp@db{ 1/#2}
        coordinate (vp-q) at (#1,#2,#3);
        fi
        },
        r/.code args={(#1,#2,#3)}{
        pgfmathparse{int(round(#3))}
        ifnumpgfmathresult=0else
        pgfmathsetmacroH@tpp@ac{#1/#3}
        pgfmathsetmacroH@tpp@bc{#2/#3}
        pgfmathsetmacroH@tpp@dc{ 1/#3}
        coordinate (vp-r) at (#1,#2,#3);
        fi
        },
        coordinate/.code args={#1,#2,#3}{
        pgfmathsetmacrotpp@x{#1} %<- Max' fix
        pgfmathsetmacrotpp@y{#2}
        pgfmathsetmacrotpp@z{#3}
        },
        }

        tikzset{
        view/.code 2 args={
        pgfmathsetmacrorot@main@theta{#1}
        pgfmathsetmacrorot@main@phi{#2}
        % Row 1
        pgfmathsetmacroH@rot@aa{cos(rot@main@phi)}
        pgfmathsetmacroH@rot@ab{sin(rot@main@phi)}
        pgfmathsetmacroH@rot@ac{0}
        % Row 2
        pgfmathsetmacroH@rot@ba{-cos(rot@main@theta)*sin(rot@main@phi)}
        pgfmathsetmacroH@rot@bb{cos(rot@main@phi)*cos(rot@main@theta)}
        pgfmathsetmacroH@rot@bc{sin(rot@main@theta)}
        % Row 3
        pgfmathsetmacroH@m@ca{sin(rot@main@phi)*sin(rot@main@theta)}
        pgfmathsetmacroH@m@cb{-cos(rot@main@phi)*sin(rot@main@theta)}
        pgfmathsetmacroH@m@cc{cos(rot@main@theta)}
        % Set vector values
        pgfmathsetmacrovec@x@x{H@rot@aa}
        pgfmathsetmacrovec@y@x{H@rot@ab}
        pgfmathsetmacrovec@z@x{H@rot@ac}
        pgfmathsetmacrovec@x@y{H@rot@ba}
        pgfmathsetmacrovec@y@y{H@rot@bb}
        pgfmathsetmacrovec@z@y{H@rot@bc}
        % Set pgf vectors
        pgfsetxvec{pgfpoint{vec@x@x cm}{vec@x@y cm}}
        pgfsetyvec{pgfpoint{vec@y@x cm}{vec@y@y cm}}
        pgfsetzvec{pgfpoint{vec@z@x cm}{vec@z@y cm}}
        },
        }

        tikzset{
        perspective/.code={pgfkeys{/three point perspective/.cd,#1}},
        perspective/.default={p={(15,0,0)},q={(0,15,0)},r={(0,0,50)}},
        }

        tikzdeclarecoordinatesystem{three point perspective}{
        pgfkeys{/three point perspective/.cd,coordinate={#1}}
        pgfmathsetmacrotemp@p@w{H@tpp@da*tpp@x + H@tpp@db*tpp@y + H@tpp@dc*tpp@z + 1}
        pgfmathsetmacrotemp@p@x{(H@tpp@aa*tpp@x + H@tpp@ab*tpp@y + H@tpp@ac*tpp@z)/temp@p@w}
        pgfmathsetmacrotemp@p@y{(H@tpp@ba*tpp@x + H@tpp@bb*tpp@y + H@tpp@bc*tpp@z)/temp@p@w}
        pgfmathsetmacrotemp@p@z{(H@tpp@ca*tpp@x + H@tpp@cb*tpp@y + H@tpp@cc*tpp@z)/temp@p@w}
        pgfpointxyz{temp@p@x}{temp@p@y}{temp@p@z}
        }
        tikzaliascoordinatesystem{tpp}{three point perspective}

        makeatother

        begin{document}
        tdplotsetmaincoords{70}{0}
        foreach X [evaluate=X as vq using {X*X}]in {2,2.1,...,4,3.9,3.8,...,2.1}{
        begin{tikzpicture}[scale=pi,%tdplot_main_coords
        view={tdplotmaintheta}{tdplotmainphi},
        perspective={
        p = {(0,0,10)},
        q = {(0,vq,1.25)},
        }
        ]
        path[tdplot_screen_coords] (-2,-1) rectangle (2,2);
        foreach Y in {-1,1}
        {foreach X in {1,-1}
        {shade[top color=gray!50,bottom color=gray!60,middle color=gray!20,
        shading angle=90] (tpp cs:X*0.9,Y*0.9,1) -- (tpp cs:X*0.89,Y*0.9,0)
        to[bend left=X*12]
        (tpp cs:X*0.81,Y*0.9,0) -- (tpp cs:X*0.8,Y*0.8,1);}}
        node[cylinder,draw,minimum width=4mm,minimum height=5mm,aspect=0.5,inner
        sep=3pt,rotate=90,cylinder uses custom fill,cylinder end fill=gray!50!black,
        cylinder body fill=black,label={[font=sffamily]below left:2}] (c2) at
        (tpp cs:0,0,0.1){};
        draw[name path=line] (c2.top|-c2.before top) -- (tpp cs:0,0,1);
        draw[gray!50,fill=gray!50]
        (tpp cs:-1,-1,1) -- (tpp cs:1,-1,1) -- (tpp cs:1,1,1) -- (tpp cs:-1,1,1) -- cycle;
        draw[gray!50,fill=white,thick]
        (tpp cs:-1,-1,1) -- (tpp cs:1,-1,1)
        -- (tpp cs:1,-1,0.9) -- (tpp cs:-1,-1,0.9) -- cycle;

        draw[dashed,fill=gray!25,name path=circle] plot[variable=x,smooth,domain=0:360]
        (tpp cs:{0.8*cos(x)},{0.8*sin(x)},1);
        node[cylinder,draw,minimum width=4mm,minimum height=2mm,aspect=0.5,inner
        sep=3pt,rotate=85,cylinder uses custom fill,cylinder end fill=gray!50!black,
        cylinder body fill=black] (c1) at
        (tpp cs:0.4,0.1,1.2){};
        node[anchor=north,font=sffamily] at ([yshift=-1mm]c1){1};
        draw[dashed,name intersections={of=circle and line}] (intersection-1)
        -- (tpp cs:0,0,1);
        draw (tpp cs:0,0,1) -- (c1.west);
        end{tikzpicture}}
        end{document}


        enter image description here



        And if you replace the loop by



         foreach X [evaluate=X as vq using {X*X}]in {3.5}{


        say, you'll get.



        enter image description here



        Of course, you may find that another choice of parameters reproduces your screen shot more closely. Apart from the entries of q you can also play with the view angles.






        share|improve this answer















        All credits go to Max' answer. All I do is to truncate his general projection to a simpler case, which may help to understand better what's going on here. Max' picture shows very nicely what his code does: it transforms the objects in such a way that the edges that are parallel to the x axis meet in p, the ones parallel to the y axis in q and the ones parallel to the z axis in r. (Yes, that's just a sloppy definition of "vanishing points".) However, in order to reproduce something like your screenshot, we only need to play with q, which is what the following animation does.



        documentclass[tikz,border=3.14mm]{standalone}
        usepackage{tikz-3dplot}
        usetikzlibrary{shapes.geometric,intersections}
        usepgfmodule{nonlineartransformations}
        % Max magic
        makeatletter
        % the first part is not in use here
        deftikz@scan@transform@one@point#1{%
        tikz@scan@one@pointpgf@process#1%
        pgf@pos@transform{pgf@x}{pgf@y}}
        tikzset{%
        grid source opposite corners/.code args={#1and#2}{%
        pgfextract@processtikz@transform@source@southwest{%
        tikz@scan@transform@one@point{#1}}%
        pgfextract@processtikz@transform@source@northeast{%
        tikz@scan@transform@one@point{#2}}%
        },
        grid target corners/.code args={#1--#2--#3--#4}{%
        pgfextract@processtikz@transform@target@southwest{%
        tikz@scan@transform@one@point{#1}}%
        pgfextract@processtikz@transform@target@southeast{%
        tikz@scan@transform@one@point{#2}}%
        pgfextract@processtikz@transform@target@northeast{%
        tikz@scan@transform@one@point{#3}}%
        pgfextract@processtikz@transform@target@northwest{%
        tikz@scan@transform@one@point{#4}}%
        }
        }

        deftikzgridtransform{%
        pgfextract@processtikz@current@point{}%
        pgf@process{%
        pgfpointdiff{tikz@transform@source@southwest}%
        {tikz@transform@source@northeast}%
        }%
        pgf@xc=pgf@xpgf@yc=pgf@y%
        pgf@process{%
        pgfpointdiff{tikz@transform@source@southwest}{tikz@current@point}%
        }%
        pgfmathparse{pgf@x/pgf@xc}lettikz@tx=pgfmathresult%
        pgfmathparse{pgf@y/pgf@yc}lettikz@ty=pgfmathresult%
        %
        pgfpointlineattime{tikz@ty}{%
        pgfpointlineattime{tikz@tx}{tikz@transform@target@southwest}%
        {tikz@transform@target@southeast}}{%
        pgfpointlineattime{tikz@tx}{tikz@transform@target@northwest}%
        {tikz@transform@target@northeast}}%
        }

        % Initialize H matrix for perspective view
        pgfmathsetmacroH@tpp@aa{1}pgfmathsetmacroH@tpp@ab{0}pgfmathsetmacroH@tpp@ac{0}%pgfmathsetmacroH@tpp@ad{0}
        pgfmathsetmacroH@tpp@ba{0}pgfmathsetmacroH@tpp@bb{1}pgfmathsetmacroH@tpp@bc{0}%pgfmathsetmacroH@tpp@bd{0}
        pgfmathsetmacroH@tpp@ca{0}pgfmathsetmacroH@tpp@cb{0}pgfmathsetmacroH@tpp@cc{1}%pgfmathsetmacroH@tpp@cd{0}
        pgfmathsetmacroH@tpp@da{0}pgfmathsetmacroH@tpp@db{0}pgfmathsetmacroH@tpp@dc{0}%pgfmathsetmacroH@tpp@dd{1}

        %Initialize H matrix for main rotation
        pgfmathsetmacroH@rot@aa{1}pgfmathsetmacroH@rot@ab{0}pgfmathsetmacroH@rot@ac{0}%pgfmathsetmacroH@rot@ad{0}
        pgfmathsetmacroH@rot@ba{0}pgfmathsetmacroH@rot@bb{1}pgfmathsetmacroH@rot@bc{0}%pgfmathsetmacroH@rot@bd{0}
        pgfmathsetmacroH@rot@ca{0}pgfmathsetmacroH@rot@cb{0}pgfmathsetmacroH@rot@cc{1}%pgfmathsetmacroH@rot@cd{0}
        %pgfmathsetmacroH@rot@da{0}pgfmathsetmacroH@rot@db{0}pgfmathsetmacroH@rot@dc{0}pgfmathsetmacroH@rot@dd{1}

        pgfkeys{
        /three point perspective/.cd,
        p/.code args={(#1,#2,#3)}{
        pgfmathparse{int(round(#1))}
        ifnumpgfmathresult=0else
        pgfmathsetmacroH@tpp@ba{#2/#1}
        pgfmathsetmacroH@tpp@ca{#3/#1}
        pgfmathsetmacroH@tpp@da{ 1/#1}
        coordinate (vp-p) at (#1,#2,#3);
        fi
        },
        q/.code args={(#1,#2,#3)}{
        pgfmathparse{int(round(#2))}
        ifnumpgfmathresult=0else
        pgfmathsetmacroH@tpp@ab{#1/#2}
        pgfmathsetmacroH@tpp@cb{#3/#2}
        pgfmathsetmacroH@tpp@db{ 1/#2}
        coordinate (vp-q) at (#1,#2,#3);
        fi
        },
        r/.code args={(#1,#2,#3)}{
        pgfmathparse{int(round(#3))}
        ifnumpgfmathresult=0else
        pgfmathsetmacroH@tpp@ac{#1/#3}
        pgfmathsetmacroH@tpp@bc{#2/#3}
        pgfmathsetmacroH@tpp@dc{ 1/#3}
        coordinate (vp-r) at (#1,#2,#3);
        fi
        },
        coordinate/.code args={#1,#2,#3}{
        pgfmathsetmacrotpp@x{#1} %<- Max' fix
        pgfmathsetmacrotpp@y{#2}
        pgfmathsetmacrotpp@z{#3}
        },
        }

        tikzset{
        view/.code 2 args={
        pgfmathsetmacrorot@main@theta{#1}
        pgfmathsetmacrorot@main@phi{#2}
        % Row 1
        pgfmathsetmacroH@rot@aa{cos(rot@main@phi)}
        pgfmathsetmacroH@rot@ab{sin(rot@main@phi)}
        pgfmathsetmacroH@rot@ac{0}
        % Row 2
        pgfmathsetmacroH@rot@ba{-cos(rot@main@theta)*sin(rot@main@phi)}
        pgfmathsetmacroH@rot@bb{cos(rot@main@phi)*cos(rot@main@theta)}
        pgfmathsetmacroH@rot@bc{sin(rot@main@theta)}
        % Row 3
        pgfmathsetmacroH@m@ca{sin(rot@main@phi)*sin(rot@main@theta)}
        pgfmathsetmacroH@m@cb{-cos(rot@main@phi)*sin(rot@main@theta)}
        pgfmathsetmacroH@m@cc{cos(rot@main@theta)}
        % Set vector values
        pgfmathsetmacrovec@x@x{H@rot@aa}
        pgfmathsetmacrovec@y@x{H@rot@ab}
        pgfmathsetmacrovec@z@x{H@rot@ac}
        pgfmathsetmacrovec@x@y{H@rot@ba}
        pgfmathsetmacrovec@y@y{H@rot@bb}
        pgfmathsetmacrovec@z@y{H@rot@bc}
        % Set pgf vectors
        pgfsetxvec{pgfpoint{vec@x@x cm}{vec@x@y cm}}
        pgfsetyvec{pgfpoint{vec@y@x cm}{vec@y@y cm}}
        pgfsetzvec{pgfpoint{vec@z@x cm}{vec@z@y cm}}
        },
        }

        tikzset{
        perspective/.code={pgfkeys{/three point perspective/.cd,#1}},
        perspective/.default={p={(15,0,0)},q={(0,15,0)},r={(0,0,50)}},
        }

        tikzdeclarecoordinatesystem{three point perspective}{
        pgfkeys{/three point perspective/.cd,coordinate={#1}}
        pgfmathsetmacrotemp@p@w{H@tpp@da*tpp@x + H@tpp@db*tpp@y + H@tpp@dc*tpp@z + 1}
        pgfmathsetmacrotemp@p@x{(H@tpp@aa*tpp@x + H@tpp@ab*tpp@y + H@tpp@ac*tpp@z)/temp@p@w}
        pgfmathsetmacrotemp@p@y{(H@tpp@ba*tpp@x + H@tpp@bb*tpp@y + H@tpp@bc*tpp@z)/temp@p@w}
        pgfmathsetmacrotemp@p@z{(H@tpp@ca*tpp@x + H@tpp@cb*tpp@y + H@tpp@cc*tpp@z)/temp@p@w}
        pgfpointxyz{temp@p@x}{temp@p@y}{temp@p@z}
        }
        tikzaliascoordinatesystem{tpp}{three point perspective}

        makeatother

        begin{document}
        tdplotsetmaincoords{70}{0}
        foreach X [evaluate=X as vq using {X*X}]in {2,2.1,...,4,3.9,3.8,...,2.1}{
        begin{tikzpicture}[scale=pi,%tdplot_main_coords
        view={tdplotmaintheta}{tdplotmainphi},
        perspective={
        p = {(0,0,10)},
        q = {(0,vq,1.25)},
        }
        ]
        path[tdplot_screen_coords] (-2,-1) rectangle (2,2);
        foreach Y in {-1,1}
        {foreach X in {1,-1}
        {shade[top color=gray!50,bottom color=gray!60,middle color=gray!20,
        shading angle=90] (tpp cs:X*0.9,Y*0.9,1) -- (tpp cs:X*0.89,Y*0.9,0)
        to[bend left=X*12]
        (tpp cs:X*0.81,Y*0.9,0) -- (tpp cs:X*0.8,Y*0.8,1);}}
        node[cylinder,draw,minimum width=4mm,minimum height=5mm,aspect=0.5,inner
        sep=3pt,rotate=90,cylinder uses custom fill,cylinder end fill=gray!50!black,
        cylinder body fill=black,label={[font=sffamily]below left:2}] (c2) at
        (tpp cs:0,0,0.1){};
        draw[name path=line] (c2.top|-c2.before top) -- (tpp cs:0,0,1);
        draw[gray!50,fill=gray!50]
        (tpp cs:-1,-1,1) -- (tpp cs:1,-1,1) -- (tpp cs:1,1,1) -- (tpp cs:-1,1,1) -- cycle;
        draw[gray!50,fill=white,thick]
        (tpp cs:-1,-1,1) -- (tpp cs:1,-1,1)
        -- (tpp cs:1,-1,0.9) -- (tpp cs:-1,-1,0.9) -- cycle;

        draw[dashed,fill=gray!25,name path=circle] plot[variable=x,smooth,domain=0:360]
        (tpp cs:{0.8*cos(x)},{0.8*sin(x)},1);
        node[cylinder,draw,minimum width=4mm,minimum height=2mm,aspect=0.5,inner
        sep=3pt,rotate=85,cylinder uses custom fill,cylinder end fill=gray!50!black,
        cylinder body fill=black] (c1) at
        (tpp cs:0.4,0.1,1.2){};
        node[anchor=north,font=sffamily] at ([yshift=-1mm]c1){1};
        draw[dashed,name intersections={of=circle and line}] (intersection-1)
        -- (tpp cs:0,0,1);
        draw (tpp cs:0,0,1) -- (c1.west);
        end{tikzpicture}}
        end{document}


        enter image description here



        And if you replace the loop by



         foreach X [evaluate=X as vq using {X*X}]in {3.5}{


        say, you'll get.



        enter image description here



        Of course, you may find that another choice of parameters reproduces your screen shot more closely. Apart from the entries of q you can also play with the view angles.







        share|improve this answer














        share|improve this answer



        share|improve this answer








        edited 2 hours ago

























        answered 4 hours ago









        marmotmarmot

        91.9k4107200




        91.9k4107200






























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