How can I give this perspective with Tikz?












7















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



enter image description here










share|improve this question

























  • Can you show us the code you already have?

    – Sigur
    Jan 16 at 23:02






  • 1





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

    – marmot
    Jan 16 at 23:05











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

    – Eduardo
    Jan 16 at 23:12






  • 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
    Jan 16 at 23:44
















7















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



enter image description here










share|improve this question

























  • Can you show us the code you already have?

    – Sigur
    Jan 16 at 23:02






  • 1





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

    – marmot
    Jan 16 at 23:05











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

    – Eduardo
    Jan 16 at 23:12






  • 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
    Jan 16 at 23:44














7












7








7


6






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



enter image description here










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



enter image description here







tikz-pgf






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Jan 17 at 21:39







Eduardo

















asked Jan 16 at 23:01









EduardoEduardo

976




976













  • Can you show us the code you already have?

    – Sigur
    Jan 16 at 23:02






  • 1





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

    – marmot
    Jan 16 at 23:05











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

    – Eduardo
    Jan 16 at 23:12






  • 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
    Jan 16 at 23:44



















  • Can you show us the code you already have?

    – Sigur
    Jan 16 at 23:02






  • 1





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

    – marmot
    Jan 16 at 23:05











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

    – Eduardo
    Jan 16 at 23:12






  • 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
    Jan 16 at 23:44

















Can you show us the code you already have?

– Sigur
Jan 16 at 23:02





Can you show us the code you already have?

– Sigur
Jan 16 at 23:02




1




1





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

– marmot
Jan 16 at 23:05





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

– marmot
Jan 16 at 23:05













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

– Eduardo
Jan 16 at 23:12





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

– Eduardo
Jan 16 at 23:12




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
Jan 16 at 23:44





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
Jan 16 at 23:44










1 Answer
1






active

oldest

votes


















16














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. (UPDATE: Took into account the additional screen shot added by the OP.)



documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{arrows.meta,bending,shapes.geometric,intersections,arrows.meta,%
decorations.markings,3d}
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
tikzset{set mark/.style args={#1|#2}{
postaction={decorate,decoration={markings,
mark=at position #1 with {coordinate(#2);}}}}}
begin{document}
foreach X [evaluate=X as vq using {X*X},evaluate=X as Y using {X*180+135}]
in
{2,2.05,...,4,3.95,3.9,...,2.1}{
%{3.5}{
tdplotsetmaincoords{77}{0}
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);}}
path (tpp cs:0,0,0.1) coordinate (p2);
draw[fill,shift={(p2)}]
plot[variable=x,domain=180:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0)
-- plot[variable=x,domain=360:180] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},-0.2)
--cycle;
draw[fill=gray,shift={(p2)}]
plot[variable=x,domain=00:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0);
node[font=sffamily,anchor=north west] at ([yshift=-2mm]p2){2};
draw[name path=line] (p2) -- (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,red,fill=gray!25,name path=circle,
set mark/.list={0.19|1,0.21|2,0.23|3,0.25|4,0.69|5,0.71|6,0.73|7,0.75|8}] plot[variable=x,smooth,domain=0:360]
(tpp cs:{0.8*cos(x)},{0.8*sin(x)},1);
begin{scope}[canvas is xy plane at z=0]
%pgflowlevelsynccm % doesn't work :-(
draw[red,dashed,-{Latex[length=8pt,bend]}] plot[variable=x,samples at={1,...,4}]
(x);
draw[red,dashed,-{Latex[length=8pt,bend]}] plot[variable=x,samples at={5,...,8}]
(x);
end{scope}
draw (tpp cs:0,0,1) -- (tpp cs:{0.8*cos(Y)},{0.8*sin(Y)},1) coordinate (p1);
draw[fill,shift={(p1)}]
plot[variable=x,domain=180:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0)
-- plot[variable=x,domain=360:180] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0.1)
--cycle;
draw[fill=gray,shift={(p1)}]
plot[variable=x,domain=00:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0.1);
node[anchor=north,font=sffamily] at ([yshift=-1pt]p1){1};

draw[dashed,name intersections={of=circle and line}] (intersection-1)
-- (tpp cs:0,0,1);

end{tikzpicture}}
end{document}


enter image description here



And if you replace the loop by



foreach X [evaluate=X as vq using {X*X},evaluate=X as Y using {X*180+135}] 
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


























  • Incredible :-) simply fantastic your work.

    – Sebastiano
    Jan 17 at 9:06






  • 1





    @AlexG Yes, it does. Also the circle on top of the table gets transformed. The only things that do not get transformed here are the little cylinders, but this is simply because I could not interpret the screen shot in the question well enough to understand what these really are, so I added random symbols there. Note that transform shape won't transform them correctly here. Yet you can draw almost every conceivable object with draw plot ...., and these objects will get transformed correctly since the plot points get transformed.

    – marmot
    Jan 17 at 15:56






  • 1





    @Eduardo OK, I adjusted the code.

    – marmot
    Jan 17 at 23:09






  • 2





    @AlexG In the updated version the cylinders get transformed, too.

    – marmot
    Jan 17 at 23:10






  • 1





    Marmot is a magician!!

    – Julien-Elie Taieb
    Jan 17 at 23:36











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1 Answer
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1 Answer
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active

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active

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16














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. (UPDATE: Took into account the additional screen shot added by the OP.)



documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{arrows.meta,bending,shapes.geometric,intersections,arrows.meta,%
decorations.markings,3d}
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
tikzset{set mark/.style args={#1|#2}{
postaction={decorate,decoration={markings,
mark=at position #1 with {coordinate(#2);}}}}}
begin{document}
foreach X [evaluate=X as vq using {X*X},evaluate=X as Y using {X*180+135}]
in
{2,2.05,...,4,3.95,3.9,...,2.1}{
%{3.5}{
tdplotsetmaincoords{77}{0}
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);}}
path (tpp cs:0,0,0.1) coordinate (p2);
draw[fill,shift={(p2)}]
plot[variable=x,domain=180:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0)
-- plot[variable=x,domain=360:180] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},-0.2)
--cycle;
draw[fill=gray,shift={(p2)}]
plot[variable=x,domain=00:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0);
node[font=sffamily,anchor=north west] at ([yshift=-2mm]p2){2};
draw[name path=line] (p2) -- (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,red,fill=gray!25,name path=circle,
set mark/.list={0.19|1,0.21|2,0.23|3,0.25|4,0.69|5,0.71|6,0.73|7,0.75|8}] plot[variable=x,smooth,domain=0:360]
(tpp cs:{0.8*cos(x)},{0.8*sin(x)},1);
begin{scope}[canvas is xy plane at z=0]
%pgflowlevelsynccm % doesn't work :-(
draw[red,dashed,-{Latex[length=8pt,bend]}] plot[variable=x,samples at={1,...,4}]
(x);
draw[red,dashed,-{Latex[length=8pt,bend]}] plot[variable=x,samples at={5,...,8}]
(x);
end{scope}
draw (tpp cs:0,0,1) -- (tpp cs:{0.8*cos(Y)},{0.8*sin(Y)},1) coordinate (p1);
draw[fill,shift={(p1)}]
plot[variable=x,domain=180:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0)
-- plot[variable=x,domain=360:180] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0.1)
--cycle;
draw[fill=gray,shift={(p1)}]
plot[variable=x,domain=00:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0.1);
node[anchor=north,font=sffamily] at ([yshift=-1pt]p1){1};

draw[dashed,name intersections={of=circle and line}] (intersection-1)
-- (tpp cs:0,0,1);

end{tikzpicture}}
end{document}


enter image description here



And if you replace the loop by



foreach X [evaluate=X as vq using {X*X},evaluate=X as Y using {X*180+135}] 
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


























  • Incredible :-) simply fantastic your work.

    – Sebastiano
    Jan 17 at 9:06






  • 1





    @AlexG Yes, it does. Also the circle on top of the table gets transformed. The only things that do not get transformed here are the little cylinders, but this is simply because I could not interpret the screen shot in the question well enough to understand what these really are, so I added random symbols there. Note that transform shape won't transform them correctly here. Yet you can draw almost every conceivable object with draw plot ...., and these objects will get transformed correctly since the plot points get transformed.

    – marmot
    Jan 17 at 15:56






  • 1





    @Eduardo OK, I adjusted the code.

    – marmot
    Jan 17 at 23:09






  • 2





    @AlexG In the updated version the cylinders get transformed, too.

    – marmot
    Jan 17 at 23:10






  • 1





    Marmot is a magician!!

    – Julien-Elie Taieb
    Jan 17 at 23:36
















16














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. (UPDATE: Took into account the additional screen shot added by the OP.)



documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{arrows.meta,bending,shapes.geometric,intersections,arrows.meta,%
decorations.markings,3d}
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
tikzset{set mark/.style args={#1|#2}{
postaction={decorate,decoration={markings,
mark=at position #1 with {coordinate(#2);}}}}}
begin{document}
foreach X [evaluate=X as vq using {X*X},evaluate=X as Y using {X*180+135}]
in
{2,2.05,...,4,3.95,3.9,...,2.1}{
%{3.5}{
tdplotsetmaincoords{77}{0}
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);}}
path (tpp cs:0,0,0.1) coordinate (p2);
draw[fill,shift={(p2)}]
plot[variable=x,domain=180:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0)
-- plot[variable=x,domain=360:180] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},-0.2)
--cycle;
draw[fill=gray,shift={(p2)}]
plot[variable=x,domain=00:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0);
node[font=sffamily,anchor=north west] at ([yshift=-2mm]p2){2};
draw[name path=line] (p2) -- (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,red,fill=gray!25,name path=circle,
set mark/.list={0.19|1,0.21|2,0.23|3,0.25|4,0.69|5,0.71|6,0.73|7,0.75|8}] plot[variable=x,smooth,domain=0:360]
(tpp cs:{0.8*cos(x)},{0.8*sin(x)},1);
begin{scope}[canvas is xy plane at z=0]
%pgflowlevelsynccm % doesn't work :-(
draw[red,dashed,-{Latex[length=8pt,bend]}] plot[variable=x,samples at={1,...,4}]
(x);
draw[red,dashed,-{Latex[length=8pt,bend]}] plot[variable=x,samples at={5,...,8}]
(x);
end{scope}
draw (tpp cs:0,0,1) -- (tpp cs:{0.8*cos(Y)},{0.8*sin(Y)},1) coordinate (p1);
draw[fill,shift={(p1)}]
plot[variable=x,domain=180:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0)
-- plot[variable=x,domain=360:180] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0.1)
--cycle;
draw[fill=gray,shift={(p1)}]
plot[variable=x,domain=00:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0.1);
node[anchor=north,font=sffamily] at ([yshift=-1pt]p1){1};

draw[dashed,name intersections={of=circle and line}] (intersection-1)
-- (tpp cs:0,0,1);

end{tikzpicture}}
end{document}


enter image description here



And if you replace the loop by



foreach X [evaluate=X as vq using {X*X},evaluate=X as Y using {X*180+135}] 
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


























  • Incredible :-) simply fantastic your work.

    – Sebastiano
    Jan 17 at 9:06






  • 1





    @AlexG Yes, it does. Also the circle on top of the table gets transformed. The only things that do not get transformed here are the little cylinders, but this is simply because I could not interpret the screen shot in the question well enough to understand what these really are, so I added random symbols there. Note that transform shape won't transform them correctly here. Yet you can draw almost every conceivable object with draw plot ...., and these objects will get transformed correctly since the plot points get transformed.

    – marmot
    Jan 17 at 15:56






  • 1





    @Eduardo OK, I adjusted the code.

    – marmot
    Jan 17 at 23:09






  • 2





    @AlexG In the updated version the cylinders get transformed, too.

    – marmot
    Jan 17 at 23:10






  • 1





    Marmot is a magician!!

    – Julien-Elie Taieb
    Jan 17 at 23:36














16












16








16







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. (UPDATE: Took into account the additional screen shot added by the OP.)



documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{arrows.meta,bending,shapes.geometric,intersections,arrows.meta,%
decorations.markings,3d}
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
tikzset{set mark/.style args={#1|#2}{
postaction={decorate,decoration={markings,
mark=at position #1 with {coordinate(#2);}}}}}
begin{document}
foreach X [evaluate=X as vq using {X*X},evaluate=X as Y using {X*180+135}]
in
{2,2.05,...,4,3.95,3.9,...,2.1}{
%{3.5}{
tdplotsetmaincoords{77}{0}
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);}}
path (tpp cs:0,0,0.1) coordinate (p2);
draw[fill,shift={(p2)}]
plot[variable=x,domain=180:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0)
-- plot[variable=x,domain=360:180] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},-0.2)
--cycle;
draw[fill=gray,shift={(p2)}]
plot[variable=x,domain=00:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0);
node[font=sffamily,anchor=north west] at ([yshift=-2mm]p2){2};
draw[name path=line] (p2) -- (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,red,fill=gray!25,name path=circle,
set mark/.list={0.19|1,0.21|2,0.23|3,0.25|4,0.69|5,0.71|6,0.73|7,0.75|8}] plot[variable=x,smooth,domain=0:360]
(tpp cs:{0.8*cos(x)},{0.8*sin(x)},1);
begin{scope}[canvas is xy plane at z=0]
%pgflowlevelsynccm % doesn't work :-(
draw[red,dashed,-{Latex[length=8pt,bend]}] plot[variable=x,samples at={1,...,4}]
(x);
draw[red,dashed,-{Latex[length=8pt,bend]}] plot[variable=x,samples at={5,...,8}]
(x);
end{scope}
draw (tpp cs:0,0,1) -- (tpp cs:{0.8*cos(Y)},{0.8*sin(Y)},1) coordinate (p1);
draw[fill,shift={(p1)}]
plot[variable=x,domain=180:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0)
-- plot[variable=x,domain=360:180] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0.1)
--cycle;
draw[fill=gray,shift={(p1)}]
plot[variable=x,domain=00:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0.1);
node[anchor=north,font=sffamily] at ([yshift=-1pt]p1){1};

draw[dashed,name intersections={of=circle and line}] (intersection-1)
-- (tpp cs:0,0,1);

end{tikzpicture}}
end{document}


enter image description here



And if you replace the loop by



foreach X [evaluate=X as vq using {X*X},evaluate=X as Y using {X*180+135}] 
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. (UPDATE: Took into account the additional screen shot added by the OP.)



documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{arrows.meta,bending,shapes.geometric,intersections,arrows.meta,%
decorations.markings,3d}
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
tikzset{set mark/.style args={#1|#2}{
postaction={decorate,decoration={markings,
mark=at position #1 with {coordinate(#2);}}}}}
begin{document}
foreach X [evaluate=X as vq using {X*X},evaluate=X as Y using {X*180+135}]
in
{2,2.05,...,4,3.95,3.9,...,2.1}{
%{3.5}{
tdplotsetmaincoords{77}{0}
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);}}
path (tpp cs:0,0,0.1) coordinate (p2);
draw[fill,shift={(p2)}]
plot[variable=x,domain=180:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0)
-- plot[variable=x,domain=360:180] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},-0.2)
--cycle;
draw[fill=gray,shift={(p2)}]
plot[variable=x,domain=00:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0);
node[font=sffamily,anchor=north west] at ([yshift=-2mm]p2){2};
draw[name path=line] (p2) -- (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,red,fill=gray!25,name path=circle,
set mark/.list={0.19|1,0.21|2,0.23|3,0.25|4,0.69|5,0.71|6,0.73|7,0.75|8}] plot[variable=x,smooth,domain=0:360]
(tpp cs:{0.8*cos(x)},{0.8*sin(x)},1);
begin{scope}[canvas is xy plane at z=0]
%pgflowlevelsynccm % doesn't work :-(
draw[red,dashed,-{Latex[length=8pt,bend]}] plot[variable=x,samples at={1,...,4}]
(x);
draw[red,dashed,-{Latex[length=8pt,bend]}] plot[variable=x,samples at={5,...,8}]
(x);
end{scope}
draw (tpp cs:0,0,1) -- (tpp cs:{0.8*cos(Y)},{0.8*sin(Y)},1) coordinate (p1);
draw[fill,shift={(p1)}]
plot[variable=x,domain=180:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0)
-- plot[variable=x,domain=360:180] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0.1)
--cycle;
draw[fill=gray,shift={(p1)}]
plot[variable=x,domain=00:360] (tpp cs:{0.1*cos(x)},{0.1*sin(x)},0.1);
node[anchor=north,font=sffamily] at ([yshift=-1pt]p1){1};

draw[dashed,name intersections={of=circle and line}] (intersection-1)
-- (tpp cs:0,0,1);

end{tikzpicture}}
end{document}


enter image description here



And if you replace the loop by



foreach X [evaluate=X as vq using {X*X},evaluate=X as Y using {X*180+135}] 
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 Jan 17 at 23:22

























answered Jan 17 at 1:36









marmotmarmot

94.1k4109209




94.1k4109209













  • Incredible :-) simply fantastic your work.

    – Sebastiano
    Jan 17 at 9:06






  • 1





    @AlexG Yes, it does. Also the circle on top of the table gets transformed. The only things that do not get transformed here are the little cylinders, but this is simply because I could not interpret the screen shot in the question well enough to understand what these really are, so I added random symbols there. Note that transform shape won't transform them correctly here. Yet you can draw almost every conceivable object with draw plot ...., and these objects will get transformed correctly since the plot points get transformed.

    – marmot
    Jan 17 at 15:56






  • 1





    @Eduardo OK, I adjusted the code.

    – marmot
    Jan 17 at 23:09






  • 2





    @AlexG In the updated version the cylinders get transformed, too.

    – marmot
    Jan 17 at 23:10






  • 1





    Marmot is a magician!!

    – Julien-Elie Taieb
    Jan 17 at 23:36



















  • Incredible :-) simply fantastic your work.

    – Sebastiano
    Jan 17 at 9:06






  • 1





    @AlexG Yes, it does. Also the circle on top of the table gets transformed. The only things that do not get transformed here are the little cylinders, but this is simply because I could not interpret the screen shot in the question well enough to understand what these really are, so I added random symbols there. Note that transform shape won't transform them correctly here. Yet you can draw almost every conceivable object with draw plot ...., and these objects will get transformed correctly since the plot points get transformed.

    – marmot
    Jan 17 at 15:56






  • 1





    @Eduardo OK, I adjusted the code.

    – marmot
    Jan 17 at 23:09






  • 2





    @AlexG In the updated version the cylinders get transformed, too.

    – marmot
    Jan 17 at 23:10






  • 1





    Marmot is a magician!!

    – Julien-Elie Taieb
    Jan 17 at 23:36

















Incredible :-) simply fantastic your work.

– Sebastiano
Jan 17 at 9:06





Incredible :-) simply fantastic your work.

– Sebastiano
Jan 17 at 9:06




1




1





@AlexG Yes, it does. Also the circle on top of the table gets transformed. The only things that do not get transformed here are the little cylinders, but this is simply because I could not interpret the screen shot in the question well enough to understand what these really are, so I added random symbols there. Note that transform shape won't transform them correctly here. Yet you can draw almost every conceivable object with draw plot ...., and these objects will get transformed correctly since the plot points get transformed.

– marmot
Jan 17 at 15:56





@AlexG Yes, it does. Also the circle on top of the table gets transformed. The only things that do not get transformed here are the little cylinders, but this is simply because I could not interpret the screen shot in the question well enough to understand what these really are, so I added random symbols there. Note that transform shape won't transform them correctly here. Yet you can draw almost every conceivable object with draw plot ...., and these objects will get transformed correctly since the plot points get transformed.

– marmot
Jan 17 at 15:56




1




1





@Eduardo OK, I adjusted the code.

– marmot
Jan 17 at 23:09





@Eduardo OK, I adjusted the code.

– marmot
Jan 17 at 23:09




2




2





@AlexG In the updated version the cylinders get transformed, too.

– marmot
Jan 17 at 23:10





@AlexG In the updated version the cylinders get transformed, too.

– marmot
Jan 17 at 23:10




1




1





Marmot is a magician!!

– Julien-Elie Taieb
Jan 17 at 23:36





Marmot is a magician!!

– Julien-Elie Taieb
Jan 17 at 23:36


















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