Bdtyk

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!

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}

And if you replace the loop by

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

say, you'll get.

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.