Cfrgtkky

I am adapting code from a response offered by Jan Hlavacek years ago. How do the following commands put perspective into the drawing?

coordinate (front_right) at ($(top_front)!5!(top_right)$);

coordinate (front_left) at ($(top_front)!5!(top_left)$);

coordinate (front_bottom) at ($(top_front)!15!(bottom_front)$);

How would I label three edges so that the label is at the midpoint, 0.1cm from the edge, and sloped? If one of the diagonals of the box were to be drawn, how would it be labeled similarly?

documentclass{amsart}



usepackage{tikz}

usetikzlibrary{calc,intersections}







begin{document}





begin{tikzpicture}



%clip (-3,-3) rectangle (3,3);

coordinate (top_front) at (0,0);

coordinate (bottom_front) at (0,-3);

coordinate (top_right) at (15:2.5cm);

coordinate (top_left) at (165:2.5cm);



%You can change the perspective by playing with the 5, 5, 15:

coordinate (front_right) at ($(top_front)!5!(top_right)$);

coordinate (front_left) at ($(top_front)!5!(top_left)$);

coordinate (front_bottom) at ($(top_front)!15!(bottom_front)$);



path[name path=bottom_right_path] (bottom_front) -- (front_right);   

path[name path=right_back_path] (top_right) -- (front_bottom);

path[name path=back_left_path] (bottom_front) -- (front_left);

path[name path=left_back_path] (top_left) -- (front_bottom);

path[name path=top_right_path] (top_left) -- (front_right);

path[name path=top_left_path] (top_right) -- (front_left);







coordinate[name intersections={of=bottom_right_path and right_back_path, by=back_right}];

coordinate[name intersections={of=back_left_path and left_back_path, by=back_left}];

coordinate[name intersections={of=top_right_path and top_left_path, by=top_back}];



%shade[right color=gray!10, left color=black!50, shading angle=105] (top_front) -- (bottom_front) -- (back_left) -- (top_left) -- cycle;

%shade[left color=gray!10, right color=black!50, shading angle=75] (top_front) -- (bottom_front) -- (back_right) -- (top_right) -- cycle;



begin{scope}

clip (top_front) -- (top_right) -- (top_back) -- (top_left) -- cycle;

shade[inner color = gray!5, outer color=black!50, shading=radial] (top_front) ellipse (3cm and 1.5cm);

end{scope}



draw (top_front) -- (bottom_front);

draw (top_front) -- (top_right);

draw (top_front) -- (top_left);

draw (top_right) -- (back_right);

draw (bottom_front) -- (back_right);

draw (top_left) -- (back_left);

draw (bottom_front) -- (back_left);

draw (top_back) -- (top_right);

draw (top_back) -- (top_left);







end{tikzpicture}



end{document}

To answer this problem in the mind of the person who wrote it, I started by visualizing the different points used for construction by drawing the paths that have not been drawn and naming these points, we get this figure with a reduction of 0.4 scale=.4:

%clip (-3,-3) rectangle (3,3);

coordinate[label={[blue]left:top-front}] (top_front) at (0,0);

coordinate[label={[blue]left:bottom-front}] (bottom_front) at (0,-3);

coordinate[label={[blue]right:top-right}] (top_right) at (15:2.5cm);

coordinate[label={[blue]left:top-left}] (top_left) at (165:2.5cm);



%You can change the perspective by playing with the 5, 5, 15:

coordinate[label={right:front-right}]  (front_right) at ($(top_front)!5!(top_right)$);

coordinate [label={left:front-left}] (front_left) at ($(top_front)!5!(top_left)$);

coordinate [label={below:front-bottom}](front_bottom) at ($(top_front)!15!(bottom_front)$);

With the normal size scale=1 and with clip (-6,-4) rectangle (6,4);, we get this:

begin{tikzpicture}[scale=1]



clip (-6,-4) rectangle (6,4);

coordinate[label={[blue]left:top-front}] (top_front) at (0,0);

coordinate[label={[blue]left:bottom-front}] (bottom_front) at (0,-3);

coordinate[label={[blue]right:top-right}] (top_right) at (15:2.5cm);

coordinate[label={[blue]left:top-left}] (top_left) at (165:2.5cm);

To place labels on the edges, simply place a node when building the edge cases and you get this:

draw (top_front) -- (bottom_front)node[midway,above,sloped]{label 1};

draw (top_front) -- (top_right)node[midway,above,sloped]{label 2};

draw (top_front) -- (top_left)node[midway,above,sloped]{label 3};

draw (top_right) -- (back_right)node[midway,above,sloped]{label 4};

draw (bottom_front) -- (back_right)node[midway,above,sloped]{label 5};

draw (top_left) -- (back_left)node[midway,above,sloped]{label 6};

draw (bottom_front) -- (back_left)node[midway,above,sloped]{label 7};

draw (top_back) -- (top_right)node[midway,above,sloped]{label 8};

draw (top_back) -- (top_left)node[midway,above,sloped]{label 9};

For a diagonal, it is enough to create a path between two of its vertices. For example, for the diagonal (top_left)--(bottom_front), we may not draw this diagonal and mark the text as follows:

path (top_left)--(bottom_front)node[midway,above,sloped]{diagonal 1};

By drawing the diagonal in dotted lines:

we write this:

path[draw,dashed] (top_left)--(bottom_front)node[midway,above,sloped]{diagonal 1};

or just as well this:

draw[dashed] (top_left)--(bottom_front)node[midway,above,sloped]{diagonal 1};

complete code :

documentclass{amsart}



usepackage{tikz}

usetikzlibrary{calc,intersections}



begin{document}

begin{tikzpicture}[scale=1]



clip (-6,-4) rectangle (6,4);

coordinate[label={[blue]left:top-front}] (top_front) at (0,0);

coordinate[label={[blue]left:bottom-front}] (bottom_front) at (0,-3);

coordinate[label={[blue]right:top-right}] (top_right) at (15:2.5cm);

coordinate[label={[blue]left:top-left}] (top_left) at (165:2.5cm);



%You can change the perspective by playing with the 5, 5, 15:

coordinate (front_right) at ($(top_front)!5!(top_right)$);

coordinate (front_left) at ($(top_front)!5!(top_left)$);

coordinate (front_bottom) at ($(top_front)!15!(bottom_front)$);



path[name path=bottom_right_path] (bottom_front) -- (front_right);   

path[name path=right_back_path] (top_right) -- (front_bottom);

path[name path=back_left_path] (bottom_front) -- (front_left);

path[name path=left_back_path] (top_left) -- (front_bottom);

path[name path=top_right_path] (top_left) -- (front_right);

path[name path=top_left_path] (top_right) -- (front_left);



coordinate[name intersections={of=bottom_right_path and right_back_path, by=back_right}];

coordinate[name intersections={of=back_left_path and left_back_path, by=back_left}];

coordinate[name intersections={of=top_right_path and top_left_path, by=top_back}];



%shade[right color=gray!10, left color=black!50, shading angle=105] (top_front) -- (bottom_front) -- (back_left) -- (top_left) -- cycle;

%shade[left color=gray!10, right color=black!50, shading angle=75] (top_front) -- (bottom_front) -- (back_right) -- (top_right) -- cycle;



begin{scope}

clip (top_front) -- (top_right) -- (top_back) -- (top_left) -- cycle;

shade[inner color = gray!5, outer color=black!50, shading=radial] (top_front) ellipse (3cm and 1.5cm);

end{scope}



draw (top_front) -- (bottom_front)node[midway,above,sloped]{label 1};

draw (top_front) -- (top_right)node[midway,above,sloped]{label 2};

draw (top_front) -- (top_left)node[midway,above,sloped]{label 3};

draw (top_right) -- (back_right)node[midway,above,sloped]{label 4};

draw (bottom_front) -- (back_right)node[midway,above,sloped]{label 5};

draw (top_left) -- (back_left)node[midway,above,sloped]{label 6};

draw (bottom_front) -- (back_left)node[midway,above,sloped]{label 7};

draw (top_back) -- (top_right)node[midway,above,sloped]{label 8};

draw (top_back) -- (top_left)node[midway,above,sloped]{label 9};



path (top_left)--(bottom_front)node[midway,above,sloped]{diagonal 1};



end{tikzpicture}



end{document}

Update: Creation of the bottom_back vertex of the cube.

% Creation of the bottom_back vertex of the cube.

% definition of 2 new paths

path[name path=bottom_left_path] (back_left) -- (front_right);

path[name path=back_right_path] (back_right) -- (front_left);

% vertex bottom_back definition

coordinate[name intersections={of=bottom_left_path and back_right_path, by=bottom_back}];



%node[red] at (back_right){back-right};

%node[red] at (back_left){back-left};

%node[red] at (top_back){top-back};

%node[red] at (bottom_back){bottom-back};



% hidden sides

draw[dashed] (back_left) -- (bottom_back);

draw [dashed](back_right) -- (bottom_back);

draw[dashed] (top_back) -- (bottom_back);



draw[dashed,blue] (back_right) -- (top_left)node[midway, sloped, above]{diagonal};

I drew the hidden sides were drawn in dotted lines.

You will notice that the vertex (top_back), (top_front), (bottom_back) and (bottom_back) are aligned, the diagonal (bottom_back)--(top_front) will not be visible.

To do this, you must change the perspective. Which I'll leave it to you to do.

So I drew the visible diagonal (back_right) -- (top_left)

Complete code updated:

documentclass{amsart}



usepackage{tikz}

usetikzlibrary{calc,intersections}



begin{document}

begin{tikzpicture}[scale=1]



clip (-6,-4) rectangle (6,4);

coordinate[label={[blue]left:top-front}] 

(top_front) at (0,0);

coordinate[label={[blue]left:bottom-front}] 

(bottom_front) at (0,-3);

coordinate[label={[blue]right:top-right}] 

(top_right) at (15:2.5cm);

coordinate[label={[blue]left:top-left}]

 (top_left) at (165:2.5cm);



%You can change the perspective by playing with the 5, 5, 15:

coordinate%[label={right:front-right}]  

(front_right) at ($(top_front)!5!(top_right)$);

coordinate% [label={left:front-left}] 

(front_left) at ($(top_front)!5!(top_left)$);

coordinate %[label={below:front-bottom}]

(front_bottom) at ($(top_front)!15!(bottom_front)$);



path[name path=bottom_right_path] (bottom_front) -- (front_right);   

path[name path=right_back_path] (top_right) -- (front_bottom);

path[name path=back_left_path] (bottom_front) -- (front_left);

path[name path=left_back_path] (top_left) -- (front_bottom);

path[name path=top_right_path] (top_left) -- (front_right);

path[name path=top_left_path] (top_right) -- (front_left);



coordinate[name intersections={of=bottom_right_path and right_back_path, by=back_right}];

coordinate[name intersections={of=back_left_path and left_back_path, by=back_left}];

coordinate[name intersections={of=top_right_path and top_left_path, by=top_back}];



%shade[right color=gray!10, left color=black!50, shading angle=105] (top_front) -- (bottom_front) -- (back_left) -- (top_left) -- cycle;

%shade[left color=gray!10, right color=black!50, shading angle=75] (top_front) -- (bottom_front) -- (back_right) -- (top_right) -- cycle;



begin{scope}

clip (top_front) -- (top_right) -- (top_back) -- (top_left) -- cycle;

%shade[inner color = gray!5, outer color=black!50, shading=radial] (top_front) ellipse (3cm and 1.5cm);

end{scope}



draw (top_front) -- (bottom_front);

draw (top_front) -- (top_right);

draw (top_front) -- (top_left);

draw (top_right) -- (back_right);

draw (bottom_front) -- (back_right);

draw (top_left) -- (back_left);

draw (bottom_front) -- (back_left);

draw (top_back) -- (top_right);

draw (top_back) -- (top_left);





path[draw,dashed,red] (top_left)--(bottom_front)node[midway,above,sloped]{diagonal 1};



% Creation of the bottom_back vertex of the cube.

% definition of 2 new paths

path[name path=bottom_left_path] (back_left) -- (front_right);

path[name path=back_right_path] (back_right) -- (front_left);

% vertex bottom_back definition

coordinate[name intersections={of=bottom_left_path and back_right_path, by=bottom_back}];



% vertex names

node[red] at (back_right){back-right};

node[red] at (back_left){back-left};

node[red] at (top_back){top-back};

node[red] at (bottom_back){bottom-back};



% hidden sides

draw[dashed] (back_left) -- (bottom_back);

draw [dashed](back_right) -- (bottom_back);

draw[dashed] (top_back) -- (bottom_back);



draw[dashed,blue] (back_right) -- (top_left)node[midway, sloped, above]{diagonal 2};

end{tikzpicture}



end{document}

It would be great if you could try to reword your question a bit. In the meantime, I'd like to draw your attention to this great answer which allows you to draw 3d objects with perspective. All I did was to use the preamble of this answer to draw a cube in perspective, and to add a few elements. No intersections etc. are needed here.

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

usepgfmodule{nonlineartransformations}

% Max magic https://tex.stackexchange.com/a/447120/121799

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}{-22.5}

  begin{tikzpicture}[scale=6,font=sffamily,

  view={tdplotmaintheta}{tdplotmainphi},

            perspective={

                p = {(4,0,1.5)},

                q = {(0,4,1.5)},

            }

  ]

  begin{scope} % top face

   draw[clip]   (tpp cs:0,0,1) coordinate (top_front)

  -- (tpp cs:1,0,1) coordinate (top_right)

   -- (tpp cs:1,1,1) coordinate (top_back)

   -- (tpp cs:0,1,1) coordinate (top_left) --

    cycle;

    shade[inner color = gray!5, outer color=black!50, shading=radial] (top_front) ellipse (3cm and 1.5cm);

  end{scope}

  % right face  

  draw   (top_front) -- (top_right) -- (tpp cs:1,0,0) coordinate (bottom_right)

  -- (tpp cs:0,0,0)  coordinate (bottom_front) --   cycle;

  % top face  

  draw   (top_front) -- (top_left) -- (tpp cs:0,1,0) coordinate (bottom_left)

  -- (bottom_front) --  cycle;

  % your midway coordinates with Max perspective coordinate system

  coordinate (front_right) at (tpp cs:0.5,0,1);

  coordinate (front_left) at (tpp cs:0,0.5,1);

  coordinate (front_bottom) at (tpp cs:0,0,0.5);

  path (0,0,0.5) -- (1,0,0.5) node[pos=0.1,sloped] {a label};

  draw (top_left) -- (bottom_front) node[midway,sloped,above] {a sloped label};

  end{tikzpicture}

end{document}

In principle, this great answer also provides tools to write text in perspective. Is this what you are asking here?