mjhjmtu

I need to make quite a few "first-angle projection" in Tikz (see Wikipedia ) for an exercise sheet, so I was wondering if there is a routine to make them?

By this I mean that I could give a certain number of 3d coordinates for points, define the edges (and perhaps the surfaces too) and then get the 6 required planar projections (without having to change each time the code for the planar coordinates of the projected points, ideally without having to specify which edges/surfaces are above the other).

Of course, the solution for just one planar projection would be enough...

Here is an example of such a solid. Of course I could write the planar projections by hand, but that would be very tedious to do that for all the others again.

documentclassstandalone
usepackagetikz
usetikzlibrarycalc
begindocument
tikzset
MyPersp/.style=scale=1,x=(-0.35355cm,-0.35355cm),y=(1cm,0cm), z=(0cm,1cm)

begintikzpicture[line cap=round, rounded corners=.1mm,MyPersp]
 % vertices
coordinate (A) at (0,0,0);
coordinate (B) at (2,0,0);
coordinate (C) at (2,2,0);
coordinate (D) at (0,2,0);
coordinate (E1) at (0,0,1);
coordinate (E2) at (0,1,2);
coordinate (E3) at (1,0,2);
coordinate (F) at (2,0,2);
coordinate (G) at (2,2,2);
coordinate (H) at (0,2,2);
% edges and surfaces
fill[white,opacity=.5,draw=black,thick] (A) -- (D) -- (H) -- (E2) -- (E1) -- (A);
fill[white,opacity=.5,draw=black,thick] (A) -- (B) -- (C) -- (D) -- (A);
fill[white,opacity=.5,draw=black,thick] (E1) -- (E2) -- (E3) -- (E1);
fill[white,opacity=.5,draw=black,thick] (A) -- (B) -- (F) -- (E3) -- (E1) -- (A);
fill[white,opacity=.5,draw=black,thick] (C) -- (D) -- (H) -- (G) -- (C);
fill[white,opacity=.5,draw=black,thick] (B) -- (C) -- (G) -- (F) -- (B);
fill[white,opacity=.5,draw=black,thick] (F) -- (G) -- (H) -- (E2) -- (E3) -- (F);
% names
draw (A) nodeA;
draw (B) nodeB;
draw (C) nodeC;
draw (D) nodeD;
draw (F) nodeF;
draw (G) nodeG;
draw (H) nodeH;
endtikzpicture
enddocument

Using Tikz, there is no easy way to determine what to draw and what is hidden behind other faces. Fortunately, the pgfplots package is capable of exactly that:

documentclass[tikz,margin=2mm]standalone
usepackagetikz,pgfplots,pgfplotstable,filecontents

usepgfplotslibrarypatchplots

pgfplotssetcompat=1.16,
 projection/.style=
 hide axis,
 enlargelimits=false,
 scale only axis,
 width=4cm,
 height=4cm,
 axis equal,
 view=11530,
 clip=false,
 ,
 front view/.style=projection,view=900,title=Front view,
 back view/.style=projection,view=-900,title=Back view,
 right view/.style=projection,view=1800,title=Right view,
 left view/.style=projection,view=00,title=Left view,
 top view/.style=projection,view=9090,title=Top view,
 bottom view/.style=projection,view=90-90,title=Bottom view,
 patch plot style/.style=
 patch,
 patch type=polygon,
 vertex count=5,
 patch table with point meta=PatchesTable.dat,
 white,
 opacity=0.5,
 thick,
 faceted color=black,
 ,


beginfilecontents*PatchesTable.dat
%pt1 pt2 pt3 pt4 pt5 meta
 0 3 9 5 4 1 % (A) -- (D) -- (H) -- (E2) -- (E1) -- (A);
 0 1 2 3 3 1 % (A) -- (B) -- (C) -- (D) -- (A);
 4 5 6 6 6 1 % (E1) -- (E2) -- (E3) -- (E1);
 0 1 7 6 4 1 % (A) -- (B) -- (F) -- (E3) -- (E1) -- (A);
 2 3 9 8 8 1 % (C) -- (D) -- (H) -- (G) -- (C);
 1 2 8 7 1 1 % (B) -- (C) -- (G) -- (F) -- (B);
 7 8 9 5 6 1 % (F) -- (G) -- (H) -- (E2) -- (E3) -- (F);
endfilecontents*
beginfilecontents*PointsTable.dat
 x y z
 0 0 0 % 0 (A) 
 2 0 0 % 1 (B) 
 2 2 0 % 2 (C) 
 0 2 0 % 3 (D) 
 0 0 1 % 4 (E1)
 0 1 2 % 5 (E2)
 1 0 2 % 6 (E3)
 2 0 2 % 7 (F) 
 2 2 2 % 8 (G) 
 0 2 2 % 9 (H) 
endfilecontents*

begindocument

pgfplotstablereadPointsTable.datPointsTable

begintikzpicture
 beginaxis[projection,at=(5cm,5cm)]
 addplot3 [patch plot style] table PointsTable;
 endaxis

 foreach view/x/y in 
 left view/-5/0,
 front view/0/0,
 right view/5/0,
 back view/10/0,
 top view/0/5,
 bottom view/0/-5
 
 beginaxis[view,at=(x cm,y cm)]
 addplot3 [patch plot style] table PointsTable;
 endaxis
 
endtikzpicture
enddocument

Edit

Because we use Tikz and pgfplots to make things look stunning, I had to try marmot's comment. This indeed looks very nice, and it made me discover that the right view and back view are not entirely correct. This seems to be due to the painter's algorithm that pgfplots uses to determine what is one top. An (ugly) fix to this could be to change the right and back view to:

back view/.style=projection,view=-900.02,title=Back view,
right view/.style=projection,view=1800.02,title=Right view,

Thus with a very small elevation angle. This very slightly stretches the line widths of the horizontal lines, but does help the drawing order. The results is:

This is not an answer, but work in progress and to pay tribute to Max' stellar answer: a partly successful attempt to arrange the projections in a 3D-like manner around the shape. (UPDATE: Fixed the alignment of some texts, big thanks to ARG!)

documentclass[tikz,margin=2mm]standalone
usepackagetikz,tikz-3dplot,pgfplots,pgfplotstable,filecontents
usetikzlibrary3d
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
makeatletter
tikzoptioncanvas is xy plane at z%
 deftikz@plane@originpgfpointxyz00#1%
 deftikz@plane@xpgfpointxyz10#1%
 deftikz@plane@ypgfpointxyz01#1%
 tikz@canvas@is@plane
makeatother

newsaveboxmybox
newsaveboxmainbox
usepgfplotslibrarypatchplots

pgfplotssetcompat=1.16,
 projection/.style=
 hide axis,
 enlargelimits=false,
 scale only axis,
 width=4cm,
 height=4cm,
 axis equal,
 view=11530,
 clip=false,
 ,
 front view/.style=projection,view=900,title=Front view,
 %back view/.style=projection,view=-900,title=Back view,
 %right view/.style=projection,view=1800,title=Right view,
 left view/.style=projection,view=00,title=Left view,
 top view/.style=projection,view=90-90,title=Top view,
 title style=at=(0.5,-0.25),yscale=-1,
 bottom view/.style=projection,view=90-90,title=Bottom view,
 title style=at=(0.5,-0.25),scale=-1,
 back view/.style=projection,view=900,title=Back view,
 title style=xscale=-1, % adjusted
 right view/.style=projection,view=00.02,title=Right view,
 title style=xscale=-1, 
 patch plot style/.style=
 patch,
 patch type=polygon,
 vertex count=5,
 patch table with point meta=PatchesTable.dat,
 %white,
 opacity=0.2,
 thick,
 faceted color=black,
 ,


beginfilecontents*PatchesTable.dat
%pt1 pt2 pt3 pt4 pt5 meta
 0 3 9 5 4 1 % (A) -- (D) -- (H) -- (E2) -- (E1) -- (A);
 0 1 2 3 3 1 % (A) -- (B) -- (C) -- (D) -- (A);
 4 5 6 6 6 2 % (E1) -- (E2) -- (E3) -- (E1);
 0 1 7 6 4 1 % (A) -- (B) -- (F) -- (E3) -- (E1) -- (A);
 2 3 9 8 8 1 % (C) -- (D) -- (H) -- (G) -- (C);
 1 2 8 7 1 1 % (B) -- (C) -- (G) -- (F) -- (B);
 7 8 9 5 6 1 % (F) -- (G) -- (H) -- (E2) -- (E3) -- (F);
endfilecontents*
beginfilecontents*PointsTable.dat
 x y z
 0 0 0 % 0 (A) 
 2 0 0 % 1 (B) 
 2 2 0 % 2 (C) 
 0 2 0 % 3 (D) 
 0 0 1 % 4 (E1)
 0 1 2 % 5 (E2)
 1 0 2 % 6 (E3)
 2 0 2 % 7 (F) 
 2 2 2 % 8 (G) 
 0 2 2 % 9 (H) 
endfilecontents*

begindocument

pgfplotstablereadPointsTable.datPointsTable

begintikzpicture
 beginlrboxmainbox
 beginaxis[projection]
 addplot3 [patch plot style] table PointsTable;
 endaxis
 endlrbox
tdplotsetmaincoords115-30
path[use as bounding box] (-5,-5) rectangle (5,5);
beginscope[tdplot_main_coords]

 foreach view/x/y/Canvas in 
 left view/x/-2.5/yz,
 back view/y/-2.5/xz,
 bottom view/z/-2.5/xy%
 
 beginlrboxmybox
 beginaxis[view]
 addplot3 [patch plot style] table PointsTable;
 endaxis
 endlrbox
 beginscope[canvas is Canvasspace plane at x=y,transform shape]
 node[scale=0.75] at (0,0) useboxmybox;
 endscope
 
 %
 beginscope[canvas is xz plane at y=3]
 node at (0,0) useboxmainbox;
 endscope
 %
 foreach view/x/y/Canvas in 
 front view/y/5/xz,
 right view/x/5/yz,
 top view/z/5/xy%
 
 beginlrboxmybox
 beginaxis[view]
 addplot3 [patch plot style] table PointsTable;
 endaxis
 endlrbox
 beginscope[canvas is Canvasspace plane at x=y,
 transform shape]
 node[scale=0.75] at
 (0,0) useboxmybox;
 endscope
 
endscope 
endtikzpicture
enddocument