mjhjmtu

I used the result in this post to achieve a rotation of a cone about an 3D axis. I am unsure on how to implement the following to this image:

I would like the imaginary lines that run along the 'volume of the cone' to be dashed to promote a better sense of the 3D nature of the image. I also need to draw an arc between the central lines of both cones to label the rotation angle $vartheta$. Also is there any advice to make it look more '3D-like'?

MWE

documentclass[tikz]standalone
usepackagepgfplots 
usepackagefilecontents 
usetikzlibraryarrows,shapes,backgrounds,fit,decorations.pathreplacing,chains,snakes,positioning,angles,quotes 


newcommandsavedx0
newcommandsavedy0
newcommandsavedz0

tikzset
pics/tester/.style n args=3
code = % 

defx1
defy3.4
defRx+0.009
defycy+0.08
defe0.6


shade[right color=white,left color=blue,opacity=#1]
(-x,y) -- (-x,yc) arc (180:360:R and e) -- (x,y) -- (0,0) -- cycle;
draw[fill=#2,#3]
(0,yc) circle (R and e);
draw[#3]
(-x,y) -- (0,0) -- (x,y);
draw[#3]
(0,yc) circle (R and e);

draw[line width=1pt] (0,0,0) -- (0,4,0);





newcommandrotateRPY[4][0/0/0]% point to be saved to savedxyz, roll, pitch, yaw
 pgfmathsetmacrorollangle#2
pgfmathsetmacropitchangle#3
pgfmathsetmacroyawangle#4

% to what vector is the x unit vector transformed, and which 2D vector is this?
pgfmathsetmacronewxxcos(yawangle)*cos(pitchangle)% a
pgfmathsetmacronewxysin(yawangle)*cos(pitchangle)% d
pgfmathsetmacronewxz-sin(pitchangle)% g
path (newxx,newxy,newxz);
pgfgetlastxynxxnxy;

% to what vector is the y unit vector transformed, and which 2D vector is this?
pgfmathsetmacronewyxcos(yawangle)*sin(pitchangle)*sin(rollangle)-sin(yawangle)*cos(rollangle)% b
pgfmathsetmacronewyysin(yawangle)*sin(pitchangle)*sin(rollangle)+ cos(yawangle)*cos(rollangle)% e
pgfmathsetmacronewyzcos(pitchangle)*sin(rollangle)% h
path (newyx,newyy,newyz);
pgfgetlastxynyxnyy;

% to what vector is the z unit vector transformed, and which 2D vector is this?
pgfmathsetmacronewzxcos(yawangle)*sin(pitchangle)*cos(rollangle)+ sin(yawangle)*sin(rollangle)
pgfmathsetmacronewzysin(yawangle)*sin(pitchangle)*cos(rollangle)-cos(yawangle)*sin(rollangle)
pgfmathsetmacronewzzcos(pitchangle)*cos(rollangle)
path (newzx,newzy,newzz);
pgfgetlastxynzxnzy;

% transform the point given by #1
foreach x/y/z in #1
 pgfmathsetmacrotransformedxx*newxx+y*newyx+z*newzx
 pgfmathsetmacrotransformedyx*newxy+y*newyy+z*newzy
 pgfmathsetmacrotransformedzx*newxz+y*newyz+z*newzz
 xdefsavedxtransformedx
 xdefsavedytransformedy
 xdefsavedztransformedz 



tikzsetRPY/.style=x=(nxx,nxy),y=(nyx,nyy),z=(nzx,nzy)

pgfplotssetcompat=newest

begindocument

begintikzpicture
pic tester=0.08black!6!whitedensely dashed;
rotateRPY0091
beginscope[RPY]
pic tester=0.2blue!14!white;
endscope
endtikzpicture


enddocument

I would like then like to overlay both of the cones with a similar one that is squashed in one direction, but stretched by an equivalent factor in the other direction. The above MWE has a few flaws in achieving this which shows for one of the cones:

Namely, bases of the cones are not in the same plane. The red cone is stretched in one direction, but is not squeezed in the other direction.

I would like to argue that such things are drawn much more conveniently with the tikz-3dplot package and the 3d library.

documentclass[tikz,border=3.14mm]standalone
usepackagetikz-3dplot 
usetikzlibrary3d,shadings
makeatletter
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
 tikzoptioncanvas is xy plane at z%
 deftikz@plane@originpgfpointxyz00#1%
 deftikz@plane@xpgfpointxyz10#1%
 deftikz@plane@ypgfpointxyz01#1%
 tikz@canvas@is@plane
makeatother

begindocument

tdplotsetmaincoords110-165 % - because of difference between active and passive transformations...
begintikzpicture
 %draw (-5,-2.5) rectangle (1.5,5);
 beginscope[tdplot_main_coords,thick]
 % just in case you want to get an intuition for the coordinates/projections
 % draw[-latex] (0,0,0) -- (1,0,0) coordinate (X) node[below]$x$;
 % draw[-latex] (0,0,0) -- (0,1,0) coordinate (Y) node[right]$y$;
 % draw[-latex] (0,0,0) -- (0,0,1) coordinate (Z) node[left]$z$;
 % origin
 coordinate (O) at (0,0,0);
 % top
 beginscope[canvas is xy plane at z=4,dashed]
 draw[thick,solid] (O) -- (0,0);
 shadedraw[fill opacity=0.3,left color=blue,right color=white] (tdplotmainphi:1) 
 arc(tdplotmainphi:tdplotmainphi+180:1) -- (O) -- cycle;
 draw[fill opacity=0.3,fill=gray!80] circle (1);
 endscope
 % left
 beginscope[canvas is yz plane at x=4]
 draw[thick] (O) -- (0,0);
 pgfmathsetmacroMyThetaMaxatan(tan(tdplotmaintheta)*sin(90+tdplotmainphi))
 shadedraw[line join=bevel,fill opacity=0.3,upper right=white,lower left=blue] 
 (MyThetaMax:1) 
 arc(MyThetaMax:MyThetaMax+180:1) -- (O) -- cycle;
 draw[fill opacity=0.3,fill=gray] circle (1);
 endscope
 % arc
 beginscope[canvas is xz plane at y=0,xscale=-1]
 draw[-latex] (0,1) arc(90:180:1) node[midway,above left]$vartheta$;
 endscope
 endscope
endtikzpicture
enddocument

The advantage is that you can change the view angles at will.

documentclass[tikz,border=3.14mm]standalone
usepackagetikz-3dplot 
usetikzlibrary3d,shadings
makeatletter
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
 tikzoptioncanvas is xy plane at z%
 deftikz@plane@originpgfpointxyz00#1%
 deftikz@plane@xpgfpointxyz10#1%
 deftikz@plane@ypgfpointxyz01#1%
 tikz@canvas@is@plane
makeatother

begindocument
foreach X in 5,15,...,355
tdplotsetmaincoords120+20*sin(X)X % - because of difference between active and passive transformations...
begintikzpicture
 path[use as bounding box] (-5,-2.5) rectangle (5,5);
 beginscope[tdplot_main_coords,thick]
 % just in case you want to get an intuition for the coordinates/projections
 % draw[-latex] (0,0,0) -- (1,0,0) coordinate (X) node[below]$x$;
 % draw[-latex] (0,0,0) -- (0,1,0) coordinate (Y) node[right]$y$;
 % draw[-latex] (0,0,0) -- (0,0,1) coordinate (Z) node[left]$z$;
 % origin
 coordinate (O) at (0,0,0);
 % left
 beginscope[canvas is yz plane at x=4]
 pgfmathtruncatemacrottestsign(cos(tdplotmainphi+90))
 ifnumttest=1
 pgfmathsetmacroMyThetaMaxatan(tan(tdplotmaintheta)*sin(90+tdplotmainphi))
 shadedraw[line join=bevel,fill opacity=0.3,upper right=white,lower left=blue] 
 (MyThetaMax:1) 
 arc(MyThetaMax:MyThetaMax+180:1) -- (O) -- cycle;
 draw[fill=gray!30] circle (1);
 draw[thick] (O) -- (0,0);
 else
 draw[fill=gray!30] circle (1);
 draw[thick] (O) -- (0,0);
 pgfmathsetmacroMyThetaMaxatan(tan(tdplotmaintheta)*sin(90+tdplotmainphi))
 shadedraw[line join=bevel,fill opacity=0.3,upper right=white,lower left=blue] 
 (MyThetaMax:1) 
 arc(MyThetaMax:MyThetaMax+180:1) -- (O) -- cycle;
 fi 
 endscope
 % top
 beginscope[canvas is xy plane at z=4,dashed]
 draw[thick,solid] (O) -- (0,0);1
 shadedraw[fill opacity=0.3,left color=blue,right color=white] (tdplotmainphi:1) 
 arc(tdplotmainphi:tdplotmainphi+180:1) -- (O) -- cycle;
 draw[fill opacity=0.3,fill=gray!80] circle (1);
 endscope
 % arc
% beginscope[canvas is xz plane at y=0,xscale=-1]
% draw[-latex] (0,1) arc(90:180:1) node[midway,above left]$vartheta$;
% endscope
 endscope
endtikzpicture
enddocument

As for the "squashed" shape: it took me some time to derive the (hopefully) correct formula for the visibility angle MyThetaMax. Other than that it is almost trivial: draw ellipses in the respective planes and then repeat the above.

documentclass[tikz,border=3.14mm]standalone
usepackagetikz-3dplot 
usetikzlibrary3d,shadings

makeatletter
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
 tikzoptioncanvas is xy plane at z%
 deftikz@plane@originpgfpointxyz00#1%
 deftikz@plane@xpgfpointxyz10#1%
 deftikz@plane@ypgfpointxyz01#1%
 tikz@canvas@is@plane
makeatother

begindocument

tdplotsetmaincoords110-165 % - because of difference between active and passive transformations...
begintikzpicture
 %draw (-5,-2.5) rectangle (1.5,5);
 beginscope[tdplot_main_coords,thick]
 % just in case you want to get an intuition for the coordinates/projections
 % draw[-latex] (0,0,0) -- (1,0,0) coordinate (X) node[below]$x$;
 % draw[-latex] (0,0,0) -- (0,1,0) coordinate (Y) node[right]$y$;
 % draw[-latex] (0,0,0) -- (0,0,1) coordinate (Z) node[left]$z$;
 % origin
 coordinate (O) at (0,0,0);
 % top
 beginscope[canvas is xy plane at z=4,dashed]
 draw[thick,solid] (O) -- (0,0);
 shadedraw[fill opacity=0.3,left color=blue,right color=white] (tdplotmainphi:1) 
 arc(tdplotmainphi:tdplotmainphi+180:1) -- (O) -- cycle;
 draw[fill opacity=0.3,fill=gray!80] circle (1);
 % squashed shape
 shadedraw[fill opacity=0.1,left color=red,right color=white] 
 (tdplotmainphi:2 and 1) 
 arc(tdplotmainphi:tdplotmainphi+180:2 and 1) -- (O) -- cycle;
 draw[fill opacity=0.1,fill=gray!80] circle (2 and 1);
 endscope
 % left
 beginscope[canvas is yz plane at x=4]
 draw[thick] (O) -- (0,0);
 pgfmathsetmacroMyThetaMaxatan(tan(tdplotmaintheta)*sin(90+tdplotmainphi))
 shadedraw[line join=bevel,fill opacity=0.3,upper right=white,lower left=blue] 
 (MyThetaMax:1) 
 arc(MyThetaMax:MyThetaMax+180:1) -- (O) -- cycle;
 draw[fill opacity=0.3,fill=gray] circle (1);
 % squash again
 pgfmathsetmacroMyThetaMaxatan(tan(tdplotmaintheta)*sin(90+tdplotmainphi)*2)
 shadedraw[line join=bevel,fill opacity=0.1,upper right=white,
 lower left=red] 
 (MyThetaMax:1 and 2) 
 arc(MyThetaMax:MyThetaMax+180:1 and 2) -- (O) -- cycle;
 draw[fill opacity=0.1,fill=gray] circle (1 and 2);
 endscope
 % arc
 beginscope[canvas is xz plane at y=0,xscale=-1]
 draw[-latex] (0,1) arc(90:180:1) node[midway,above left]$vartheta$;
 endscope
 endscope
endtikzpicture
enddocument

Here's another attempt. I thought the above one would match your description.

documentclass[tikz,border=3.14mm]standalone
usepackagetikz-3dplot 
usetikzlibrary3d,shadings

makeatletter
% small fix for canvas is xy plane at z % https://tex.stackexchange.com/a/48776/121799
 tikzoptioncanvas is xy plane at z%
 deftikz@plane@originpgfpointxyz00#1%
 deftikz@plane@xpgfpointxyz10#1%
 deftikz@plane@ypgfpointxyz01#1%
 tikz@canvas@is@plane
makeatother

begindocument

tdplotsetmaincoords110-165 % - because of difference between active and passive transformations...
begintikzpicture
 %draw (-5,-2.5) rectangle (1.5,5);
 beginscope[tdplot_main_coords,thick]
 % just in case you want to get an intuition for the coordinates/projections
 % draw[-latex] (0,0,0) -- (1,0,0) coordinate (X) node[below]$x$;
 % draw[-latex] (0,0,0) -- (0,1,0) coordinate (Y) node[right]$y$;
 % draw[-latex] (0,0,0) -- (0,0,1) coordinate (Z) node[left]$z$;
 % origin
 coordinate (O) at (0,0,0);
 % top
 beginscope[canvas is xy plane at z=4,dashed]
 draw[thick,solid] (O) -- (0,0);
 % squashed shape
 pgfmathsetmacroMyPhiMaxatan(tan(tdplotmainphi)*sin(90+tdplotmaintheta))
 shadedraw[fill opacity=0.1,left color=red,right color=white] 
 (MyPhiMax:2 and 0.5) 
 arc(MyPhiMax:MyPhiMax+180:2 and 0.5) -- (O) -- cycle;
 draw[fill opacity=0.1,fill=gray!80] circle (2 and 0.5);
 % unsquashed
 shadedraw[fill opacity=0.3,left color=blue,right color=white] (tdplotmainphi:1) 
 arc(tdplotmainphi:tdplotmainphi+180:1) -- (O) -- cycle;
 draw[fill opacity=0.3,fill=gray!80] circle (1);
 endscope
 % left
 beginscope[canvas is yz plane at x=4]
 draw[thick] (O) -- (0,0);
 % squash again
 pgfmathsetmacroMyThetaMaxatan(tan(tdplotmaintheta)*sin(90+tdplotmainphi)*4)
 shadedraw[line join=bevel,fill opacity=0.1,upper right=white,
 lower left=red] 
 (MyThetaMax:0.5 and 2) 
 arc(MyThetaMax:MyThetaMax+180:0.5 and 2) -- (O) -- cycle;
 draw[fill opacity=0.1,fill=gray] circle (0.5 and 2);
 % unsquashed
 pgfmathsetmacroMyThetaMaxatan(tan(tdplotmaintheta)*sin(90+tdplotmainphi))
 shadedraw[line join=bevel,fill opacity=0.3,upper right=white,lower left=blue] 
 (MyThetaMax:1) 
 arc(MyThetaMax:MyThetaMax+180:1) -- (O) -- cycle;
 draw[fill opacity=0.3,fill=gray] circle (1);
 endscope
 % arc
 beginscope[canvas is xz plane at y=0,xscale=-1]
 draw[-latex] (0,1) arc(90:180:1) node[midway,above left]$vartheta$;
 endscope
 endscope
endtikzpicture
enddocument