Htydjtk

I am trying to fill in the area under this 3D graph, using the idea from this post. Here is a MWE for the function I want to plot under:

PassOptionsToPackage{usenames,dvipsnames,table,x11names}{xcolor}

documentclass[a4paper, 12pt]{article}

usepackage{pgfplots}

usepgfplotslibrary{colormaps,fillbetween}



begin{document}



begin{tikzpicture}

pgfdeclarelayer{pre main}

pgfsetlayers{pre main,main}



begin{axis}[

zmax=1.25,

view = {45}{45},

grid=minor,

colormap={mycol}{color=(SteelBlue3), color=(SteelBlue3)},

xlabel = $x$,

ylabel = $y$,

zlabel = {$f(x,y)$},

]



addplot3[

surf,

samples=30,

domain=0:2,

shader=interp,

opacity=0.5,

]

{exp(-(x^2+y^2))};



end{axis}

end{tikzpicture}



end{document}

Here is the result:

Now, here is the MWE with the code that should shade in the sides:

PassOptionsToPackage{usenames,dvipsnames,table,x11names}{xcolor}

documentclass[a4paper, 12pt]{article}

usepackage{pgfplots}

usepgfplotslibrary{colormaps,fillbetween}



begin{document}



begin{tikzpicture}

pgfdeclarelayer{pre main}

pgfsetlayers{pre main,main}



begin{axis}[

zmax=1.25,

view = {45}{45},

grid=minor,

colormap={mycol}{color=(SteelBlue3), color=(SteelBlue3)},

xlabel = $x$,

ylabel = $y$,

zlabel = {$f(x,y)$},

]



begin{pgfonlayer}{pre main}

addplot3[

surf,

samples=30,

domain=0:2,

shader=interp,

opacity=0.5,

]

{exp(-(x^2+y^2))};

end{pgfonlayer}



addplot3 [name path = xline, draw = none] (x,0,0);

 % x is the variable

 % second 0 is the y coordinate of the leftmost part of the graph

 % third 0 is height

addplot3 [name path = yline, draw = none] (2,y,0);

 % y is the variable

 % first 2 is the x coordinate of the rightmost part of the graph

 % third 0 is height

addplot3 [name path = xcurve, y domain = 0:0, draw = none] 

    (x, 0, {exp(-x^2)});

 % now instead of height being 0, it is height of function

addplot3 [name path = ycurve, y domain = 0:0, draw = none]

  (2, x, {exp(-(x^2 + 4))});

 % same idea

addplot [color = SteelBlue3, opacity = 0.5, draw = none]

  fill between[of = xcurve and xline];

 % fills in x axis

addplot [color = SteelBlue3, opacity = 0.5, draw = none]

  fill between[of = yline and ycurve, reverse = true];



end{axis}

end{tikzpicture}



end{document}

And this is the result:

Can anyone make any suggestions as to what is going on? It seems when I add multiple functions to the same plot via addplot3, everything gets messed up.

Sorry if this seems like a "just fix this for me," but I have no idea what I'm doing wrong.

EDIT

I now see that for some reason, when adding the new plots to shade in the side, the domain was changed from (0,2) to (-4,4), so setting the domain as you add the plots helps:

PassOptionsToPackage{usenames,dvipsnames,table,x11names}{xcolor}

documentclass[a4paper, 12pt]{article}

usepackage{pgfplots}

usepgfplotslibrary{colormaps,fillbetween}



begin{document}



begin{tikzpicture}

pgfdeclarelayer{pre main}

pgfsetlayers{pre main,main}



begin{axis}[

zmax=1.25,

view = {45}{45},

grid=minor,

colormap={mycol}{color=(SteelBlue3), color=(SteelBlue3)},

xlabel = $x$,

ylabel = $y$,

zlabel = {$f(x,y)$},

]



begin{pgfonlayer}{pre main}

addplot3[

surf,

samples=30,

domain=0:2,

shader=interp,

opacity=0.5,

]

{exp(-(x^2+y^2))};

end{pgfonlayer}



addplot3 [name path = xline, draw = none, domain=0:2] (x,0,0);

 % x is the variable

 % second 0 is the y coordinate of the leftmost part of the graph

 % third 0 is height

addplot3 [name path = yline, draw = none, domain=0:2] (2,y,0);

 % y is the variable

 % first 2 is the x coordinate of the rightmost part of the graph

 % third 0 is height

addplot3 [name path = xcurve, domain=0:2, y domain = 0:0, draw = none] 

    (x, 0, {exp(-x^2)});

 % now instead of height being 0, it is height of function

addplot3 [name path = ycurve, domain=0:2, y domain = 0:0, draw = none]

  (2, x, {exp(-(x^2 + 4))});

 % same idea

addplot [color = SteelBlue3, opacity = 0.5, draw = none]

  fill between[of = xcurve and xline];

 % fills in x axis

addplot [color = SteelBlue3, opacity = 0.5, draw = none]

  fill between[of = yline and ycurve, reverse = true];



end{axis}

end{tikzpicture}



end{document}

And here is the result:

My question now is, why is the original function shifted up?

ANOTHER EDIT

I have figured out a way to get what I want (not including the excellent answers below), but I still have some more concerns. Here is a MWE with a good result:

PassOptionsToPackage{usenames,dvipsnames,table,x11names}{xcolor}

documentclass[a4paper, 12pt]{article}

usepackage{pgfplots}

usepgfplotslibrary{colormaps,fillbetween}



begin{document}



begin{tikzpicture}



begin{axis}[

zmax=1.25,

zmin=0,

view = {45}{45},

grid=minor,

colormap={mycol}{color=(SteelBlue3), color=(SteelBlue3)},

xlabel = $x$,

ylabel = $y$,

zlabel = {$f(x,y)$},

]



addplot3[

surf,

samples=30,

domain=0:2,

%shader=interp,

opacity=0.5,

]

{exp(-(x^2+y^2))};



addplot3 [name path = xline, draw = none, domain=0:2] (x,0,0);

 % x is the variable

 % second 0 is the y coordinate of the leftmost part of the graph

 % third 0 is height

addplot3 [name path = yline, draw = none, domain=0:2] (2,y,0);

 % y is the variable

 % first 2 is the x coordinate of the rightmost part of the graph

 % third 0 is height

addplot3 [name path = xcurve, domain=0:2, y domain = 0:0, draw = none] 

    (x, 0, {exp(-x^2)});

 % now instead of height being 0, it is height of function

addplot3 [name path = ycurve, domain=0:2, y domain = 0:0, draw = none]

  (2, x, {exp(-(x^2 + 4))});

 % same idea

addplot [color = SteelBlue3, opacity = 0.5, draw = none]

  fill between[of = xcurve and xline];

 % fills in x axis

addplot [color = SteelBlue3, opacity = 0.5, draw = none]

  fill between[of = yline and ycurve, reverse = true];



end{axis}

end{tikzpicture}



end{document}

Which give this result:

Now, the issue is the %shader=interp, line. When I uncomment this out, this happens:

So does this command force the graph to shift upwards for some reason? Why does this happen?

Something like this?

PassOptionsToPackage{usenames,dvipsnames,table,x11names}{xcolor}

documentclass[a4paper, 12pt]{article}

usepackage{pgfplots}

pgfplotsset{compat=1.16}

usepgfplotslibrary{colormaps,fillbetween}



begin{document}



begin{tikzpicture}[declare function={f(x,y)=exp(-(x*x+y*y));}]

pgfdeclarelayer{pre main}

pgfsetlayers{pre main,main}



begin{axis}[

zmax=1.25,

view = {45}{45},

grid=minor,

colormap={mycol}{color=(SteelBlue3), color=(SteelBlue3)},

xlabel = $x$,

ylabel = $y$,

zlabel = {$f(x,y)$},

]



addplot3[

surf,

samples=30,

domain=0:2,

shader=interp,

opacity=0.5,

]

{f(x,y)};



fill[blue] (0,0,-1) -- plot[variable=x,domain=0:2] (x,0,{f(x,0)}) -- (2,0,-1) --

cycle;

fill[blue!80] (2,0,-1) -- plot[variable=y,domain=0:2] (2,y,{f(2,y)}) 

-- (2,2,-1) --cycle;



end{axis}

end{tikzpicture}



end{document}

Or, if you do the fills with

fill[SteelBlue3] (0,0,-1) -- plot[variable=x,domain=0:2] (x,0,{f(x,0)}) -- (2,0,-1) --

cycle;

fill[SteelBlue3] (2,0,-1) -- plot[variable=y,domain=0:2] (2,y,{f(2,y)}) 

-- (2,2,-1) --cycle;

you get

Notice that I added pgfplotsset{compat=1.16}. If you do not want that, you need to prepend the coordinates with axis cs:

fill[SteelBlue3] (axis cs:0,0,-1) -- plot[variable=x,domain=0:2] (axis cs:x,0,{f(x,0)}) -- (axis cs:2,0,-1) --

cycle;

fill[SteelBlue3] (axis cs:2,0,-1) -- plot[variable=y,domain=0:2] (axis cs:2,y,{f(2,y)}) 

-- (axis cs:2,2,-1) --cycle;