Cfrgtkky

I am trying to draw a line moving along with a 3D graph to represent the region of integration.

So for this, the black line on the bottom represents the cut off for the region of integration. I would like to have a trace of the line moving along the surface of the function. Here is the MWE:

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

documentclass[a4paper, 12pt]{article}

usepackage{pgfplots}

usepgfplotslibrary{colormaps,fillbetween}



begin{document}



begin{tikzpicture}



begin{axis}[

zmax=15,

zmin=0,

view = {45}{45},

grid=minor,

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

xlabel = $s$,

ylabel = $h$,

zlabel = {$f(s,h)$},

ticks = none,

]



addplot3[

surf,

samples=30,

domain=0:1.5,

opacity=0.5,

]

{12*exp(-(4*x+3*y))};



draw[black, thick] (0,0,0) -- (1.5,1.5,0);



addplot3 [name path = xline, draw = none, domain=0:1.5] (x,0,0);

addplot3 [name path = xcurve, domain=0:1.5, y domain = 0:0, draw = none] 

    (x, 0, {12*exp(-(4*x))});

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

  fill between[of = xcurve and xline];



addplot3[

mesh,

draw=Bittersweet,

samples=30,

domain=0:1.5,

opacity = 0.75

]

{12*exp(-(4*x+3*y))};



% Attempt 1

%addplot3 [domain=0:1.5, black, thick, samples=30] (x,x,{12*exp(-(4*x+3*y))});



%Attempt 2

%addplot3 [domain=0:1.5, black, thick, samples=30] (x,x,{12*exp(-(7*x))});



end{axis}

end{tikzpicture}

The two commented out lines toward the end, which I called Attempt 1 and Attempt 2, are namely my two attempts at doing this. Here is the result for each of them:

Attempt 1

Attempt 2

Attempt 1 is a mess, but Attempt 2 is very close to what I want, but it draws a line across the start and end points of the function. Any suggestions as to how I could fix this?

You already were on the right track. You can achieve what you want by adding samples y=1 to your second attempt.

(Besides that I did some minor optimazations to your code. See the comments in the code for details.)

% used PGFPlots v1.16

documentclass[border=5pt]{standalone}

usepackage[dvipsnames]{xcolor}

usepackage{pgfplots}

    usepgfplotslibrary{fillbetween}

    pgfplotsset{

        compat=1.16,

    }

begin{document}

begin{tikzpicture}

    begin{axis}[

        zmax=15,

        zmin=0,

        view={45}{45},

        grid=minor,

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

        xlabel=$s$,

        ylabel=$h$,

        zlabel={$f(s,h)$},

        ticks=none,

        % (moved common options here)

        domain=0:1.5,

        samples=30,

    ]



        addplot3[

            surf,

            opacity=0.5,

            % removed one `addplot' by adding the next line

            faceted color=Bittersweet,

        ] {12*exp(-(4*x+3*y))};



        draw [black, thick] (0,0,0) -- (1.5,1.5,0);



        addplot3 [

            name path=xline,

            draw=none,

        ] (x,0,0);

        addplot3 [

            name path=xcurve,

            % replaced this ...

%            y domain=0:0,

            % by ...

            samples y=1,

            draw=none,

        ] (x,0,{12*exp(-(4*x))});

        addplot [color=Tan, opacity=0.5]

            fill between [of=xcurve and xline];





        % Attempt 2

        addplot3 [

            black,

            thick,

            samples y=1,        % <-- added

        ] (x,x,{12*exp(-7*x)});



    end{axis}

end{tikzpicture}

end{document}