How to draw bar chart from a function

Question

I'd like to know how to draw a bar (step) chart from a given function. The code for a (continuous) chart is:
documentclass[preview,border=2pt,2pt]{standalone}

usepackage{tikz}
usetikzlibrary{shapes,backgrounds}
usetikzlibrary{calc}
usetikzlibrary{decorations.shapes}
usetikzlibrary{arrows.meta}
tikzset{decorate sep/.style 2 args=
    {decorate,decoration={shape backgrounds,shape=circle,shape size=#1,shape sep=#2}}}
tikzset{>={Latex[width=1mm,length=3mm]}}

begin{document}    
    begin{tikzpicture}
    tikzstyle{line} = [arrows=<->,line width=0.7pt]
    tikzstyle{line2} = [line width=0.7pt]
    
    defr{0.6pt} %define the radius of spot
    defax{3.3} %define the length of x-axis
    defay{4} %define the length of y-axis
    defy{3} %define the height of T=1
    defb{2} %define the postion of b
    
    tikzset{
        declare function={
            normpdf(x,m,s,r)=r*exp(-((x-m)/s)^4);
        }
    }
    
    %first chart
    draw[line] (0,ay) coordinate node [below left] {$T$} -- (0,0) coordinate node[below] {$0$} -- (ax, 0) coordinate node [below left] {$x$};
    draw[scale=1, domain=-2:2, smooth, variable=x] plot ({x}, {normpdf(x,0,1.3,y)});
    draw[line2] (0,0) -- (-ax+0.5, 0);
    
    filldraw (0,y) circle (r) node[left] at (0,y+0.2) {$1$};
    filldraw (b,0) circle (r) node[below] at (b,0) {$b$};
    filldraw (-b,0) circle (r) node[below] at (-b,0) {$-b$};

end{tikzpicture}
end{document}

I want to know how to draw a bar chart like a digitized one from the function given above.  The number of steps should be specified. Thanks.

SebGlav · Accepted Answer

I came with something that could be a good start.
documentclass{standalone}
usepackage{tikz}

begin{document}
    
    begin{tikzpicture}[yscale=3]
    
        defr{0.6pt} %define the radius of spot
        defb{3} %define the postion of b
        defs{1.3}
        defm{0}
        
        defn{50} % number of bars
        defxmin{-b} defxmax{b}
        
        % compute the bar length        
        pgfmathparse{(xmax-xmin+1)/n}edefbarlen{pgfmathresult}%
        pgfmathparse{(xmin+barlen)}edefxminb{pgfmathresult}%
        
        draw (xmin-0.2,0)--(xmax+0.2,0) (0,-.2) --(0,1);
        foreach x in {xmin,xminb,...,xmax}
            {
            pgfmathparse{r*2.718^(-((x-m)/s)^4)}edefy{pgfmathresult}%
            pgfmathparse{x-(barlen)/2}edefxstart{pgfmathresult}%
            draw (xstart,0) rectangle++ (barlen,y);
            }

end{tikzpicture}   
    
end{document}

You can play with variable n which is the number of bars you want.
Here, I tried to center the bars on the exploited x value. It might not be what you are looking for, just ask.
n=150

n=50

n=21

n=14

n=7

SebGlav · Answer

Here's another solution, maybe way better than my previous one (which has some inaccuracies in calculations for the bar length), now with pgfplots.
documentclass[border=10pt]{standalone}
usepackage{pgfplots}

begin{document}
    begin{tikzpicture}
    
    defr{0.6pt} %define the radius of spot
    defax{3.3} %define the length of x-axis
    defay{4} %define the length of y-axis
    defy{3} %define the height of T=1
    defb{2} %define the postion of b
    
    defs{1.3}
    defm{0}
    
    defn{50} % number of bars

begin{axis}[
    declare function = {normpdf(x,m,s,r)=r*exp(-((x-m)/s)^4);},
    axis lines=middle,
    ymin=0, ymax=.7,  ylabel=$y$,
    xmin=-3, xmax=3,  xlabel=$x$,
    ytick=empty,
    xtick={-3,...,3},
    ticklabel style = {font=footnotesize},
    no marks
            ]
        addplot [domain=-3:3, thick, blue,samples=100] {normpdf(x,m,s,r)};
        addplot [domain=-3:3,  ybar interval=1, fill=orange, fill opacity=0.3, samples=n]{normpdf(x,m,s,r)};
        
end{axis}
    end{tikzpicture}
end{document}

20 bars

50 bars

100 bars

How to draw bar chart from a function

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