Hatching Shear and moment diagrams using Stanli package in 2D and 3D

Question

Regarding drawing internal force diagrams through the use of the Stanli package. The following parameters are required for 2D internal forces command:

Start point
End point
Value at start point
Value at end point
Parabola height
Color
Bend position

In addition, the 3D internal forces commands uses the same parameters with 2 extra ones

Plane
Plane distance
Start point
End point
Value at start point
Value at end point
Parabola height
Color
Bend position

How can I add an two additional optional parameters to hatch the area under diagram (Area between the parabola and the beam):

A parameter to select a hatching pattern
Another parameter to set color of such hatching pattern

Such that if such patterns are not entered, no hatching is applied
MWE is shown below

documentclass{article}
usepackage{amsmath} 
usepackage{stanli}

begin{document}

begin{center}
begin{tikzpicture}

draw[help lines,step=0.5](0,0) grid(15,24);

%%%%%%%%%%%%%%%%%%%%%%%%Loading%%%%%%%%%%%%%%%%

point{a-LD}{0}{22.5};
point{b-LD}{10}{22.5};
point{su-LD}{2}{22.5+1.5};
point{s-LD}{2}{22.5};
point{sl-LD}{2}{22.5-0.5};
point{TL-LD}{10}{22.5+2};
point{CAP-LD}{10/2}{22.5-2.5};

% Elements

beam{4}{a-LD}{b-LD};

%Supports

support {1}{a-LD};
support {2}{b-LD};

%Loads

lineload{1}{a-LD}{b-LD}[0][2][0.035]

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%First diagram%%%%%%%%%%%%%%%%%%

point{a-FBD}{0}{22.5-6};
point{b-FBD}{10}{22.5-6};
point{TL-FBD}{2*10/3}{22.5-6};
point{TLA-FBD}{2*10/3}{22.5-6+1.75};
point{HR}{0-1.5}{22.5-6};
point{VRA}{0}{22.5-6-1};
point{VRB}{10}{22.5-6-1};
point{CAP-FBD}{10/2}{22.5-6-3.5};

% Elements

beam{4}{a-FBD}{b-FBD};

%%%%%%%%%%%%%%%%%Second diagram%%%%%%%%%%%%%%%%%%

internalforces{a-FBD}{b-FBD}{-3}{6}[0][red]%[0]

point{a-SFD}{0}{22.5-14};
point{b-SFD}{10}{22.5-14};
point{TL-SFD}{2*10/3}{22.5-14};
point{TLA-SFD}{2*10/3}{22.5-14+1.75};
point{VRA}{0}{22.5-14-1};
point{VRB}{10}{22.5-14-1};
point{CAP-SFD}{10/2}{22.5-14-3.5};

% Elements

beam{4}{a-SFD}{b-SFD};

internalforces{a-SFD}{b-SFD}{-3}{6}[3][red]%[0]

end{tikzpicture}
end{center}

newpage

begin{tikzpicture}[coords]
dpoint{a}{0}{0}{0}; 
dpoint{b}{0}{3}{-1};
dpoint{c}{1.5}{3}{ -1};
dbeam{1}{a}{b}[0][1]; 
dbeam{1}{b}{c};
dinternalforces{yz}{a}{b}{.5}{-1}[ -.4][blue];
dinternalforces{xz}{b}{c}{1}{0};
end{tikzpicture}

end{document}

This is the macro for the internal force command
%       internalforces
%------------------------------------------------
%           internalforces{initial point}{end point}{initial value}{end value}[parabola height][color][bend position]
%               [parabola height][color][bend position] are optional
%

newcommandx{internalforces}[7][5=0,6=red,7=.6667]{%
    coordinate (internalforcesVarA) at ($ (#1)!#3cm!-90:(#2) $);
    coordinate (internalforcesVarB) at ($ (#2)!#4cm!90:(#1)$);
    coordinate (internalforcesVarAB) at ($ (internalforcesVarA)!.5!(internalforcesVarB)$);
    coordinate (internalforcesVarC) at ($ (internalforcesVarAB)+2*(0,#5)$);
    coordinate (internalforcesVarAC) at ($ (internalforcesVarA)!#7!(internalforcesVarC)$);
    coordinate (internalforcesVarBC) at ($ (internalforcesVarB)!#7!(internalforcesVarC)$);
    ifthenelse{equal{#5}{0}}{
        draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) -- (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (bigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (bigLineWidth/2);
        fill [color=#6] (#1) circle (bigLineWidth/2);
        fill [color=#6] (#2) circle (bigLineWidth/2);
    }
    {
        %draw [bigLine,color=#6](internalforcesVarA) parabola[parabola height=#5cm] (internalforcesVarB);
        %draw [bigLine,color=#6](internalforcesVarA)--(internalforcesVarAC)--(internalforcesVarBC)--(internalforcesVarB);
        %draw [bigLine,color=blue](internalforcesVarA)--(internalforcesVarB)
        %(internalforcesVarAB) -- (internalforcesVarC);
        draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) .. controls (internalforcesVarAC) and (internalforcesVarBC) .. (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (bigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (bigLineWidth/2);
        fill [color=#6] (#1) circle (bigLineWidth/2);
        fill [color=#6] (#2) circle (bigLineWidth/2);
    }
    
}

Macro for points
%------------------------------------------------
%       point
%------------------------------------------------
%           point{name}{x-coordiante}{y-coordiante}
%

newcommandx{point}[3]{
    node[coordinate][
        shift={(#2*scalingParameter,#3*scalingParameter)}](#1){};
}
`````````````````````````````````````````````````
Macro for beam
`````````````````````````````````````````````````
%------------------------------------------------
%       beam
%------------------------------------------------
%           beam{type}{initial point}{end point}[rounded initial point][rounded end point]

newcommandx{beam}[5][4=0,5=0]{
    ifthenelse{equal{#1}{1}}{     %
        draw [hugeLine] (#2) -- (#3);
        coordinate (barVarA) at ($ (#2)!barGap!-barAngle:(#3) $);
        coordinate (barVarB) at ($ (#3)!barGap!barAngle:(#2) $);
        draw [smallLine,dashed] (barVarA) -- (barVarB);
        ifthenelse{equal{#4}{0}}{}
            {fill (#2) circle (hugeLineWidth/2);}
        ifthenelse{equal{#5}{0}}{}
            {fill (#3) circle (hugeLineWidth/2);}
    }{}

ifthenelse{equal{#1}{2}}{     %
        draw [bigLine] (#2) -- (#3);
        ifthenelse{equal{#4}{0}}{}
            {fill (#2) circle (bigLineWidth/2);}
        ifthenelse{equal{#5}{0}}{}
            {fill (#3) circle (bigLineWidth/2);}
    }{}
    
    ifthenelse{equal{#1}{3}}{     %
        draw [normalLine,dashed] (#2) -- (#3);
    }{}
    
    ifthenelse{equal{#1}{4}}{     %
        draw [hugeLine] (#2) -- (#3);
        ifthenelse{equal{#4}{0}}{}
            {fill (#2) circle (hugeLineWidth/2);}
        ifthenelse{equal{#5}{0}}{}
            {fill (#3) circle (hugeLineWidth/2);}
    }{}
}

%------------------------------------------------

MAcro for 3Dinternal forces command
``````````````````````````````````````````````

%------------------------------------------------
%       3dinternalforces
%------------------------------------------------
%           dinternalforces{plane}[plane distance]{initial point}{end point}{initial value}{end value}[parabola height][color][bend position];
%

newcommandx{dinternalforces}[9][2=0,7=0,8=red,9=.6667]{
    %
    ifthenelse{equal{#1}{xy}}
        {renewcommand{DhelpVarA}{z}}{}
    ifthenelse{equal{#1}{yx}}
        {renewcommand{DhelpVarA}{z}}{}
    ifthenelse{equal{#1}{xz}}
        {renewcommand{DhelpVarA}{y}}{}
    ifthenelse{equal{#1}{zx}}
        {renewcommand{DhelpVarA}{y}}{}
    ifthenelse{equal{#1}{yz}}
        {renewcommand{DhelpVarA}{x}}{}
    ifthenelse{equal{#1}{zy}}
        {renewcommand{DhelpVarA}{x}}{}

begin{scope}[canvas is #1 plane at DhelpVarA=#2]
        subinternalforces{#3}{#4}{#5}{#6}[#7][#8][#9];
    end{scope}
}

newcommandx{subinternalforces}[7][5=0,6=red,7=.6667]{%
    coordinate (internalforcesVarA) at ($ (#1)!#3cm!-90:(#2) $);
    coordinate (internalforcesVarB) at ($ (#2)!#4cm!90:(#1)$);
    coordinate (internalforcesVarAB) at ($ (internalforcesVarA)!.5!(internalforcesVarB)$);
    coordinate (internalforcesVarC) at ($ (internalforcesVarAB)+2*(0,#5)$);
    coordinate (internalforcesVarAC) at ($ (internalforcesVarA)!#7!(internalforcesVarC)$);
    coordinate (internalforcesVarBC) at ($ (internalforcesVarB)!#7!(internalforcesVarC)$);
    ifthenelse{equal{#5}{0}}{
        draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) -- (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (DbigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (DbigLineWidth/2);
        fill [color=#6] (#1) circle (DbigLineWidth/2);
        fill [color=#6] (#2) circle (DbigLineWidth/2);
    }
    {
        draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) .. controls (internalforcesVarAC) and (internalforcesVarBC) .. (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (DbigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (DbigLineWidth/2);
        fill [color=#6] (#1) circle (DbigLineWidth/2);
        fill [color=#6] (#2) circle (DbigLineWidth/2);
    }
    
}
``````````````````````````````````````````````

[![enter image description here][1]][1]

[![enter image description here][2]][2]

[1]: https://i.stack.imgur.com/IQTkm.jpg
  [2]: https://i.stack.imgur.com/m9li2.jpg

M.Ahmadi · Accepted Answer

code 1: No arguments
documentclass[border=12mm]{standalone}
usepackage{stanli}

newcommandx{internalforcesx}[7][5=0,6=red,7=.6667]{%
    coordinate (internalforcesVarA) at ($ (#1)!#3cm!-90:(#2) $);
    coordinate (internalforcesVarB) at ($ (#2)!#4cm!90:(#1)$);
    coordinate (internalforcesVarAB) at ($ (internalforcesVarA)!.5!(internalforcesVarB)$);
    coordinate (internalforcesVarC) at ($ (internalforcesVarAB)+2*(0,#5)$);
    coordinate (internalforcesVarAC) at ($ (internalforcesVarA)!#7!(internalforcesVarC)$);
    coordinate (internalforcesVarBC) at ($ (internalforcesVarB)!#7!(internalforcesVarC)$);
ifthenelse{equal{#5}{0}}{
fill [pattern=north west lines,pattern color=blue]  (#1) -- (internalforcesVarA)  --(internalforcesVarB) -- (#2)--cycle;
draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) -- (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (bigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (bigLineWidth/2);
        fill [color=#6] (#1) circle (bigLineWidth/2);
        fill [color=#6] (#2) circle (bigLineWidth/2);
}{      
fill [pattern=north east lines,pattern color=blue] (#1) -- (internalforcesVarA) .. controls (internalforcesVarAC) and (internalforcesVarBC) ..(internalforcesVarB) -- (#2)--cycle;
draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) .. controls (internalforcesVarAC) and (internalforcesVarBC) .. (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (bigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (bigLineWidth/2);
        fill [color=#6] (#1) circle (bigLineWidth/2);
        fill [color=#6] (#2) circle (bigLineWidth/2);
}}

pagestyle{empty}

begin{document}

begin{tikzpicture}
draw[help lines,step=1](0,0) grid(11,20);

point{a-FBD}{0}{22.5-6};
point{b-FBD}{10}{22.5-6};

internalforcesx{a-FBD}{b-FBD}{-3}{6}[0][red]%[0]
beam{4}{a-FBD}{b-FBD};
%+++++++++++++++++++++++
point{a-SFD}{0}{22.5-14}; 
point{b-SFD}{10}{22.5-14};

internalforcesx{a-SFD}{b-SFD}{-3}{6}[3][red]%[0]
beam{4}{a-SFD}{b-SFD};

end{tikzpicture}

end{document}

code 2: def with arguments
note: Renamed , internalforces to internalforcesx
newcommandx{internalforcesx}[9][5=0,6=red,7=.6667,8=north west lines,9=white]{%
    coordinate (internalforcesVarA) at ($ (#1)!#3cm!-90:(#2) $);
    coordinate (internalforcesVarB) at ($ (#2)!#4cm!90:(#1)$);
    coordinate (internalforcesVarAB) at ($ (internalforcesVarA)!.5!(internalforcesVarB)$);
    coordinate (internalforcesVarC) at ($ (internalforcesVarAB)+2*(0,#5)$);
    coordinate (internalforcesVarAC) at ($ (internalforcesVarA)!#7!(internalforcesVarC)$);
    coordinate (internalforcesVarBC) at ($ (internalforcesVarB)!#7!(internalforcesVarC)$);
ifthenelse{equal{#5}{0}}{
fill [pattern=#8,pattern color=#9]  (#1) -- (internalforcesVarA)  --(internalforcesVarB) -- (#2);
draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) -- (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (bigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (bigLineWidth/2);
        fill [color=#6] (#1) circle (bigLineWidth/2);
        fill [color=#6] (#2) circle (bigLineWidth/2);
}{      
fill [pattern=#8,pattern color=#9] (#1) -- (internalforcesVarA) .. controls (internalforcesVarAC) and (internalforcesVarBC) ..(internalforcesVarB) -- (#2);
draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) .. controls (internalforcesVarAC) and (internalforcesVarBC) .. (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (bigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (bigLineWidth/2);
        fill [color=#6] (#1) circle (bigLineWidth/2);
        fill [color=#6] (#2) circle (bigLineWidth/2);
}}

%+++++++++++++++++++++++++++++++++
documentclass[border=12mm]{standalone}
usepackage{stanli}

newcommandx{internalforcesx}[9][5=0,6=red,7=.6667,8=north west lines,9=white]{%
    coordinate (internalforcesVarA) at ($ (#1)!#3cm!-90:(#2) $);
    coordinate (internalforcesVarB) at ($ (#2)!#4cm!90:(#1)$);
    coordinate (internalforcesVarAB) at ($ (internalforcesVarA)!.5!(internalforcesVarB)$);
    coordinate (internalforcesVarC) at ($ (internalforcesVarAB)+2*(0,#5)$);
    coordinate (internalforcesVarAC) at ($ (internalforcesVarA)!#7!(internalforcesVarC)$);
    coordinate (internalforcesVarBC) at ($ (internalforcesVarB)!#7!(internalforcesVarC)$);
ifthenelse{equal{#5}{0}}{
fill [pattern=#8,pattern color=#9]  (#1) -- (internalforcesVarA)  --(internalforcesVarB) -- (#2);
draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) -- (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (bigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (bigLineWidth/2);
        fill [color=#6] (#1) circle (bigLineWidth/2);
        fill [color=#6] (#2) circle (bigLineWidth/2);
}{      
fill [pattern=#8,pattern color=#9] (#1) -- (internalforcesVarA) .. controls (internalforcesVarAC) and (internalforcesVarBC) ..(internalforcesVarB) -- (#2);
draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) .. controls (internalforcesVarAC) and (internalforcesVarBC) .. (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (bigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (bigLineWidth/2);
        fill [color=#6] (#1) circle (bigLineWidth/2);
        fill [color=#6] (#2) circle (bigLineWidth/2);
}}

pagestyle{empty}

begin{document}

begin{tikzpicture}
draw[help lines,step=1](0,0) grid(11,20);

point{a-FBD}{0}{22.5-6};
point{b-FBD}{10}{22.5-6};

internalforcesx{a-FBD}{b-FBD}{-3}{6}[0][red][.6667][north west lines][blue]
beam{4}{a-FBD}{b-FBD};
%+++++++++++++++++++++++
point{a-SFD}{0}{22.5-14}; 
point{b-SFD}{10}{22.5-14};

%internalforcesx{a-SFD}{b-SFD}{-3}{6}[3][red][.6667][north east lines][blue]
%internalforcesx{a-SFD}{b-SFD}{-3}{6}[3][red][.6667][dots][blue]
internalforcesx{a-SFD}{b-SFD}{-3}{6}[3][red][.6667][crosshatch dots light steel blue]%[blue]
%internalforcesx{a-SFD}{b-SFD}{-3}{6}[3][red][.6667][fivepointed stars][yellow]
beam{4}{a-SFD}{b-SFD};

end{tikzpicture}

end{document}

output:

for 3D: A maximum of 9 arguments can be written, see xargs.pdf or xargs.sty.
documentclass{article}
usepackage{stanli}

%   dinternalforces{plane}[plane distance]{initial point}{end point}{initial value}{end value}[parabola height][color][bend position];
newcommandx{dinternalforcesx}[9][2=0,7=0,8=red,9=.6667]{
    %
    ifthenelse{equal{#1}{xy}}
        {renewcommand{DhelpVarA}{z}}{}
    ifthenelse{equal{#1}{yx}}
        {renewcommand{DhelpVarA}{z}}{}
    ifthenelse{equal{#1}{xz}}
        {renewcommand{DhelpVarA}{y}}{}
    ifthenelse{equal{#1}{zx}}
        {renewcommand{DhelpVarA}{y}}{}
    ifthenelse{equal{#1}{yz}}
        {renewcommand{DhelpVarA}{x}}{}
    ifthenelse{equal{#1}{zy}}
        {renewcommand{DhelpVarA}{x}}{}

begin{scope}[canvas is #1 plane at DhelpVarA=#2]
        subinternalforcesx{#3}{#4}{#5}{#6}[#7][#8][#9];
    end{scope}
}

newcommandx{subinternalforcesx}[7][5=0,6=red,7=.6667]{%
    coordinate (internalforcesVarA) at ($ (#1)!#3cm!-90:(#2) $);
    coordinate (internalforcesVarB) at ($ (#2)!#4cm!90:(#1)$);
    coordinate (internalforcesVarAB) at ($ (internalforcesVarA)!.5!(internalforcesVarB)$);
    coordinate (internalforcesVarC) at ($ (internalforcesVarAB)+2*(0,#5)$);
    coordinate (internalforcesVarAC) at ($ (internalforcesVarA)!#7!(internalforcesVarC)$);
    coordinate (internalforcesVarBC) at ($ (internalforcesVarB)!#7!(internalforcesVarC)$);
    ifthenelse{equal{#5}{0}}{
fill[pattern=north west lines,pattern color=green] (#1) -- (internalforcesVarA) -- (internalforcesVarB) -- (#2)--cycle;
        draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) -- (internalforcesVarB) (internalforcesVarB) -- (#2);
        fill [color=#6] (internalforcesVarA) circle (DbigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (DbigLineWidth/2);
        fill [color=#6] (#1) circle (DbigLineWidth/2);
        fill [color=#6] (#2) circle (DbigLineWidth/2);
    }
    {
fill [pattern=north west lines,pattern color=green] (#1) -- (internalforcesVarA)  .. controls (internalforcesVarAC) and (internalforcesVarBC) .. (internalforcesVarB) -- (#2);
draw [bigLine,color=#6] (#1) -- (internalforcesVarA) (internalforcesVarA) .. controls (internalforcesVarAC) and (internalforcesVarBC) .. (internalforcesVarB) (internalforcesVarB) -- (#2);
        
        fill [color=#6] (internalforcesVarA) circle (DbigLineWidth/2);
        fill [color=#6] (internalforcesVarB) circle (DbigLineWidth/2);
        fill [color=#6] (#1) circle (DbigLineWidth/2);
        fill [color=#6] (#2) circle (DbigLineWidth/2);
    }
}

begin{document}

begin{tikzpicture}[coords]
dpoint{a}{0}{0}{0}; 
dpoint{b}{0}{3}{-1};
dpoint{c}{1.5}{3}{ -1};

dinternalforcesx{yz}{a}{b}{.5}{-1}[ -.4][blue];
dinternalforcesx{xz}{b}{c}{1}{0};

dbeam{1}{a}{b}[0][1]; 
dbeam{1}{b}{c};
end{tikzpicture}

end{document}

output:

Hatching Shear and moment diagrams using Stanli package in 2D and 3D

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