How can I make a cone from a cube and view the cube with different angles?












7















I am trying to draw a cone with vertex C and base is circle BDG and want to view the cube with different angles like some following pictures.
enter image description here



I tried



documentclass[border=2mm,12pt,tikz]{standalone} 
usepackage{tikz,tikz-3dplot}
usepackage{fouriernc}
usepackage{tkz-euclide}
usetkzobj{all}
makeatletter
newcounter{smuggle}
DeclareRobustCommandsmuggleone[1]{%
stepcounter{smuggle}%
expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%
aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname
}
DeclareRobustCommandsmuggle[2][1]{%
smuggleone{#2}%
ifnum#1>1
aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%
fi
}
makeatother
% based on tex.stackexchange.com/a/12033/…
tikzset{reverseclip/.style={insert path={(current bounding box.south west)rectangle
(current bounding box.north east)} }}

defparsecoord(#1,#2,#3)>(#4,#5,#6){%
def#4{#1}%
def#5{#2}%
def#6{#3}%
smuggle{#4}%
smuggle{#5}%
smuggle{#6}%
}
defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}
defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}
defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}
defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}
newcommand{RotationAnglesForPlaneWithNormal}[5]{%typeout{N=(#1,#2,#3)}
foreach XS in {1,-1}
{foreach YS in {1,-1}
{pgfmathsetmacro{mybeta}{XS*acos(#3)}
pgfmathsetmacro{myalpha}{YS*acos(#1/sin(mybeta))}
pgfmathsetmacro{ntest}{abs(cos(myalpha)*sin(mybeta)-#1)%
+abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3)}
ifdimntest pt<0.1pt
xdef#4{myalpha}
xdef#5{mybeta}
fi
}}
}
tikzset{circle in plane with normal/.style args={#1 with radius #2 around #3}{
/utils/exec={edeftemp{noexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
temp
pgfmathsetmacro{myNx}{myNx}
pgfmathsetmacro{myNy}{myNy}
pgfmathsetmacro{myNz}{myNz}
pgfmathsetmacro{myNormalization}{sqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2))}
pgfmathsetmacro{myNx}{myNx/myNormalization}
pgfmathsetmacro{myNy}{myNy/myNormalization}
pgfmathsetmacro{myNz}{myNz/myNormalization}
% compute the rotation angles that transform us in the corresponding plabe
RotationAnglesForPlaneWithNormal{myNx}{myNy}{myNz}{tmpalpha}{tmpbeta}
%typeout{N=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3}
tdplotsetrotatedcoords{tmpalpha}{tmpbeta}{0}},
insert path={[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape]
#3 circle[radius=#2]}
}}


begin{document}
tdplotsetmaincoords{70}{195}
begin{tikzpicture}[tdplot_main_coords,scale=1,line join = round, line cap = round]

pgfmathsetmacroa{3}
pgfmathsetmacror{2/3*sqrt(6)*a}
path
coordinate (A) at (a,-a,-a)
coordinate (B) at (a,a,-a)
coordinate (C) at (-a,a,-a)
coordinate (D) at (-a,-a,-a)
coordinate (E) at ($(A)+ (0,0,2*a)$)
coordinate (F) at ($(B)+ (0,0,2*a)$)
coordinate (G) at ($(C)+ (0,0,2*a)$)
coordinate (H) at ($(D)+ (0,0,2*a)$)
coordinate (O) at (0,0,0)
coordinate (I) at (-1/3*a, 1/3*a, -1/3*a)
;
parsecoord(a,a,-a)>(myBx,myBy,myBz)
parsecoord(-a,a,a)>(myGx,myGy,myGz)
parsecoord(-a,-a,-a)>(myDx,myDy,myDz)
defmynormal{VPTD({myDx-myBx},{myDy-myBy},{myDz-myBz})x({myDx-myGx},{myDy-myGy},{myDz-myGz})}
edeftemp{noexpandparsecoordmynormal>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
begin{scope}
draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
clip (B) -- (C) -- (D) -- (G) -- cycle [reverseclip];
draw[red,ultra thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
end{scope}
foreach point/position in {A/below,B/below,C/below,D/right,E/above,F/left,G/above,H/above,O/above,I/below}
{fill (point) circle (2.0pt);
node[position=2pt] at (point) {$point$};
}

begin{scope}[tdplot_screen_coords]
fill[ball color=gray, opacity=0.1] (I) circle (r); % 3D lighting effect
end{scope}

draw[very thick] (E) -- (F) -- (B)
(B) --(C)--(G)--(F)
(E) --(F) --(G)-- (H) --cycle
(C)--(D) --(H)--(G)--cycle
;

draw[very thick, blue] (G) -- (D) (G) -- (B);
draw[dashed, thick]
(B) -- (A) -- (E) (D) --(A) (D) --(C) (D) --(H) (E) --(C) (I) -- (B) (I) -- (G) (I) --(D)
;
draw[dashed, blue] (B) -- (D);
end{tikzpicture}
end{document}


I got



enter image description here



My questions are:




  1. How can I draw some generators (not CB, CG, CD) of the cone?

  2. How can I view the cube with different angles?


enter image description here



enter image description here










share|improve this question





























    7















    I am trying to draw a cone with vertex C and base is circle BDG and want to view the cube with different angles like some following pictures.
    enter image description here



    I tried



    documentclass[border=2mm,12pt,tikz]{standalone} 
    usepackage{tikz,tikz-3dplot}
    usepackage{fouriernc}
    usepackage{tkz-euclide}
    usetkzobj{all}
    makeatletter
    newcounter{smuggle}
    DeclareRobustCommandsmuggleone[1]{%
    stepcounter{smuggle}%
    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%
    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname
    }
    DeclareRobustCommandsmuggle[2][1]{%
    smuggleone{#2}%
    ifnum#1>1
    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%
    fi
    }
    makeatother
    % based on tex.stackexchange.com/a/12033/…
    tikzset{reverseclip/.style={insert path={(current bounding box.south west)rectangle
    (current bounding box.north east)} }}

    defparsecoord(#1,#2,#3)>(#4,#5,#6){%
    def#4{#1}%
    def#5{#2}%
    def#6{#3}%
    smuggle{#4}%
    smuggle{#5}%
    smuggle{#6}%
    }
    defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}
    defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}
    defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}
    defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}
    newcommand{RotationAnglesForPlaneWithNormal}[5]{%typeout{N=(#1,#2,#3)}
    foreach XS in {1,-1}
    {foreach YS in {1,-1}
    {pgfmathsetmacro{mybeta}{XS*acos(#3)}
    pgfmathsetmacro{myalpha}{YS*acos(#1/sin(mybeta))}
    pgfmathsetmacro{ntest}{abs(cos(myalpha)*sin(mybeta)-#1)%
    +abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3)}
    ifdimntest pt<0.1pt
    xdef#4{myalpha}
    xdef#5{mybeta}
    fi
    }}
    }
    tikzset{circle in plane with normal/.style args={#1 with radius #2 around #3}{
    /utils/exec={edeftemp{noexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
    temp
    pgfmathsetmacro{myNx}{myNx}
    pgfmathsetmacro{myNy}{myNy}
    pgfmathsetmacro{myNz}{myNz}
    pgfmathsetmacro{myNormalization}{sqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2))}
    pgfmathsetmacro{myNx}{myNx/myNormalization}
    pgfmathsetmacro{myNy}{myNy/myNormalization}
    pgfmathsetmacro{myNz}{myNz/myNormalization}
    % compute the rotation angles that transform us in the corresponding plabe
    RotationAnglesForPlaneWithNormal{myNx}{myNy}{myNz}{tmpalpha}{tmpbeta}
    %typeout{N=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3}
    tdplotsetrotatedcoords{tmpalpha}{tmpbeta}{0}},
    insert path={[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape]
    #3 circle[radius=#2]}
    }}


    begin{document}
    tdplotsetmaincoords{70}{195}
    begin{tikzpicture}[tdplot_main_coords,scale=1,line join = round, line cap = round]

    pgfmathsetmacroa{3}
    pgfmathsetmacror{2/3*sqrt(6)*a}
    path
    coordinate (A) at (a,-a,-a)
    coordinate (B) at (a,a,-a)
    coordinate (C) at (-a,a,-a)
    coordinate (D) at (-a,-a,-a)
    coordinate (E) at ($(A)+ (0,0,2*a)$)
    coordinate (F) at ($(B)+ (0,0,2*a)$)
    coordinate (G) at ($(C)+ (0,0,2*a)$)
    coordinate (H) at ($(D)+ (0,0,2*a)$)
    coordinate (O) at (0,0,0)
    coordinate (I) at (-1/3*a, 1/3*a, -1/3*a)
    ;
    parsecoord(a,a,-a)>(myBx,myBy,myBz)
    parsecoord(-a,a,a)>(myGx,myGy,myGz)
    parsecoord(-a,-a,-a)>(myDx,myDy,myDz)
    defmynormal{VPTD({myDx-myBx},{myDy-myBy},{myDz-myBz})x({myDx-myGx},{myDy-myGy},{myDz-myGz})}
    edeftemp{noexpandparsecoordmynormal>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
    begin{scope}
    draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
    clip (B) -- (C) -- (D) -- (G) -- cycle [reverseclip];
    draw[red,ultra thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
    end{scope}
    foreach point/position in {A/below,B/below,C/below,D/right,E/above,F/left,G/above,H/above,O/above,I/below}
    {fill (point) circle (2.0pt);
    node[position=2pt] at (point) {$point$};
    }

    begin{scope}[tdplot_screen_coords]
    fill[ball color=gray, opacity=0.1] (I) circle (r); % 3D lighting effect
    end{scope}

    draw[very thick] (E) -- (F) -- (B)
    (B) --(C)--(G)--(F)
    (E) --(F) --(G)-- (H) --cycle
    (C)--(D) --(H)--(G)--cycle
    ;

    draw[very thick, blue] (G) -- (D) (G) -- (B);
    draw[dashed, thick]
    (B) -- (A) -- (E) (D) --(A) (D) --(C) (D) --(H) (E) --(C) (I) -- (B) (I) -- (G) (I) --(D)
    ;
    draw[dashed, blue] (B) -- (D);
    end{tikzpicture}
    end{document}


    I got



    enter image description here



    My questions are:




    1. How can I draw some generators (not CB, CG, CD) of the cone?

    2. How can I view the cube with different angles?


    enter image description here



    enter image description here










    share|improve this question



























      7












      7








      7








      I am trying to draw a cone with vertex C and base is circle BDG and want to view the cube with different angles like some following pictures.
      enter image description here



      I tried



      documentclass[border=2mm,12pt,tikz]{standalone} 
      usepackage{tikz,tikz-3dplot}
      usepackage{fouriernc}
      usepackage{tkz-euclide}
      usetkzobj{all}
      makeatletter
      newcounter{smuggle}
      DeclareRobustCommandsmuggleone[1]{%
      stepcounter{smuggle}%
      expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%
      aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname
      }
      DeclareRobustCommandsmuggle[2][1]{%
      smuggleone{#2}%
      ifnum#1>1
      aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%
      fi
      }
      makeatother
      % based on tex.stackexchange.com/a/12033/…
      tikzset{reverseclip/.style={insert path={(current bounding box.south west)rectangle
      (current bounding box.north east)} }}

      defparsecoord(#1,#2,#3)>(#4,#5,#6){%
      def#4{#1}%
      def#5{#2}%
      def#6{#3}%
      smuggle{#4}%
      smuggle{#5}%
      smuggle{#6}%
      }
      defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}
      defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}
      defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}
      defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}
      newcommand{RotationAnglesForPlaneWithNormal}[5]{%typeout{N=(#1,#2,#3)}
      foreach XS in {1,-1}
      {foreach YS in {1,-1}
      {pgfmathsetmacro{mybeta}{XS*acos(#3)}
      pgfmathsetmacro{myalpha}{YS*acos(#1/sin(mybeta))}
      pgfmathsetmacro{ntest}{abs(cos(myalpha)*sin(mybeta)-#1)%
      +abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3)}
      ifdimntest pt<0.1pt
      xdef#4{myalpha}
      xdef#5{mybeta}
      fi
      }}
      }
      tikzset{circle in plane with normal/.style args={#1 with radius #2 around #3}{
      /utils/exec={edeftemp{noexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
      temp
      pgfmathsetmacro{myNx}{myNx}
      pgfmathsetmacro{myNy}{myNy}
      pgfmathsetmacro{myNz}{myNz}
      pgfmathsetmacro{myNormalization}{sqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2))}
      pgfmathsetmacro{myNx}{myNx/myNormalization}
      pgfmathsetmacro{myNy}{myNy/myNormalization}
      pgfmathsetmacro{myNz}{myNz/myNormalization}
      % compute the rotation angles that transform us in the corresponding plabe
      RotationAnglesForPlaneWithNormal{myNx}{myNy}{myNz}{tmpalpha}{tmpbeta}
      %typeout{N=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3}
      tdplotsetrotatedcoords{tmpalpha}{tmpbeta}{0}},
      insert path={[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape]
      #3 circle[radius=#2]}
      }}


      begin{document}
      tdplotsetmaincoords{70}{195}
      begin{tikzpicture}[tdplot_main_coords,scale=1,line join = round, line cap = round]

      pgfmathsetmacroa{3}
      pgfmathsetmacror{2/3*sqrt(6)*a}
      path
      coordinate (A) at (a,-a,-a)
      coordinate (B) at (a,a,-a)
      coordinate (C) at (-a,a,-a)
      coordinate (D) at (-a,-a,-a)
      coordinate (E) at ($(A)+ (0,0,2*a)$)
      coordinate (F) at ($(B)+ (0,0,2*a)$)
      coordinate (G) at ($(C)+ (0,0,2*a)$)
      coordinate (H) at ($(D)+ (0,0,2*a)$)
      coordinate (O) at (0,0,0)
      coordinate (I) at (-1/3*a, 1/3*a, -1/3*a)
      ;
      parsecoord(a,a,-a)>(myBx,myBy,myBz)
      parsecoord(-a,a,a)>(myGx,myGy,myGz)
      parsecoord(-a,-a,-a)>(myDx,myDy,myDz)
      defmynormal{VPTD({myDx-myBx},{myDy-myBy},{myDz-myBz})x({myDx-myGx},{myDy-myGy},{myDz-myGz})}
      edeftemp{noexpandparsecoordmynormal>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
      begin{scope}
      draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
      clip (B) -- (C) -- (D) -- (G) -- cycle [reverseclip];
      draw[red,ultra thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
      end{scope}
      foreach point/position in {A/below,B/below,C/below,D/right,E/above,F/left,G/above,H/above,O/above,I/below}
      {fill (point) circle (2.0pt);
      node[position=2pt] at (point) {$point$};
      }

      begin{scope}[tdplot_screen_coords]
      fill[ball color=gray, opacity=0.1] (I) circle (r); % 3D lighting effect
      end{scope}

      draw[very thick] (E) -- (F) -- (B)
      (B) --(C)--(G)--(F)
      (E) --(F) --(G)-- (H) --cycle
      (C)--(D) --(H)--(G)--cycle
      ;

      draw[very thick, blue] (G) -- (D) (G) -- (B);
      draw[dashed, thick]
      (B) -- (A) -- (E) (D) --(A) (D) --(C) (D) --(H) (E) --(C) (I) -- (B) (I) -- (G) (I) --(D)
      ;
      draw[dashed, blue] (B) -- (D);
      end{tikzpicture}
      end{document}


      I got



      enter image description here



      My questions are:




      1. How can I draw some generators (not CB, CG, CD) of the cone?

      2. How can I view the cube with different angles?


      enter image description here



      enter image description here










      share|improve this question
















      I am trying to draw a cone with vertex C and base is circle BDG and want to view the cube with different angles like some following pictures.
      enter image description here



      I tried



      documentclass[border=2mm,12pt,tikz]{standalone} 
      usepackage{tikz,tikz-3dplot}
      usepackage{fouriernc}
      usepackage{tkz-euclide}
      usetkzobj{all}
      makeatletter
      newcounter{smuggle}
      DeclareRobustCommandsmuggleone[1]{%
      stepcounter{smuggle}%
      expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%
      aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname
      }
      DeclareRobustCommandsmuggle[2][1]{%
      smuggleone{#2}%
      ifnum#1>1
      aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%
      fi
      }
      makeatother
      % based on tex.stackexchange.com/a/12033/…
      tikzset{reverseclip/.style={insert path={(current bounding box.south west)rectangle
      (current bounding box.north east)} }}

      defparsecoord(#1,#2,#3)>(#4,#5,#6){%
      def#4{#1}%
      def#5{#2}%
      def#6{#3}%
      smuggle{#4}%
      smuggle{#5}%
      smuggle{#6}%
      }
      defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}
      defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}
      defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}
      defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}
      newcommand{RotationAnglesForPlaneWithNormal}[5]{%typeout{N=(#1,#2,#3)}
      foreach XS in {1,-1}
      {foreach YS in {1,-1}
      {pgfmathsetmacro{mybeta}{XS*acos(#3)}
      pgfmathsetmacro{myalpha}{YS*acos(#1/sin(mybeta))}
      pgfmathsetmacro{ntest}{abs(cos(myalpha)*sin(mybeta)-#1)%
      +abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3)}
      ifdimntest pt<0.1pt
      xdef#4{myalpha}
      xdef#5{mybeta}
      fi
      }}
      }
      tikzset{circle in plane with normal/.style args={#1 with radius #2 around #3}{
      /utils/exec={edeftemp{noexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
      temp
      pgfmathsetmacro{myNx}{myNx}
      pgfmathsetmacro{myNy}{myNy}
      pgfmathsetmacro{myNz}{myNz}
      pgfmathsetmacro{myNormalization}{sqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2))}
      pgfmathsetmacro{myNx}{myNx/myNormalization}
      pgfmathsetmacro{myNy}{myNy/myNormalization}
      pgfmathsetmacro{myNz}{myNz/myNormalization}
      % compute the rotation angles that transform us in the corresponding plabe
      RotationAnglesForPlaneWithNormal{myNx}{myNy}{myNz}{tmpalpha}{tmpbeta}
      %typeout{N=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3}
      tdplotsetrotatedcoords{tmpalpha}{tmpbeta}{0}},
      insert path={[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape]
      #3 circle[radius=#2]}
      }}


      begin{document}
      tdplotsetmaincoords{70}{195}
      begin{tikzpicture}[tdplot_main_coords,scale=1,line join = round, line cap = round]

      pgfmathsetmacroa{3}
      pgfmathsetmacror{2/3*sqrt(6)*a}
      path
      coordinate (A) at (a,-a,-a)
      coordinate (B) at (a,a,-a)
      coordinate (C) at (-a,a,-a)
      coordinate (D) at (-a,-a,-a)
      coordinate (E) at ($(A)+ (0,0,2*a)$)
      coordinate (F) at ($(B)+ (0,0,2*a)$)
      coordinate (G) at ($(C)+ (0,0,2*a)$)
      coordinate (H) at ($(D)+ (0,0,2*a)$)
      coordinate (O) at (0,0,0)
      coordinate (I) at (-1/3*a, 1/3*a, -1/3*a)
      ;
      parsecoord(a,a,-a)>(myBx,myBy,myBz)
      parsecoord(-a,a,a)>(myGx,myGy,myGz)
      parsecoord(-a,-a,-a)>(myDx,myDy,myDz)
      defmynormal{VPTD({myDx-myBx},{myDy-myBy},{myDz-myBz})x({myDx-myGx},{myDy-myGy},{myDz-myGz})}
      edeftemp{noexpandparsecoordmynormal>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
      begin{scope}
      draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
      clip (B) -- (C) -- (D) -- (G) -- cycle [reverseclip];
      draw[red,ultra thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
      end{scope}
      foreach point/position in {A/below,B/below,C/below,D/right,E/above,F/left,G/above,H/above,O/above,I/below}
      {fill (point) circle (2.0pt);
      node[position=2pt] at (point) {$point$};
      }

      begin{scope}[tdplot_screen_coords]
      fill[ball color=gray, opacity=0.1] (I) circle (r); % 3D lighting effect
      end{scope}

      draw[very thick] (E) -- (F) -- (B)
      (B) --(C)--(G)--(F)
      (E) --(F) --(G)-- (H) --cycle
      (C)--(D) --(H)--(G)--cycle
      ;

      draw[very thick, blue] (G) -- (D) (G) -- (B);
      draw[dashed, thick]
      (B) -- (A) -- (E) (D) --(A) (D) --(C) (D) --(H) (E) --(C) (I) -- (B) (I) -- (G) (I) --(D)
      ;
      draw[dashed, blue] (B) -- (D);
      end{tikzpicture}
      end{document}


      I got



      enter image description here



      My questions are:




      1. How can I draw some generators (not CB, CG, CD) of the cone?

      2. How can I view the cube with different angles?


      enter image description here



      enter image description here







      tikz-pgf tikz-3dplot






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 14 hours ago









      TeXnician

      25.9k63491




      25.9k63491










      asked 15 hours ago









      minhthien_2016minhthien_2016

      1,4741917




      1,4741917






















          1 Answer
          1






          active

          oldest

          votes


















          4














          TikZ does not have a 3d engine, so one has to distinguish many cases. I hope this does not contain too many bugs. (There is also something that keeps track of the bounding boxes, meaning you have to compile the file twice.)



          documentclass[border=2mm,12pt,tikz]{standalone} 
          usepackage{tikz-3dplot}
          makeatletter
          newcounter{smuggle}
          DeclareRobustCommandsmuggleone[1]{%
          stepcounter{smuggle}%
          expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%
          aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname
          }
          DeclareRobustCommandsmuggle[2][1]{%
          smuggleone{#2}%
          ifnum#1>1
          aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%
          fi
          }
          defSaveBBox{%
          immediatewrite@mainaux{xdefstringxmin{xmin}relax}
          immediatewrite@mainaux{xdefstringxmax{xmax}relax}
          immediatewrite@mainaux{xdefstringymin{ymin}relax}
          immediatewrite@mainaux{xdefstringymax{ymax}relax}}
          makeatother
          % based on tex.stackexchange.com/a/12033/AAA
          tikzset{reverseclip/.style={insert path={(current bounding box.south west)rectangle
          (current bounding box.north east)} }}

          defparsecoord(#1,#2,#3)>(#4,#5,#6){%
          def#4{#1}%
          def#5{#2}%
          def#6{#3}%
          smuggle{#4}%
          smuggle{#5}%
          smuggle{#6}%
          }
          defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}
          defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}
          defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}
          defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}
          newcommand{RotationAnglesForPlaneWithNormal}[5]{%typeout{N=(#1,#2,#3)}
          foreach XS in {1,-1}
          {foreach YS in {1,-1}
          {pgfmathsetmacro{mybeta}{XS*acos(#3)}
          pgfmathsetmacro{myalpha}{YS*acos(#1/sin(mybeta))}
          pgfmathsetmacro{ntest}{abs(cos(myalpha)*sin(mybeta)-#1)%
          +abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3)}
          ifdimntest pt<0.1pt
          xdef#4{myalpha}
          xdef#5{mybeta}
          fi
          }}
          }
          tikzset{circle in plane with normal/.style args={#1 with radius #2 around #3}{
          /utils/exec={edeftemp{noexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
          temp
          pgfmathsetmacro{myNx}{myNx}
          pgfmathsetmacro{myNy}{myNy}
          pgfmathsetmacro{myNz}{myNz}
          pgfmathsetmacro{myNormalization}{sqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2))}
          pgfmathsetmacro{myNx}{myNx/myNormalization}
          pgfmathsetmacro{myNy}{myNy/myNormalization}
          pgfmathsetmacro{myNz}{myNz/myNormalization}
          % compute the rotation angles that transform us in the corresponding plabe
          RotationAnglesForPlaneWithNormal{myNx}{myNy}{myNz}{tmpalpha}{tmpbeta}
          %typeout{N=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3}
          tdplotsetrotatedcoords{tmpalpha}{tmpbeta}{0}},
          insert path={[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape]
          #3 circle[radius=#2]}
          }}


          begin{document}
          tdplotsetmaincoords{70}{195}
          foreach Angle in {5,15,...,355} % {5}
          {
          tdplotsetmaincoords{70}{Angle}
          begin{tikzpicture}[tdplot_main_coords,scale=1,line join = round, line cap = round]
          ifdefinedxmin
          else
          defxmin{0}
          fi
          ifdefinedxmax
          else
          defxmax{0}
          fi
          ifdefinedymin
          else
          defymin{0}
          fi
          ifdefinedymax
          else
          defymax{0}
          fi
          path[tdplot_screen_coords] (xmin pt,ymin pt) rectangle (xmax pt,ymax pt);
          pgfmathsetmacroa{3}
          pgfmathsetmacror{2/3*sqrt(6)*a}
          path
          coordinate (A) at (a,-a,-a)
          coordinate (B) at (a,a,-a)
          coordinate (C) at (-a,a,-a)
          coordinate (D) at (-a,-a,-a)
          coordinate (E) at ($(A)+ (0,0,2*a)$)
          coordinate (F) at ($(B)+ (0,0,2*a)$)
          coordinate (G) at ($(C)+ (0,0,2*a)$)
          coordinate (H) at ($(D)+ (0,0,2*a)$)
          coordinate (O) at (0,0,0)
          coordinate (I) at (-1/3*a, 1/3*a, -1/3*a)
          ;
          parsecoord(a,a,-a)>(myBx,myBy,myBz)
          parsecoord(-a,a,a)>(myGx,myGy,myGz)
          parsecoord(-a,-a,-a)>(myDx,myDy,myDz)
          defmynormal{VPTD({myDx-myBx},{myDy-myBy},{myDz-myBz})x({myDx-myGx},{myDy-myGy},{myDz-myGz})}
          edeftemp{noexpandparsecoordmynormal>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
          draw[very thick, blue] (G) -- (D) (G) -- (B);
          draw[very thick] (E) --(F) --(G)-- (H) --cycle;
          ifnumAngle<90
          draw[very thick] (D) --(A) --(B) (D) -- (H) (A)--(E) (B) -- (F);
          draw[dashed, thick] (D) -- (C) -- (B) (C) -- (G);
          begin{scope}
          draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          clip (F) -- (G) -- (H) -- (D) -- (A) -- (B) -- cycle [reverseclip];
          draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          end{scope}
          else
          ifnumAngle<180
          draw[very thick] (E) --(A) --(B) -- (C) -- (G) (B) -- (F);
          draw[dashed, thick] (A) -- (D) -- (C) (D) -- (H);
          begin{scope}
          draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          ifnumAngle<150
          clip (G) -- (H) -- (E) -- (A) -- (B) -- cycle [reverseclip];
          else
          clip (B) -- (C) -- (G) -- cycle [reverseclip];
          fi
          draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          end{scope}
          else
          ifnumAngle<180
          draw[very thick] (E) -- (F) -- (B)
          (B) --(C)--(G)--(F)
          (C)--(D) --(H)--(G)--cycle ;
          draw[dashed, thick]
          (B) -- (A) -- (E) (D) --(A) (D) --(C) (D) --(H) (E) --(C) (I) -- (B) (I) -- (G) (I) --(D);
          begin{scope}
          draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          clip (B) -- (C) -- (D) -- (G) -- cycle [reverseclip];
          draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          end{scope}
          else
          ifnumAngle<270
          draw[very thick] (F) -- (B) -- (C) -- (D) -- (H) (C) -- (G);
          draw[dashed, thick] (B) -- (A) -- (D) (A) -- (E);
          begin{scope}
          draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          ifnumAngle<230
          clip (G) -- (C) -- (D) -- cycle [reverseclip];
          draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          else
          clip (G) -- (B) -- (C) -- (D) -- cycle [reverseclip];
          draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          fi
          end{scope}
          else
          draw[very thick] (G) -- (C) -- (D) -- (A) -- (E) (D) -- (H);
          draw[dashed, thick] (A) -- (B) -- (C) (B) -- (F);
          begin{scope}
          draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          ifnumAngle<300
          clip (C) -- (D) -- (G) -- cycle [reverseclip];
          draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          else
          clip (G) -- (D) -- (A) -- (E) -- (H) -- cycle [reverseclip];
          draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
          fi
          end{scope}
          fi
          fi
          fi
          fi

          foreach point/position in {A/below,B/below,C/below,D/right,E/above,F/left,G/above,H/above,O/above,I/below}
          {fill (point) circle (2.0pt);
          node[position=2pt] at (point) {$point$};
          }

          draw[dashed, blue] (B) -- (D);
          path[tdplot_screen_coords] let p1=(current bounding box.south west),
          p2=(current bounding box.north east)
          in [/utils/exec=pgfmathsetmacro{xmin}{min(xmin pt,x1)}
          pgfmathsetmacro{xmax}{max(xmax pt,x2)}
          pgfmathsetmacro{ymin}{min(ymin pt,y1)}
          pgfmathsetmacro{ymax}{max(ymax pt,y2)}
          xdefxmin{xmin}xdefxmax{xmax}xdefymin{ymin}xdefymax{ymax}];
          %node[tdplot_screen_coords] at (current bounding box.center) {angle=Angle};
          SaveBBox
          end{tikzpicture}
          }
          end{document}


          enter image description here






          share|improve this answer
























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            1 Answer
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            1 Answer
            1






            active

            oldest

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            active

            oldest

            votes






            active

            oldest

            votes









            4














            TikZ does not have a 3d engine, so one has to distinguish many cases. I hope this does not contain too many bugs. (There is also something that keeps track of the bounding boxes, meaning you have to compile the file twice.)



            documentclass[border=2mm,12pt,tikz]{standalone} 
            usepackage{tikz-3dplot}
            makeatletter
            newcounter{smuggle}
            DeclareRobustCommandsmuggleone[1]{%
            stepcounter{smuggle}%
            expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%
            aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname
            }
            DeclareRobustCommandsmuggle[2][1]{%
            smuggleone{#2}%
            ifnum#1>1
            aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%
            fi
            }
            defSaveBBox{%
            immediatewrite@mainaux{xdefstringxmin{xmin}relax}
            immediatewrite@mainaux{xdefstringxmax{xmax}relax}
            immediatewrite@mainaux{xdefstringymin{ymin}relax}
            immediatewrite@mainaux{xdefstringymax{ymax}relax}}
            makeatother
            % based on tex.stackexchange.com/a/12033/AAA
            tikzset{reverseclip/.style={insert path={(current bounding box.south west)rectangle
            (current bounding box.north east)} }}

            defparsecoord(#1,#2,#3)>(#4,#5,#6){%
            def#4{#1}%
            def#5{#2}%
            def#6{#3}%
            smuggle{#4}%
            smuggle{#5}%
            smuggle{#6}%
            }
            defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}
            defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}
            defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}
            defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}
            newcommand{RotationAnglesForPlaneWithNormal}[5]{%typeout{N=(#1,#2,#3)}
            foreach XS in {1,-1}
            {foreach YS in {1,-1}
            {pgfmathsetmacro{mybeta}{XS*acos(#3)}
            pgfmathsetmacro{myalpha}{YS*acos(#1/sin(mybeta))}
            pgfmathsetmacro{ntest}{abs(cos(myalpha)*sin(mybeta)-#1)%
            +abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3)}
            ifdimntest pt<0.1pt
            xdef#4{myalpha}
            xdef#5{mybeta}
            fi
            }}
            }
            tikzset{circle in plane with normal/.style args={#1 with radius #2 around #3}{
            /utils/exec={edeftemp{noexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
            temp
            pgfmathsetmacro{myNx}{myNx}
            pgfmathsetmacro{myNy}{myNy}
            pgfmathsetmacro{myNz}{myNz}
            pgfmathsetmacro{myNormalization}{sqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2))}
            pgfmathsetmacro{myNx}{myNx/myNormalization}
            pgfmathsetmacro{myNy}{myNy/myNormalization}
            pgfmathsetmacro{myNz}{myNz/myNormalization}
            % compute the rotation angles that transform us in the corresponding plabe
            RotationAnglesForPlaneWithNormal{myNx}{myNy}{myNz}{tmpalpha}{tmpbeta}
            %typeout{N=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3}
            tdplotsetrotatedcoords{tmpalpha}{tmpbeta}{0}},
            insert path={[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape]
            #3 circle[radius=#2]}
            }}


            begin{document}
            tdplotsetmaincoords{70}{195}
            foreach Angle in {5,15,...,355} % {5}
            {
            tdplotsetmaincoords{70}{Angle}
            begin{tikzpicture}[tdplot_main_coords,scale=1,line join = round, line cap = round]
            ifdefinedxmin
            else
            defxmin{0}
            fi
            ifdefinedxmax
            else
            defxmax{0}
            fi
            ifdefinedymin
            else
            defymin{0}
            fi
            ifdefinedymax
            else
            defymax{0}
            fi
            path[tdplot_screen_coords] (xmin pt,ymin pt) rectangle (xmax pt,ymax pt);
            pgfmathsetmacroa{3}
            pgfmathsetmacror{2/3*sqrt(6)*a}
            path
            coordinate (A) at (a,-a,-a)
            coordinate (B) at (a,a,-a)
            coordinate (C) at (-a,a,-a)
            coordinate (D) at (-a,-a,-a)
            coordinate (E) at ($(A)+ (0,0,2*a)$)
            coordinate (F) at ($(B)+ (0,0,2*a)$)
            coordinate (G) at ($(C)+ (0,0,2*a)$)
            coordinate (H) at ($(D)+ (0,0,2*a)$)
            coordinate (O) at (0,0,0)
            coordinate (I) at (-1/3*a, 1/3*a, -1/3*a)
            ;
            parsecoord(a,a,-a)>(myBx,myBy,myBz)
            parsecoord(-a,a,a)>(myGx,myGy,myGz)
            parsecoord(-a,-a,-a)>(myDx,myDy,myDz)
            defmynormal{VPTD({myDx-myBx},{myDy-myBy},{myDz-myBz})x({myDx-myGx},{myDy-myGy},{myDz-myGz})}
            edeftemp{noexpandparsecoordmynormal>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
            draw[very thick, blue] (G) -- (D) (G) -- (B);
            draw[very thick] (E) --(F) --(G)-- (H) --cycle;
            ifnumAngle<90
            draw[very thick] (D) --(A) --(B) (D) -- (H) (A)--(E) (B) -- (F);
            draw[dashed, thick] (D) -- (C) -- (B) (C) -- (G);
            begin{scope}
            draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            clip (F) -- (G) -- (H) -- (D) -- (A) -- (B) -- cycle [reverseclip];
            draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            end{scope}
            else
            ifnumAngle<180
            draw[very thick] (E) --(A) --(B) -- (C) -- (G) (B) -- (F);
            draw[dashed, thick] (A) -- (D) -- (C) (D) -- (H);
            begin{scope}
            draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            ifnumAngle<150
            clip (G) -- (H) -- (E) -- (A) -- (B) -- cycle [reverseclip];
            else
            clip (B) -- (C) -- (G) -- cycle [reverseclip];
            fi
            draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            end{scope}
            else
            ifnumAngle<180
            draw[very thick] (E) -- (F) -- (B)
            (B) --(C)--(G)--(F)
            (C)--(D) --(H)--(G)--cycle ;
            draw[dashed, thick]
            (B) -- (A) -- (E) (D) --(A) (D) --(C) (D) --(H) (E) --(C) (I) -- (B) (I) -- (G) (I) --(D);
            begin{scope}
            draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            clip (B) -- (C) -- (D) -- (G) -- cycle [reverseclip];
            draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            end{scope}
            else
            ifnumAngle<270
            draw[very thick] (F) -- (B) -- (C) -- (D) -- (H) (C) -- (G);
            draw[dashed, thick] (B) -- (A) -- (D) (A) -- (E);
            begin{scope}
            draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            ifnumAngle<230
            clip (G) -- (C) -- (D) -- cycle [reverseclip];
            draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            else
            clip (G) -- (B) -- (C) -- (D) -- cycle [reverseclip];
            draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            fi
            end{scope}
            else
            draw[very thick] (G) -- (C) -- (D) -- (A) -- (E) (D) -- (H);
            draw[dashed, thick] (A) -- (B) -- (C) (B) -- (F);
            begin{scope}
            draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            ifnumAngle<300
            clip (C) -- (D) -- (G) -- cycle [reverseclip];
            draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            else
            clip (G) -- (D) -- (A) -- (E) -- (H) -- cycle [reverseclip];
            draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
            fi
            end{scope}
            fi
            fi
            fi
            fi

            foreach point/position in {A/below,B/below,C/below,D/right,E/above,F/left,G/above,H/above,O/above,I/below}
            {fill (point) circle (2.0pt);
            node[position=2pt] at (point) {$point$};
            }

            draw[dashed, blue] (B) -- (D);
            path[tdplot_screen_coords] let p1=(current bounding box.south west),
            p2=(current bounding box.north east)
            in [/utils/exec=pgfmathsetmacro{xmin}{min(xmin pt,x1)}
            pgfmathsetmacro{xmax}{max(xmax pt,x2)}
            pgfmathsetmacro{ymin}{min(ymin pt,y1)}
            pgfmathsetmacro{ymax}{max(ymax pt,y2)}
            xdefxmin{xmin}xdefxmax{xmax}xdefymin{ymin}xdefymax{ymax}];
            %node[tdplot_screen_coords] at (current bounding box.center) {angle=Angle};
            SaveBBox
            end{tikzpicture}
            }
            end{document}


            enter image description here






            share|improve this answer




























              4














              TikZ does not have a 3d engine, so one has to distinguish many cases. I hope this does not contain too many bugs. (There is also something that keeps track of the bounding boxes, meaning you have to compile the file twice.)



              documentclass[border=2mm,12pt,tikz]{standalone} 
              usepackage{tikz-3dplot}
              makeatletter
              newcounter{smuggle}
              DeclareRobustCommandsmuggleone[1]{%
              stepcounter{smuggle}%
              expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%
              aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname
              }
              DeclareRobustCommandsmuggle[2][1]{%
              smuggleone{#2}%
              ifnum#1>1
              aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%
              fi
              }
              defSaveBBox{%
              immediatewrite@mainaux{xdefstringxmin{xmin}relax}
              immediatewrite@mainaux{xdefstringxmax{xmax}relax}
              immediatewrite@mainaux{xdefstringymin{ymin}relax}
              immediatewrite@mainaux{xdefstringymax{ymax}relax}}
              makeatother
              % based on tex.stackexchange.com/a/12033/AAA
              tikzset{reverseclip/.style={insert path={(current bounding box.south west)rectangle
              (current bounding box.north east)} }}

              defparsecoord(#1,#2,#3)>(#4,#5,#6){%
              def#4{#1}%
              def#5{#2}%
              def#6{#3}%
              smuggle{#4}%
              smuggle{#5}%
              smuggle{#6}%
              }
              defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}
              defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}
              defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}
              defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}
              newcommand{RotationAnglesForPlaneWithNormal}[5]{%typeout{N=(#1,#2,#3)}
              foreach XS in {1,-1}
              {foreach YS in {1,-1}
              {pgfmathsetmacro{mybeta}{XS*acos(#3)}
              pgfmathsetmacro{myalpha}{YS*acos(#1/sin(mybeta))}
              pgfmathsetmacro{ntest}{abs(cos(myalpha)*sin(mybeta)-#1)%
              +abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3)}
              ifdimntest pt<0.1pt
              xdef#4{myalpha}
              xdef#5{mybeta}
              fi
              }}
              }
              tikzset{circle in plane with normal/.style args={#1 with radius #2 around #3}{
              /utils/exec={edeftemp{noexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
              temp
              pgfmathsetmacro{myNx}{myNx}
              pgfmathsetmacro{myNy}{myNy}
              pgfmathsetmacro{myNz}{myNz}
              pgfmathsetmacro{myNormalization}{sqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2))}
              pgfmathsetmacro{myNx}{myNx/myNormalization}
              pgfmathsetmacro{myNy}{myNy/myNormalization}
              pgfmathsetmacro{myNz}{myNz/myNormalization}
              % compute the rotation angles that transform us in the corresponding plabe
              RotationAnglesForPlaneWithNormal{myNx}{myNy}{myNz}{tmpalpha}{tmpbeta}
              %typeout{N=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3}
              tdplotsetrotatedcoords{tmpalpha}{tmpbeta}{0}},
              insert path={[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape]
              #3 circle[radius=#2]}
              }}


              begin{document}
              tdplotsetmaincoords{70}{195}
              foreach Angle in {5,15,...,355} % {5}
              {
              tdplotsetmaincoords{70}{Angle}
              begin{tikzpicture}[tdplot_main_coords,scale=1,line join = round, line cap = round]
              ifdefinedxmin
              else
              defxmin{0}
              fi
              ifdefinedxmax
              else
              defxmax{0}
              fi
              ifdefinedymin
              else
              defymin{0}
              fi
              ifdefinedymax
              else
              defymax{0}
              fi
              path[tdplot_screen_coords] (xmin pt,ymin pt) rectangle (xmax pt,ymax pt);
              pgfmathsetmacroa{3}
              pgfmathsetmacror{2/3*sqrt(6)*a}
              path
              coordinate (A) at (a,-a,-a)
              coordinate (B) at (a,a,-a)
              coordinate (C) at (-a,a,-a)
              coordinate (D) at (-a,-a,-a)
              coordinate (E) at ($(A)+ (0,0,2*a)$)
              coordinate (F) at ($(B)+ (0,0,2*a)$)
              coordinate (G) at ($(C)+ (0,0,2*a)$)
              coordinate (H) at ($(D)+ (0,0,2*a)$)
              coordinate (O) at (0,0,0)
              coordinate (I) at (-1/3*a, 1/3*a, -1/3*a)
              ;
              parsecoord(a,a,-a)>(myBx,myBy,myBz)
              parsecoord(-a,a,a)>(myGx,myGy,myGz)
              parsecoord(-a,-a,-a)>(myDx,myDy,myDz)
              defmynormal{VPTD({myDx-myBx},{myDy-myBy},{myDz-myBz})x({myDx-myGx},{myDy-myGy},{myDz-myGz})}
              edeftemp{noexpandparsecoordmynormal>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
              draw[very thick, blue] (G) -- (D) (G) -- (B);
              draw[very thick] (E) --(F) --(G)-- (H) --cycle;
              ifnumAngle<90
              draw[very thick] (D) --(A) --(B) (D) -- (H) (A)--(E) (B) -- (F);
              draw[dashed, thick] (D) -- (C) -- (B) (C) -- (G);
              begin{scope}
              draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              clip (F) -- (G) -- (H) -- (D) -- (A) -- (B) -- cycle [reverseclip];
              draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              end{scope}
              else
              ifnumAngle<180
              draw[very thick] (E) --(A) --(B) -- (C) -- (G) (B) -- (F);
              draw[dashed, thick] (A) -- (D) -- (C) (D) -- (H);
              begin{scope}
              draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              ifnumAngle<150
              clip (G) -- (H) -- (E) -- (A) -- (B) -- cycle [reverseclip];
              else
              clip (B) -- (C) -- (G) -- cycle [reverseclip];
              fi
              draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              end{scope}
              else
              ifnumAngle<180
              draw[very thick] (E) -- (F) -- (B)
              (B) --(C)--(G)--(F)
              (C)--(D) --(H)--(G)--cycle ;
              draw[dashed, thick]
              (B) -- (A) -- (E) (D) --(A) (D) --(C) (D) --(H) (E) --(C) (I) -- (B) (I) -- (G) (I) --(D);
              begin{scope}
              draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              clip (B) -- (C) -- (D) -- (G) -- cycle [reverseclip];
              draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              end{scope}
              else
              ifnumAngle<270
              draw[very thick] (F) -- (B) -- (C) -- (D) -- (H) (C) -- (G);
              draw[dashed, thick] (B) -- (A) -- (D) (A) -- (E);
              begin{scope}
              draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              ifnumAngle<230
              clip (G) -- (C) -- (D) -- cycle [reverseclip];
              draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              else
              clip (G) -- (B) -- (C) -- (D) -- cycle [reverseclip];
              draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              fi
              end{scope}
              else
              draw[very thick] (G) -- (C) -- (D) -- (A) -- (E) (D) -- (H);
              draw[dashed, thick] (A) -- (B) -- (C) (B) -- (F);
              begin{scope}
              draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              ifnumAngle<300
              clip (C) -- (D) -- (G) -- cycle [reverseclip];
              draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              else
              clip (G) -- (D) -- (A) -- (E) -- (H) -- cycle [reverseclip];
              draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
              fi
              end{scope}
              fi
              fi
              fi
              fi

              foreach point/position in {A/below,B/below,C/below,D/right,E/above,F/left,G/above,H/above,O/above,I/below}
              {fill (point) circle (2.0pt);
              node[position=2pt] at (point) {$point$};
              }

              draw[dashed, blue] (B) -- (D);
              path[tdplot_screen_coords] let p1=(current bounding box.south west),
              p2=(current bounding box.north east)
              in [/utils/exec=pgfmathsetmacro{xmin}{min(xmin pt,x1)}
              pgfmathsetmacro{xmax}{max(xmax pt,x2)}
              pgfmathsetmacro{ymin}{min(ymin pt,y1)}
              pgfmathsetmacro{ymax}{max(ymax pt,y2)}
              xdefxmin{xmin}xdefxmax{xmax}xdefymin{ymin}xdefymax{ymax}];
              %node[tdplot_screen_coords] at (current bounding box.center) {angle=Angle};
              SaveBBox
              end{tikzpicture}
              }
              end{document}


              enter image description here






              share|improve this answer


























                4












                4








                4







                TikZ does not have a 3d engine, so one has to distinguish many cases. I hope this does not contain too many bugs. (There is also something that keeps track of the bounding boxes, meaning you have to compile the file twice.)



                documentclass[border=2mm,12pt,tikz]{standalone} 
                usepackage{tikz-3dplot}
                makeatletter
                newcounter{smuggle}
                DeclareRobustCommandsmuggleone[1]{%
                stepcounter{smuggle}%
                expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%
                aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname
                }
                DeclareRobustCommandsmuggle[2][1]{%
                smuggleone{#2}%
                ifnum#1>1
                aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%
                fi
                }
                defSaveBBox{%
                immediatewrite@mainaux{xdefstringxmin{xmin}relax}
                immediatewrite@mainaux{xdefstringxmax{xmax}relax}
                immediatewrite@mainaux{xdefstringymin{ymin}relax}
                immediatewrite@mainaux{xdefstringymax{ymax}relax}}
                makeatother
                % based on tex.stackexchange.com/a/12033/AAA
                tikzset{reverseclip/.style={insert path={(current bounding box.south west)rectangle
                (current bounding box.north east)} }}

                defparsecoord(#1,#2,#3)>(#4,#5,#6){%
                def#4{#1}%
                def#5{#2}%
                def#6{#3}%
                smuggle{#4}%
                smuggle{#5}%
                smuggle{#6}%
                }
                defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}
                defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}
                defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}
                defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}
                newcommand{RotationAnglesForPlaneWithNormal}[5]{%typeout{N=(#1,#2,#3)}
                foreach XS in {1,-1}
                {foreach YS in {1,-1}
                {pgfmathsetmacro{mybeta}{XS*acos(#3)}
                pgfmathsetmacro{myalpha}{YS*acos(#1/sin(mybeta))}
                pgfmathsetmacro{ntest}{abs(cos(myalpha)*sin(mybeta)-#1)%
                +abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3)}
                ifdimntest pt<0.1pt
                xdef#4{myalpha}
                xdef#5{mybeta}
                fi
                }}
                }
                tikzset{circle in plane with normal/.style args={#1 with radius #2 around #3}{
                /utils/exec={edeftemp{noexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
                temp
                pgfmathsetmacro{myNx}{myNx}
                pgfmathsetmacro{myNy}{myNy}
                pgfmathsetmacro{myNz}{myNz}
                pgfmathsetmacro{myNormalization}{sqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2))}
                pgfmathsetmacro{myNx}{myNx/myNormalization}
                pgfmathsetmacro{myNy}{myNy/myNormalization}
                pgfmathsetmacro{myNz}{myNz/myNormalization}
                % compute the rotation angles that transform us in the corresponding plabe
                RotationAnglesForPlaneWithNormal{myNx}{myNy}{myNz}{tmpalpha}{tmpbeta}
                %typeout{N=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3}
                tdplotsetrotatedcoords{tmpalpha}{tmpbeta}{0}},
                insert path={[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape]
                #3 circle[radius=#2]}
                }}


                begin{document}
                tdplotsetmaincoords{70}{195}
                foreach Angle in {5,15,...,355} % {5}
                {
                tdplotsetmaincoords{70}{Angle}
                begin{tikzpicture}[tdplot_main_coords,scale=1,line join = round, line cap = round]
                ifdefinedxmin
                else
                defxmin{0}
                fi
                ifdefinedxmax
                else
                defxmax{0}
                fi
                ifdefinedymin
                else
                defymin{0}
                fi
                ifdefinedymax
                else
                defymax{0}
                fi
                path[tdplot_screen_coords] (xmin pt,ymin pt) rectangle (xmax pt,ymax pt);
                pgfmathsetmacroa{3}
                pgfmathsetmacror{2/3*sqrt(6)*a}
                path
                coordinate (A) at (a,-a,-a)
                coordinate (B) at (a,a,-a)
                coordinate (C) at (-a,a,-a)
                coordinate (D) at (-a,-a,-a)
                coordinate (E) at ($(A)+ (0,0,2*a)$)
                coordinate (F) at ($(B)+ (0,0,2*a)$)
                coordinate (G) at ($(C)+ (0,0,2*a)$)
                coordinate (H) at ($(D)+ (0,0,2*a)$)
                coordinate (O) at (0,0,0)
                coordinate (I) at (-1/3*a, 1/3*a, -1/3*a)
                ;
                parsecoord(a,a,-a)>(myBx,myBy,myBz)
                parsecoord(-a,a,a)>(myGx,myGy,myGz)
                parsecoord(-a,-a,-a)>(myDx,myDy,myDz)
                defmynormal{VPTD({myDx-myBx},{myDy-myBy},{myDz-myBz})x({myDx-myGx},{myDy-myGy},{myDz-myGz})}
                edeftemp{noexpandparsecoordmynormal>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
                draw[very thick, blue] (G) -- (D) (G) -- (B);
                draw[very thick] (E) --(F) --(G)-- (H) --cycle;
                ifnumAngle<90
                draw[very thick] (D) --(A) --(B) (D) -- (H) (A)--(E) (B) -- (F);
                draw[dashed, thick] (D) -- (C) -- (B) (C) -- (G);
                begin{scope}
                draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                clip (F) -- (G) -- (H) -- (D) -- (A) -- (B) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                end{scope}
                else
                ifnumAngle<180
                draw[very thick] (E) --(A) --(B) -- (C) -- (G) (B) -- (F);
                draw[dashed, thick] (A) -- (D) -- (C) (D) -- (H);
                begin{scope}
                draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                ifnumAngle<150
                clip (G) -- (H) -- (E) -- (A) -- (B) -- cycle [reverseclip];
                else
                clip (B) -- (C) -- (G) -- cycle [reverseclip];
                fi
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                end{scope}
                else
                ifnumAngle<180
                draw[very thick] (E) -- (F) -- (B)
                (B) --(C)--(G)--(F)
                (C)--(D) --(H)--(G)--cycle ;
                draw[dashed, thick]
                (B) -- (A) -- (E) (D) --(A) (D) --(C) (D) --(H) (E) --(C) (I) -- (B) (I) -- (G) (I) --(D);
                begin{scope}
                draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                clip (B) -- (C) -- (D) -- (G) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                end{scope}
                else
                ifnumAngle<270
                draw[very thick] (F) -- (B) -- (C) -- (D) -- (H) (C) -- (G);
                draw[dashed, thick] (B) -- (A) -- (D) (A) -- (E);
                begin{scope}
                draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                ifnumAngle<230
                clip (G) -- (C) -- (D) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                else
                clip (G) -- (B) -- (C) -- (D) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                fi
                end{scope}
                else
                draw[very thick] (G) -- (C) -- (D) -- (A) -- (E) (D) -- (H);
                draw[dashed, thick] (A) -- (B) -- (C) (B) -- (F);
                begin{scope}
                draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                ifnumAngle<300
                clip (C) -- (D) -- (G) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                else
                clip (G) -- (D) -- (A) -- (E) -- (H) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                fi
                end{scope}
                fi
                fi
                fi
                fi

                foreach point/position in {A/below,B/below,C/below,D/right,E/above,F/left,G/above,H/above,O/above,I/below}
                {fill (point) circle (2.0pt);
                node[position=2pt] at (point) {$point$};
                }

                draw[dashed, blue] (B) -- (D);
                path[tdplot_screen_coords] let p1=(current bounding box.south west),
                p2=(current bounding box.north east)
                in [/utils/exec=pgfmathsetmacro{xmin}{min(xmin pt,x1)}
                pgfmathsetmacro{xmax}{max(xmax pt,x2)}
                pgfmathsetmacro{ymin}{min(ymin pt,y1)}
                pgfmathsetmacro{ymax}{max(ymax pt,y2)}
                xdefxmin{xmin}xdefxmax{xmax}xdefymin{ymin}xdefymax{ymax}];
                %node[tdplot_screen_coords] at (current bounding box.center) {angle=Angle};
                SaveBBox
                end{tikzpicture}
                }
                end{document}


                enter image description here






                share|improve this answer













                TikZ does not have a 3d engine, so one has to distinguish many cases. I hope this does not contain too many bugs. (There is also something that keeps track of the bounding boxes, meaning you have to compile the file twice.)



                documentclass[border=2mm,12pt,tikz]{standalone} 
                usepackage{tikz-3dplot}
                makeatletter
                newcounter{smuggle}
                DeclareRobustCommandsmuggleone[1]{%
                stepcounter{smuggle}%
                expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%
                aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname
                }
                DeclareRobustCommandsmuggle[2][1]{%
                smuggleone{#2}%
                ifnum#1>1
                aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%
                fi
                }
                defSaveBBox{%
                immediatewrite@mainaux{xdefstringxmin{xmin}relax}
                immediatewrite@mainaux{xdefstringxmax{xmax}relax}
                immediatewrite@mainaux{xdefstringymin{ymin}relax}
                immediatewrite@mainaux{xdefstringymax{ymax}relax}}
                makeatother
                % based on tex.stackexchange.com/a/12033/AAA
                tikzset{reverseclip/.style={insert path={(current bounding box.south west)rectangle
                (current bounding box.north east)} }}

                defparsecoord(#1,#2,#3)>(#4,#5,#6){%
                def#4{#1}%
                def#5{#2}%
                def#6{#3}%
                smuggle{#4}%
                smuggle{#5}%
                smuggle{#6}%
                }
                defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}
                defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}
                defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}
                defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}
                newcommand{RotationAnglesForPlaneWithNormal}[5]{%typeout{N=(#1,#2,#3)}
                foreach XS in {1,-1}
                {foreach YS in {1,-1}
                {pgfmathsetmacro{mybeta}{XS*acos(#3)}
                pgfmathsetmacro{myalpha}{YS*acos(#1/sin(mybeta))}
                pgfmathsetmacro{ntest}{abs(cos(myalpha)*sin(mybeta)-#1)%
                +abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3)}
                ifdimntest pt<0.1pt
                xdef#4{myalpha}
                xdef#5{mybeta}
                fi
                }}
                }
                tikzset{circle in plane with normal/.style args={#1 with radius #2 around #3}{
                /utils/exec={edeftemp{noexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
                temp
                pgfmathsetmacro{myNx}{myNx}
                pgfmathsetmacro{myNy}{myNy}
                pgfmathsetmacro{myNz}{myNz}
                pgfmathsetmacro{myNormalization}{sqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2))}
                pgfmathsetmacro{myNx}{myNx/myNormalization}
                pgfmathsetmacro{myNy}{myNy/myNormalization}
                pgfmathsetmacro{myNz}{myNz/myNormalization}
                % compute the rotation angles that transform us in the corresponding plabe
                RotationAnglesForPlaneWithNormal{myNx}{myNy}{myNz}{tmpalpha}{tmpbeta}
                %typeout{N=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3}
                tdplotsetrotatedcoords{tmpalpha}{tmpbeta}{0}},
                insert path={[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape]
                #3 circle[radius=#2]}
                }}


                begin{document}
                tdplotsetmaincoords{70}{195}
                foreach Angle in {5,15,...,355} % {5}
                {
                tdplotsetmaincoords{70}{Angle}
                begin{tikzpicture}[tdplot_main_coords,scale=1,line join = round, line cap = round]
                ifdefinedxmin
                else
                defxmin{0}
                fi
                ifdefinedxmax
                else
                defxmax{0}
                fi
                ifdefinedymin
                else
                defymin{0}
                fi
                ifdefinedymax
                else
                defymax{0}
                fi
                path[tdplot_screen_coords] (xmin pt,ymin pt) rectangle (xmax pt,ymax pt);
                pgfmathsetmacroa{3}
                pgfmathsetmacror{2/3*sqrt(6)*a}
                path
                coordinate (A) at (a,-a,-a)
                coordinate (B) at (a,a,-a)
                coordinate (C) at (-a,a,-a)
                coordinate (D) at (-a,-a,-a)
                coordinate (E) at ($(A)+ (0,0,2*a)$)
                coordinate (F) at ($(B)+ (0,0,2*a)$)
                coordinate (G) at ($(C)+ (0,0,2*a)$)
                coordinate (H) at ($(D)+ (0,0,2*a)$)
                coordinate (O) at (0,0,0)
                coordinate (I) at (-1/3*a, 1/3*a, -1/3*a)
                ;
                parsecoord(a,a,-a)>(myBx,myBy,myBz)
                parsecoord(-a,a,a)>(myGx,myGy,myGz)
                parsecoord(-a,-a,-a)>(myDx,myDy,myDz)
                defmynormal{VPTD({myDx-myBx},{myDy-myBy},{myDz-myBz})x({myDx-myGx},{myDy-myGy},{myDz-myGz})}
                edeftemp{noexpandparsecoordmynormal>(noexpandmyNx,noexpandmyNy,noexpandmyNz)}
                draw[very thick, blue] (G) -- (D) (G) -- (B);
                draw[very thick] (E) --(F) --(G)-- (H) --cycle;
                ifnumAngle<90
                draw[very thick] (D) --(A) --(B) (D) -- (H) (A)--(E) (B) -- (F);
                draw[dashed, thick] (D) -- (C) -- (B) (C) -- (G);
                begin{scope}
                draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                clip (F) -- (G) -- (H) -- (D) -- (A) -- (B) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                end{scope}
                else
                ifnumAngle<180
                draw[very thick] (E) --(A) --(B) -- (C) -- (G) (B) -- (F);
                draw[dashed, thick] (A) -- (D) -- (C) (D) -- (H);
                begin{scope}
                draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                ifnumAngle<150
                clip (G) -- (H) -- (E) -- (A) -- (B) -- cycle [reverseclip];
                else
                clip (B) -- (C) -- (G) -- cycle [reverseclip];
                fi
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                end{scope}
                else
                ifnumAngle<180
                draw[very thick] (E) -- (F) -- (B)
                (B) --(C)--(G)--(F)
                (C)--(D) --(H)--(G)--cycle ;
                draw[dashed, thick]
                (B) -- (A) -- (E) (D) --(A) (D) --(C) (D) --(H) (E) --(C) (I) -- (B) (I) -- (G) (I) --(D);
                begin{scope}
                draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                clip (B) -- (C) -- (D) -- (G) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                end{scope}
                else
                ifnumAngle<270
                draw[very thick] (F) -- (B) -- (C) -- (D) -- (H) (C) -- (G);
                draw[dashed, thick] (B) -- (A) -- (D) (A) -- (E);
                begin{scope}
                draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                ifnumAngle<230
                clip (G) -- (C) -- (D) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                else
                clip (G) -- (B) -- (C) -- (D) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                fi
                end{scope}
                else
                draw[very thick] (G) -- (C) -- (D) -- (A) -- (E) (D) -- (H);
                draw[dashed, thick] (A) -- (B) -- (C) (B) -- (F);
                begin{scope}
                draw[red,dashed,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                ifnumAngle<300
                clip (C) -- (D) -- (G) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                else
                clip (G) -- (D) -- (A) -- (E) -- (H) -- cycle [reverseclip];
                draw[red,thick,circle in plane with normal={{mynormal} with radius {r} around (I)}];
                fi
                end{scope}
                fi
                fi
                fi
                fi

                foreach point/position in {A/below,B/below,C/below,D/right,E/above,F/left,G/above,H/above,O/above,I/below}
                {fill (point) circle (2.0pt);
                node[position=2pt] at (point) {$point$};
                }

                draw[dashed, blue] (B) -- (D);
                path[tdplot_screen_coords] let p1=(current bounding box.south west),
                p2=(current bounding box.north east)
                in [/utils/exec=pgfmathsetmacro{xmin}{min(xmin pt,x1)}
                pgfmathsetmacro{xmax}{max(xmax pt,x2)}
                pgfmathsetmacro{ymin}{min(ymin pt,y1)}
                pgfmathsetmacro{ymax}{max(ymax pt,y2)}
                xdefxmin{xmin}xdefxmax{xmax}xdefymin{ymin}xdefymax{ymax}];
                %node[tdplot_screen_coords] at (current bounding box.center) {angle=Angle};
                SaveBBox
                end{tikzpicture}
                }
                end{document}


                enter image description here







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                answered 13 hours ago









                marmotmarmot

                115k5146277




                115k5146277






























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