Kdjykuj

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.

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

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?

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}