Bsrgvty

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 
usepackagetikz,tikz-3dplot 
usepackagefouriernc 
usepackagetkz-euclide 
usetkzobjall 
makeatletter 
newcountersmuggle 
DeclareRobustCommandsmuggleone[1]% 
 stepcountersmuggle% 
 expandafterglobalexpandafterletcsname smuggle@arabicsmuggleendcsname#1% 
 aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabicsmuggleendcsname 
 
DeclareRobustCommandsmuggle[2][1]% 
 smuggleone#2% 
 ifnum#1>1 
 aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2% 
 fi 
 
makeatother 
% based on tex.stackexchange.com/a/12033/… 
tikzsetreverseclip/.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)) 
newcommandRotationAnglesForPlaneWithNormal[5]%typeoutN=(#1,#2,#3) 
 foreach XS in 1,-1 
 foreach YS in 1,-1 
 pgfmathsetmacromybetaXS*acos(#3) 
 pgfmathsetmacromyalphaYS*acos(#1/sin(mybeta)) 
 pgfmathsetmacrontestabs(cos(myalpha)*sin(mybeta)-#1)% 
 +abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3) 
 ifdimntest pt<0.1pt 
 xdef#4myalpha 
 xdef#5mybeta 
 fi 
 
 
tikzsetcircle in plane with normal/.style args=#1 with radius #2 around #3 
 /utils/exec=edeftempnoexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz) 
 temp 
 pgfmathsetmacromyNxmyNx 
 pgfmathsetmacromyNymyNy 
 pgfmathsetmacromyNzmyNz 
 pgfmathsetmacromyNormalizationsqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2)) 
 pgfmathsetmacromyNxmyNx/myNormalization 
 pgfmathsetmacromyNymyNy/myNormalization 
 pgfmathsetmacromyNzmyNz/myNormalization 
 % compute the rotation angles that transform us in the corresponding plabe 
 RotationAnglesForPlaneWithNormalmyNxmyNymyNztmpalphatmpbeta 
 %typeoutN=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3 
 tdplotsetrotatedcoordstmpalphatmpbeta0, 
 insert path=[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape]
 #3 circle[radius=#2] 
 


begindocument 
 tdplotsetmaincoords70195 
 begintikzpicture[tdplot_main_coords,scale=1,line join = round, line cap = round] 

 pgfmathsetmacroa3 
 pgfmathsetmacror2/3*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) 
 defmynormalVPTD(myDx-myBx,myDy-myBy,myDz-myBz)x(myDx-myGx,myDy-myGy,myDz-myGz) 
 edeftempnoexpandparsecoordmynormal>(noexpandmyNx,noexpandmyNy,noexpandmyNz) 
 beginscope 
 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)]; 
 endscope 
 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) $point$; 
 

 beginscope[tdplot_screen_coords] 
 fill[ball color=gray, opacity=0.1] (I) circle (r); % 3D lighting effect 
 endscope 

 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); 
 endtikzpicture 
enddocument

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 
usepackagetikz-3dplot 
makeatletter 
newcountersmuggle 
DeclareRobustCommandsmuggleone[1]% 
stepcountersmuggle% 
expandafterglobalexpandafterletcsname smuggle@arabicsmuggleendcsname#1% 
aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabicsmuggleendcsname 
 
DeclareRobustCommandsmuggle[2][1]% 
smuggleone#2% 
ifnum#1>1 
aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2% 
fi 
 
defSaveBBox%
immediatewrite@mainauxxdefstringxminxminrelax
immediatewrite@mainauxxdefstringxmaxxmaxrelax
immediatewrite@mainauxxdefstringyminyminrelax
immediatewrite@mainauxxdefstringymaxymaxrelax
makeatother 
% based on tex.stackexchange.com/a/12033/AAA 
tikzsetreverseclip/.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)) 
newcommandRotationAnglesForPlaneWithNormal[5]%typeoutN=(#1,#2,#3) 
foreach XS in 1,-1 
foreach YS in 1,-1 
pgfmathsetmacromybetaXS*acos(#3) 
pgfmathsetmacromyalphaYS*acos(#1/sin(mybeta)) 
pgfmathsetmacrontestabs(cos(myalpha)*sin(mybeta)-#1)% 
+abs(sin(myalpha)*sin(mybeta)-#2)+abs(cos(mybeta)-#3) 
ifdimntest pt<0.1pt 
xdef#4myalpha 
xdef#5mybeta 
fi 
 
 
tikzsetcircle in plane with normal/.style args=#1 with radius #2 around #3 
/utils/exec=edeftempnoexpandparsecoord#1>(noexpandmyNx,noexpandmyNy,noexpandmyNz) 
temp 
pgfmathsetmacromyNxmyNx 
pgfmathsetmacromyNymyNy 
pgfmathsetmacromyNzmyNz 
pgfmathsetmacromyNormalizationsqrt(pow(myNx,2)+pow(myNy,2)+pow(myNz,2)) 
pgfmathsetmacromyNxmyNx/myNormalization 
pgfmathsetmacromyNymyNy/myNormalization 
pgfmathsetmacromyNzmyNz/myNormalization 
% compute the rotation angles that transform us in the corresponding plabe 
RotationAnglesForPlaneWithNormalmyNxmyNymyNztmpalphatmpbeta 
%typeoutN=(myNx,myNy,myNz),alpha=tmpalpha,beta=tmpbeta,r=#2,#3 
tdplotsetrotatedcoordstmpalphatmpbeta0, 
insert path=[tdplot_rotated_coords,canvas is xy plane at z=0,transform shape] 
#3 circle[radius=#2] 
 


begindocument 
tdplotsetmaincoords70195 
foreach Angle in 5,15,...,355 % 5

tdplotsetmaincoords70Angle 
begintikzpicture[tdplot_main_coords,scale=1,line join = round, line cap = round] 
ifdefinedxmin
else
defxmin0
fi
ifdefinedxmax
else
defxmax0
fi
ifdefinedymin
else
defymin0
fi
ifdefinedymax
else
defymax0
fi
path[tdplot_screen_coords] (xmin pt,ymin pt) rectangle (xmax pt,ymax pt);
pgfmathsetmacroa3 
pgfmathsetmacror2/3*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) 
defmynormalVPTD(myDx-myBx,myDy-myBy,myDz-myBz)x(myDx-myGx,myDy-myGy,myDz-myGz) 
edeftempnoexpandparsecoordmynormal>(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);
 beginscope 
 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)]; 
 endscope 
else
 ifnumAngle<180
 draw[very thick] (E) --(A) --(B) -- (C) -- (G) (B) -- (F);
 draw[dashed, thick] (A) -- (D) -- (C) (D) -- (H);
 beginscope 
 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)]; 
 endscope 
 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); 
 beginscope 
 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)]; 
 endscope 
 else
 ifnumAngle<270
 draw[very thick] (F) -- (B) -- (C) -- (D) -- (H) (C) -- (G);
 draw[dashed, thick] (B) -- (A) -- (D) (A) -- (E);
 beginscope 
 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 
 endscope 
 else
 draw[very thick] (G) -- (C) -- (D) -- (A) -- (E) (D) -- (H);
 draw[dashed, thick] (A) -- (B) -- (C) (B) -- (F);
 beginscope 
 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
 endscope 
 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=pgfmathsetmacroxminmin(xmin pt,x1)
pgfmathsetmacroxmaxmax(xmax pt,x2)
pgfmathsetmacroyminmin(ymin pt,y1)
pgfmathsetmacroymaxmax(ymax pt,y2)
xdefxminxminxdefxmaxxmaxxdefyminyminxdefymaxymax];
%node[tdplot_screen_coords] at (current bounding box.center) angle=Angle;
SaveBBox
endtikzpicture

enddocument