How can I make a cone from a cube and view the cube with different angles?
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:
- How can I draw some generators (not
CB, CG, CD
) of the cone? - How can I view the cube with different angles?
tikz-pgf tikz-3dplot
add a comment |
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:
- How can I draw some generators (not
CB, CG, CD
) of the cone? - How can I view the cube with different angles?
tikz-pgf tikz-3dplot
add a comment |
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:
- How can I draw some generators (not
CB, CG, CD
) of the cone? - How can I view the cube with different angles?
tikz-pgf tikz-3dplot
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:
- How can I draw some generators (not
CB, CG, CD
) of the cone? - How can I view the cube with different angles?
tikz-pgf tikz-3dplot
tikz-pgf tikz-3dplot
edited Apr 6 at 12:39
TeXnician
25.9k63491
25.9k63491
asked Apr 6 at 11:47
minhthien_2016minhthien_2016
1,4741917
1,4741917
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1 Answer
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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}
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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}
add a comment |
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}
add a comment |
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}
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}
answered Apr 6 at 14:01
marmotmarmot
116k5149280
116k5149280
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