Intersection of a line with a plane, where is wrong in third way?
1
Let SABCD be a pyramid, SA perpendicular to the plane ABC, the base of pyramid is a rectangle,SA=h, AB=a, AD=b. A plane P passing A and perpendicular to the line SC cut the lines SB, SD, SC respectively at E, F, K.
I tried it in three ways.
First way
documentclass[border=3.14mm,12pt,tikz]{standalone}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
usetikzlibrary{intersections,calc,backgrounds}
begin{document}
tdplotsetmaincoords{60}{120}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h)
coordinate (E) at ({a*h^2/(a^2+h^2)}, 0, {a^2*h/(a^2+h^2)})
coordinate (F) at (0, {b*h^2/(b^2+h^2)}, {b^2*h/(b^2+h^2)})
coordinate (K) at ({a*h^2/(a^2+b^2+h^2)}, {b*h^2/(a^2+b^2+h^2)}, {(a^2+b^2)*h/(a^2+b^2+h^2)});
begin{scope}
draw [dashed, thick, name path=B--D] (B) -- (D);
draw [dashed, thick, name path=C--A] (C) -- (A);
path [name intersections={of=B--D and C--A,by=O}];
end{scope}
begin{scope}
draw [dashed, thick, name path=S--O] (S) -- (O);
draw [dashed, thick, name path=E--F] (E) -- (F);
path [name intersections={of=S--O and E--F,by=I}];
end{scope}
begin{scope}
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);
draw [thick, dashed] (A) -- (K) (E) -- (F) ;
tkzMarkRightAngle(S,A,D)
tkzMarkRightAngle(S,A,B)
tkzMarkRightAngle(A,B,C)
tkzMarkRightAngle(B,A,D)
tkzMarkRightAngle(A,F,D)
tkzMarkRightAngle(A,E,B)
tkzMarkRightAngle(A,K,C)
end{scope}
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
Second way
documentclass[border=3mm,12pt]{standalone}
usepackage{fouriernc}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
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
}
usetikzlibrary{intersections,calc,backgrounds}
tikzset{projection of point/.style args={(#1,#2,#3) on line through (#4,#5,#6)
and (#7,#8,#9)}{%
/utils/exec=pgfmathsetmacro{myprefactor}{((#1-#4)*(#7-#4)+(#2-#5)*(#8-#5)+(#3-#6)*(#9-#6))/((#7-#4)*(#7-#4)+(#8-#5)*(#8-#5)+(#9-#6)*(#9-#6))},
insert path={%
({#4+myprefactor*(#7-#4)},{#5+myprefactor*(#8-#5)},{#6+myprefactor*(#9-#6)})}
}}
begin{document}
tdplotsetmaincoords{60}{120}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h);
path[projection of point={(0,0,0) on line through (a,0,0) and (0,0,h)}]
coordinate (E)
[projection of point={(0,0,0) on line through (0,0,h) and (0,b,0) }]
coordinate (F)
[projection of point={(0,0,0) on line through (0,0,h) and (a,b,0) }]
coordinate (K);
begin{scope}
draw [dashed, thick, name path=B--D] (B) -- (D);
draw [dashed, thick, name path=C--A] (C) -- (A);
path [name intersections={of=B--D and C--A,by=O}];
end{scope}
begin{scope}
draw [dashed, thick, name path=S--O] (S) -- (O);
draw [dashed, thick, name path=E--F] (E) -- (F);
path [name intersections={of=S--O and E--F,by=I}];
end{scope}
begin{scope}
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);
draw [thick, dashed] (A) -- (K) (E) -- (F) ;
tkzMarkRightAngle(S,A,D)
tkzMarkRightAngle(S,A,B)
tkzMarkRightAngle(A,B,C)
tkzMarkRightAngle(B,A,D)
tkzMarkRightAngle(A,F,D)
tkzMarkRightAngle(A,E,B)
tkzMarkRightAngle(A,K,C)
end{scope}
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
Third way
Base on the answer Is there a command to find coordinates of projection of a point on a plane?
I defined command defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)} and tried
documentclass[border=3.14mm,12pt,tikz]{standalone}
usepackage{tikz,tikz-3dplot}
%% smuggling from https://tex.stackexchange.com/a/470979/121799
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
}
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+#2*#5+#3*#6}
defVPTD(#1,#2,#3)x(#4,#5,#6){(#2*#6-#3*#5,#3*#4-#1*#6,#1*#5-#2*#4)}
defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)}
defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+#4,#2+#5,#3+#6)}
tikzset{intersection of line trough/.style args={#1 and #2 with plane
containing #3 and normal #4}{%
/utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-SPTD#1.#4)}
parsecoord#1>(myAx,myAy,myAz)
parsecoord#2>(myBx,myBy,myBz)
ifdimltest pt<0.01pt
typeout{Planespace andspace linespace arespace parallel!ltest}
pgfmathsetmacro{myd}{0}
else
pgfmathsetmacro{myd}{(SPTD#3.#4-SPTD#1.#4)/(SPTD#2.#4-SPTD#1.#4)}
fi
%typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}
defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}
smugglemyP},
insert path={%
myP}
}}
begin{document}
tdplotsetmaincoords{75}{110}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h);
defmynormal{VecMinus(a,b,0)-(0,0,h)}
typeout{mynormal:(a,b,-h)}
path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (E)
[intersection of line trough={(0,0,h) and (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (F)
[intersection of line trough={(0,0,h) and (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (K);
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C);
draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;
draw [thick] (E) -- (K) -- (F) ;
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
I got
tikz-pgf tikz-3dplot
asked 11 mins ago
minhthien_2016minhthien_2016
1,180816
add a comment |
1
Let SABCD be a pyramid, SA perpendicular to the plane ABC, the base of pyramid is a rectangle,SA=h, AB=a, AD=b. A plane P passing A and perpendicular to the line SC cut the lines SB, SD, SC respectively at E, F, K.
I tried it in three ways.
First way
documentclass[border=3.14mm,12pt,tikz]{standalone}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
usetikzlibrary{intersections,calc,backgrounds}
begin{document}
tdplotsetmaincoords{60}{120}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h)
coordinate (E) at ({a*h^2/(a^2+h^2)}, 0, {a^2*h/(a^2+h^2)})
coordinate (F) at (0, {b*h^2/(b^2+h^2)}, {b^2*h/(b^2+h^2)})
coordinate (K) at ({a*h^2/(a^2+b^2+h^2)}, {b*h^2/(a^2+b^2+h^2)}, {(a^2+b^2)*h/(a^2+b^2+h^2)});
begin{scope}
draw [dashed, thick, name path=B--D] (B) -- (D);
draw [dashed, thick, name path=C--A] (C) -- (A);
path [name intersections={of=B--D and C--A,by=O}];
end{scope}
begin{scope}
draw [dashed, thick, name path=S--O] (S) -- (O);
draw [dashed, thick, name path=E--F] (E) -- (F);
path [name intersections={of=S--O and E--F,by=I}];
end{scope}
begin{scope}
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);
draw [thick, dashed] (A) -- (K) (E) -- (F) ;
tkzMarkRightAngle(S,A,D)
tkzMarkRightAngle(S,A,B)
tkzMarkRightAngle(A,B,C)
tkzMarkRightAngle(B,A,D)
tkzMarkRightAngle(A,F,D)
tkzMarkRightAngle(A,E,B)
tkzMarkRightAngle(A,K,C)
end{scope}
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
Second way
documentclass[border=3mm,12pt]{standalone}
usepackage{fouriernc}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
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
}
usetikzlibrary{intersections,calc,backgrounds}
tikzset{projection of point/.style args={(#1,#2,#3) on line through (#4,#5,#6)
and (#7,#8,#9)}{%
/utils/exec=pgfmathsetmacro{myprefactor}{((#1-#4)*(#7-#4)+(#2-#5)*(#8-#5)+(#3-#6)*(#9-#6))/((#7-#4)*(#7-#4)+(#8-#5)*(#8-#5)+(#9-#6)*(#9-#6))},
insert path={%
({#4+myprefactor*(#7-#4)},{#5+myprefactor*(#8-#5)},{#6+myprefactor*(#9-#6)})}
}}
begin{document}
tdplotsetmaincoords{60}{120}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h);
path[projection of point={(0,0,0) on line through (a,0,0) and (0,0,h)}]
coordinate (E)
[projection of point={(0,0,0) on line through (0,0,h) and (0,b,0) }]
coordinate (F)
[projection of point={(0,0,0) on line through (0,0,h) and (a,b,0) }]
coordinate (K);
begin{scope}
draw [dashed, thick, name path=B--D] (B) -- (D);
draw [dashed, thick, name path=C--A] (C) -- (A);
path [name intersections={of=B--D and C--A,by=O}];
end{scope}
begin{scope}
draw [dashed, thick, name path=S--O] (S) -- (O);
draw [dashed, thick, name path=E--F] (E) -- (F);
path [name intersections={of=S--O and E--F,by=I}];
end{scope}
begin{scope}
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);
draw [thick, dashed] (A) -- (K) (E) -- (F) ;
tkzMarkRightAngle(S,A,D)
tkzMarkRightAngle(S,A,B)
tkzMarkRightAngle(A,B,C)
tkzMarkRightAngle(B,A,D)
tkzMarkRightAngle(A,F,D)
tkzMarkRightAngle(A,E,B)
tkzMarkRightAngle(A,K,C)
end{scope}
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
Third way
Base on the answer Is there a command to find coordinates of projection of a point on a plane?
I defined command defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)} and tried
documentclass[border=3.14mm,12pt,tikz]{standalone}
usepackage{tikz,tikz-3dplot}
%% smuggling from https://tex.stackexchange.com/a/470979/121799
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
}
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+#2*#5+#3*#6}
defVPTD(#1,#2,#3)x(#4,#5,#6){(#2*#6-#3*#5,#3*#4-#1*#6,#1*#5-#2*#4)}
defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)}
defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+#4,#2+#5,#3+#6)}
tikzset{intersection of line trough/.style args={#1 and #2 with plane
containing #3 and normal #4}{%
/utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-SPTD#1.#4)}
parsecoord#1>(myAx,myAy,myAz)
parsecoord#2>(myBx,myBy,myBz)
ifdimltest pt<0.01pt
typeout{Planespace andspace linespace arespace parallel!ltest}
pgfmathsetmacro{myd}{0}
else
pgfmathsetmacro{myd}{(SPTD#3.#4-SPTD#1.#4)/(SPTD#2.#4-SPTD#1.#4)}
fi
%typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}
defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}
smugglemyP},
insert path={%
myP}
}}
begin{document}
tdplotsetmaincoords{75}{110}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h);
defmynormal{VecMinus(a,b,0)-(0,0,h)}
typeout{mynormal:(a,b,-h)}
path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (E)
[intersection of line trough={(0,0,h) and (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (F)
[intersection of line trough={(0,0,h) and (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (K);
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C);
draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;
draw [thick] (E) -- (K) -- (F) ;
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
I got
tikz-pgf tikz-3dplot
asked 11 mins ago
minhthien_2016minhthien_2016
1,180816
add a comment |
1
1
1
Let SABCD be a pyramid, SA perpendicular to the plane ABC, the base of pyramid is a rectangle,SA=h, AB=a, AD=b. A plane P passing A and perpendicular to the line SC cut the lines SB, SD, SC respectively at E, F, K.
I tried it in three ways.
First way
documentclass[border=3.14mm,12pt,tikz]{standalone}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
usetikzlibrary{intersections,calc,backgrounds}
begin{document}
tdplotsetmaincoords{60}{120}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h)
coordinate (E) at ({a*h^2/(a^2+h^2)}, 0, {a^2*h/(a^2+h^2)})
coordinate (F) at (0, {b*h^2/(b^2+h^2)}, {b^2*h/(b^2+h^2)})
coordinate (K) at ({a*h^2/(a^2+b^2+h^2)}, {b*h^2/(a^2+b^2+h^2)}, {(a^2+b^2)*h/(a^2+b^2+h^2)});
begin{scope}
draw [dashed, thick, name path=B--D] (B) -- (D);
draw [dashed, thick, name path=C--A] (C) -- (A);
path [name intersections={of=B--D and C--A,by=O}];
end{scope}
begin{scope}
draw [dashed, thick, name path=S--O] (S) -- (O);
draw [dashed, thick, name path=E--F] (E) -- (F);
path [name intersections={of=S--O and E--F,by=I}];
end{scope}
begin{scope}
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);
draw [thick, dashed] (A) -- (K) (E) -- (F) ;
tkzMarkRightAngle(S,A,D)
tkzMarkRightAngle(S,A,B)
tkzMarkRightAngle(A,B,C)
tkzMarkRightAngle(B,A,D)
tkzMarkRightAngle(A,F,D)
tkzMarkRightAngle(A,E,B)
tkzMarkRightAngle(A,K,C)
end{scope}
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
Second way
documentclass[border=3mm,12pt]{standalone}
usepackage{fouriernc}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
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
}
usetikzlibrary{intersections,calc,backgrounds}
tikzset{projection of point/.style args={(#1,#2,#3) on line through (#4,#5,#6)
and (#7,#8,#9)}{%
/utils/exec=pgfmathsetmacro{myprefactor}{((#1-#4)*(#7-#4)+(#2-#5)*(#8-#5)+(#3-#6)*(#9-#6))/((#7-#4)*(#7-#4)+(#8-#5)*(#8-#5)+(#9-#6)*(#9-#6))},
insert path={%
({#4+myprefactor*(#7-#4)},{#5+myprefactor*(#8-#5)},{#6+myprefactor*(#9-#6)})}
}}
begin{document}
tdplotsetmaincoords{60}{120}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h);
path[projection of point={(0,0,0) on line through (a,0,0) and (0,0,h)}]
coordinate (E)
[projection of point={(0,0,0) on line through (0,0,h) and (0,b,0) }]
coordinate (F)
[projection of point={(0,0,0) on line through (0,0,h) and (a,b,0) }]
coordinate (K);
begin{scope}
draw [dashed, thick, name path=B--D] (B) -- (D);
draw [dashed, thick, name path=C--A] (C) -- (A);
path [name intersections={of=B--D and C--A,by=O}];
end{scope}
begin{scope}
draw [dashed, thick, name path=S--O] (S) -- (O);
draw [dashed, thick, name path=E--F] (E) -- (F);
path [name intersections={of=S--O and E--F,by=I}];
end{scope}
begin{scope}
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);
draw [thick, dashed] (A) -- (K) (E) -- (F) ;
tkzMarkRightAngle(S,A,D)
tkzMarkRightAngle(S,A,B)
tkzMarkRightAngle(A,B,C)
tkzMarkRightAngle(B,A,D)
tkzMarkRightAngle(A,F,D)
tkzMarkRightAngle(A,E,B)
tkzMarkRightAngle(A,K,C)
end{scope}
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
Third way
Base on the answer Is there a command to find coordinates of projection of a point on a plane?
I defined command defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)} and tried
documentclass[border=3.14mm,12pt,tikz]{standalone}
usepackage{tikz,tikz-3dplot}
%% smuggling from https://tex.stackexchange.com/a/470979/121799
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
}
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+#2*#5+#3*#6}
defVPTD(#1,#2,#3)x(#4,#5,#6){(#2*#6-#3*#5,#3*#4-#1*#6,#1*#5-#2*#4)}
defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)}
defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+#4,#2+#5,#3+#6)}
tikzset{intersection of line trough/.style args={#1 and #2 with plane
containing #3 and normal #4}{%
/utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-SPTD#1.#4)}
parsecoord#1>(myAx,myAy,myAz)
parsecoord#2>(myBx,myBy,myBz)
ifdimltest pt<0.01pt
typeout{Planespace andspace linespace arespace parallel!ltest}
pgfmathsetmacro{myd}{0}
else
pgfmathsetmacro{myd}{(SPTD#3.#4-SPTD#1.#4)/(SPTD#2.#4-SPTD#1.#4)}
fi
%typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}
defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}
smugglemyP},
insert path={%
myP}
}}
begin{document}
tdplotsetmaincoords{75}{110}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h);
defmynormal{VecMinus(a,b,0)-(0,0,h)}
typeout{mynormal:(a,b,-h)}
path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (E)
[intersection of line trough={(0,0,h) and (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (F)
[intersection of line trough={(0,0,h) and (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (K);
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C);
draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;
draw [thick] (E) -- (K) -- (F) ;
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
I got
tikz-pgf tikz-3dplot
asked 11 mins ago
minhthien_2016minhthien_2016
1,180816
Let SABCD be a pyramid, SA perpendicular to the plane ABC, the base of pyramid is a rectangle,SA=h, AB=a, AD=b. A plane P passing A and perpendicular to the line SC cut the lines SB, SD, SC respectively at E, F, K.
I tried it in three ways.
First way
documentclass[border=3.14mm,12pt,tikz]{standalone}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
usetikzlibrary{intersections,calc,backgrounds}
begin{document}
tdplotsetmaincoords{60}{120}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h)
coordinate (E) at ({a*h^2/(a^2+h^2)}, 0, {a^2*h/(a^2+h^2)})
coordinate (F) at (0, {b*h^2/(b^2+h^2)}, {b^2*h/(b^2+h^2)})
coordinate (K) at ({a*h^2/(a^2+b^2+h^2)}, {b*h^2/(a^2+b^2+h^2)}, {(a^2+b^2)*h/(a^2+b^2+h^2)});
begin{scope}
draw [dashed, thick, name path=B--D] (B) -- (D);
draw [dashed, thick, name path=C--A] (C) -- (A);
path [name intersections={of=B--D and C--A,by=O}];
end{scope}
begin{scope}
draw [dashed, thick, name path=S--O] (S) -- (O);
draw [dashed, thick, name path=E--F] (E) -- (F);
path [name intersections={of=S--O and E--F,by=I}];
end{scope}
begin{scope}
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);
draw [thick, dashed] (A) -- (K) (E) -- (F) ;
tkzMarkRightAngle(S,A,D)
tkzMarkRightAngle(S,A,B)
tkzMarkRightAngle(A,B,C)
tkzMarkRightAngle(B,A,D)
tkzMarkRightAngle(A,F,D)
tkzMarkRightAngle(A,E,B)
tkzMarkRightAngle(A,K,C)
end{scope}
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
Second way
documentclass[border=3mm,12pt]{standalone}
usepackage{fouriernc}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
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
}
usetikzlibrary{intersections,calc,backgrounds}
tikzset{projection of point/.style args={(#1,#2,#3) on line through (#4,#5,#6)
and (#7,#8,#9)}{%
/utils/exec=pgfmathsetmacro{myprefactor}{((#1-#4)*(#7-#4)+(#2-#5)*(#8-#5)+(#3-#6)*(#9-#6))/((#7-#4)*(#7-#4)+(#8-#5)*(#8-#5)+(#9-#6)*(#9-#6))},
insert path={%
({#4+myprefactor*(#7-#4)},{#5+myprefactor*(#8-#5)},{#6+myprefactor*(#9-#6)})}
}}
begin{document}
tdplotsetmaincoords{60}{120}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h);
path[projection of point={(0,0,0) on line through (a,0,0) and (0,0,h)}]
coordinate (E)
[projection of point={(0,0,0) on line through (0,0,h) and (0,b,0) }]
coordinate (F)
[projection of point={(0,0,0) on line through (0,0,h) and (a,b,0) }]
coordinate (K);
begin{scope}
draw [dashed, thick, name path=B--D] (B) -- (D);
draw [dashed, thick, name path=C--A] (C) -- (A);
path [name intersections={of=B--D and C--A,by=O}];
end{scope}
begin{scope}
draw [dashed, thick, name path=S--O] (S) -- (O);
draw [dashed, thick, name path=E--F] (E) -- (F);
path [name intersections={of=S--O and E--F,by=I}];
end{scope}
begin{scope}
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);
draw [thick, dashed] (A) -- (K) (E) -- (F) ;
tkzMarkRightAngle(S,A,D)
tkzMarkRightAngle(S,A,B)
tkzMarkRightAngle(A,B,C)
tkzMarkRightAngle(B,A,D)
tkzMarkRightAngle(A,F,D)
tkzMarkRightAngle(A,E,B)
tkzMarkRightAngle(A,K,C)
end{scope}
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
Third way
Base on the answer Is there a command to find coordinates of projection of a point on a plane?
I defined command defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)} and tried
documentclass[border=3.14mm,12pt,tikz]{standalone}
usepackage{tikz,tikz-3dplot}
%% smuggling from https://tex.stackexchange.com/a/470979/121799
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
}
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+#2*#5+#3*#6}
defVPTD(#1,#2,#3)x(#4,#5,#6){(#2*#6-#3*#5,#3*#4-#1*#6,#1*#5-#2*#4)}
defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)}
defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+#4,#2+#5,#3+#6)}
tikzset{intersection of line trough/.style args={#1 and #2 with plane
containing #3 and normal #4}{%
/utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-SPTD#1.#4)}
parsecoord#1>(myAx,myAy,myAz)
parsecoord#2>(myBx,myBy,myBz)
ifdimltest pt<0.01pt
typeout{Planespace andspace linespace arespace parallel!ltest}
pgfmathsetmacro{myd}{0}
else
pgfmathsetmacro{myd}{(SPTD#3.#4-SPTD#1.#4)/(SPTD#2.#4-SPTD#1.#4)}
fi
%typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}
defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}
smugglemyP},
insert path={%
myP}
}}
begin{document}
tdplotsetmaincoords{75}{110}
begin{tikzpicture}[tdplot_main_coords,scale=1.5]
pgfmathsetmacroa{3}
pgfmathsetmacrob{4}
pgfmathsetmacroh{5}
% definitions
path
coordinate(A) at (0,0,0)
coordinate (B) at (a,0,0)
coordinate (C) at (a,b,0)
coordinate (D) at (0,b,0)
coordinate (S) at (0,0,h);
defmynormal{VecMinus(a,b,0)-(0,0,h)}
typeout{mynormal:(a,b,-h)}
path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (E)
[intersection of line trough={(0,0,h) and (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (F)
[intersection of line trough={(0,0,h) and (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}] coordinate (K);
draw[dashed, thick]
(A) -- (B) (D)--(A) (S)--(A);
draw[dashed, thick]
(E) --(A) -- (F);
draw[ultra thick]
(S) -- (B) -- (C) -- (D)--cycle (S)--(C);
draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;
draw [thick] (E) -- (K) -- (F) ;
foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}
{
fill (point) circle (1.5pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
I got
tikz-pgf tikz-3dplot
tikz-pgf tikz-3dplot
asked 11 mins ago
minhthien_2016minhthien_2016
1,180816
asked 11 mins ago
minhthien_2016minhthien_2016
1,180816
asked 11 mins ago
minhthien_2016minhthien_2016
1,180816
asked 11 mins ago
minhthien_2016minhthien_2016
1,180816
asked 11 mins ago
minhthien_2016minhthien_2016
1,180816
1,180816
add a comment |
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