Intersection of a sphere and a plane knowing equations
1
I am trying draw a circle is intersection of a plane has equation 2 x − 2 y + z − 15 = 0 and the equation of the sphere is ( x − 1)^2 + ( y + 1)^ 2 + ( z − 2)^ 2 − 25 = 0.
The plane cut the sphere is a circle with centre (3,-3,3 and radius r = 4.
I can't draw the circle. I tried
documentclass[12pt,border = 2 mm]{standalone}
usepackage{tikz}
usepackage{tikz-3dplot}
usetikzlibrary{arrows,calc,backgrounds}
begin{document}
tdplotsetmaincoords{60}{110}
begin{tikzpicture}[tdplot_main_coords]
path
coordinate (T) at (3,-3,3)
coordinate (I) at (1,-1,2);
foreach v/position in {T/above,I/below} {
draw[fill=black] (v) circle (0.7pt) node [position=0.2mm] {$v$};
}
draw[dashed] (T) circle[radius={4}];
begin{scope}[tdplot_screen_coords, on background layer]
pgfmathsetmacro{R}{5}%
fill[ball color=purple, opacity=1.0] (I) circle (R);
end{scope}
end{tikzpicture}
end{document}
How can I draw the circle?
tikz-pgf tikz-3dplot
asked 41 mins ago
minhthien_2016minhthien_2016
1,3561917
add a comment |
1
I am trying draw a circle is intersection of a plane has equation 2 x − 2 y + z − 15 = 0 and the equation of the sphere is ( x − 1)^2 + ( y + 1)^ 2 + ( z − 2)^ 2 − 25 = 0.
The plane cut the sphere is a circle with centre (3,-3,3 and radius r = 4.
I can't draw the circle. I tried
documentclass[12pt,border = 2 mm]{standalone}
usepackage{tikz}
usepackage{tikz-3dplot}
usetikzlibrary{arrows,calc,backgrounds}
begin{document}
tdplotsetmaincoords{60}{110}
begin{tikzpicture}[tdplot_main_coords]
path
coordinate (T) at (3,-3,3)
coordinate (I) at (1,-1,2);
foreach v/position in {T/above,I/below} {
draw[fill=black] (v) circle (0.7pt) node [position=0.2mm] {$v$};
}
draw[dashed] (T) circle[radius={4}];
begin{scope}[tdplot_screen_coords, on background layer]
pgfmathsetmacro{R}{5}%
fill[ball color=purple, opacity=1.0] (I) circle (R);
end{scope}
end{tikzpicture}
end{document}
How can I draw the circle?
tikz-pgf tikz-3dplot
asked 41 mins ago
minhthien_2016minhthien_2016
1,3561917
I guess the issue is rather basic: you need to specify the plane in which the circle is in. Your plane has a nontrivial normal vector but you draw the circle in thexyplane, which is why it does not match up.
– marmot
32 mins ago
The plane has normal vector is (2,-2,1).
– minhthien_2016
30 mins ago
Yes, I know. Naively I would think that it is better to switch to a local coordinate system in which the center of the sphere is at(0,0,0)and the normal goes in the z direction, and then just rotate the view. Do your know this nice answer. It will allow you to draw the intersection in such a way that the visible stretch is distinguished from the hidden one. (If you do not likepgfplot, you could also use this answer.)
– marmot
27 mins ago
add a comment |
1
1
1
I am trying draw a circle is intersection of a plane has equation 2 x − 2 y + z − 15 = 0 and the equation of the sphere is ( x − 1)^2 + ( y + 1)^ 2 + ( z − 2)^ 2 − 25 = 0.
The plane cut the sphere is a circle with centre (3,-3,3 and radius r = 4.
I can't draw the circle. I tried
documentclass[12pt,border = 2 mm]{standalone}
usepackage{tikz}
usepackage{tikz-3dplot}
usetikzlibrary{arrows,calc,backgrounds}
begin{document}
tdplotsetmaincoords{60}{110}
begin{tikzpicture}[tdplot_main_coords]
path
coordinate (T) at (3,-3,3)
coordinate (I) at (1,-1,2);
foreach v/position in {T/above,I/below} {
draw[fill=black] (v) circle (0.7pt) node [position=0.2mm] {$v$};
}
draw[dashed] (T) circle[radius={4}];
begin{scope}[tdplot_screen_coords, on background layer]
pgfmathsetmacro{R}{5}%
fill[ball color=purple, opacity=1.0] (I) circle (R);
end{scope}
end{tikzpicture}
end{document}
How can I draw the circle?
tikz-pgf tikz-3dplot
asked 41 mins ago
minhthien_2016minhthien_2016
1,3561917
I am trying draw a circle is intersection of a plane has equation 2 x − 2 y + z − 15 = 0 and the equation of the sphere is ( x − 1)^2 + ( y + 1)^ 2 + ( z − 2)^ 2 − 25 = 0.
The plane cut the sphere is a circle with centre (3,-3,3 and radius r = 4.
I can't draw the circle. I tried
documentclass[12pt,border = 2 mm]{standalone}
usepackage{tikz}
usepackage{tikz-3dplot}
usetikzlibrary{arrows,calc,backgrounds}
begin{document}
tdplotsetmaincoords{60}{110}
begin{tikzpicture}[tdplot_main_coords]
path
coordinate (T) at (3,-3,3)
coordinate (I) at (1,-1,2);
foreach v/position in {T/above,I/below} {
draw[fill=black] (v) circle (0.7pt) node [position=0.2mm] {$v$};
}
draw[dashed] (T) circle[radius={4}];
begin{scope}[tdplot_screen_coords, on background layer]
pgfmathsetmacro{R}{5}%
fill[ball color=purple, opacity=1.0] (I) circle (R);
end{scope}
end{tikzpicture}
end{document}
How can I draw the circle?
tikz-pgf tikz-3dplot
tikz-pgf tikz-3dplot
asked 41 mins ago
minhthien_2016minhthien_2016
1,3561917
asked 41 mins ago
minhthien_2016minhthien_2016
1,3561917
asked 41 mins ago
minhthien_2016minhthien_2016
1,3561917
asked 41 mins ago
minhthien_2016minhthien_2016
1,3561917
asked 41 mins ago
minhthien_2016minhthien_2016
1,3561917
1,3561917
I guess the issue is rather basic: you need to specify the plane in which the circle is in. Your plane has a nontrivial normal vector but you draw the circle in thexyplane, which is why it does not match up.
– marmot
32 mins ago
The plane has normal vector is (2,-2,1).
– minhthien_2016
30 mins ago
Yes, I know. Naively I would think that it is better to switch to a local coordinate system in which the center of the sphere is at(0,0,0)and the normal goes in the z direction, and then just rotate the view. Do your know this nice answer. It will allow you to draw the intersection in such a way that the visible stretch is distinguished from the hidden one. (If you do not likepgfplot, you could also use this answer.)
– marmot
27 mins ago
add a comment |
I guess the issue is rather basic: you need to specify the plane in which the circle is in. Your plane has a nontrivial normal vector but you draw the circle in thexyplane, which is why it does not match up.
– marmot
32 mins ago
The plane has normal vector is (2,-2,1).
– minhthien_2016
30 mins ago
Yes, I know. Naively I would think that it is better to switch to a local coordinate system in which the center of the sphere is at(0,0,0)and the normal goes in the z direction, and then just rotate the view. Do your know this nice answer. It will allow you to draw the intersection in such a way that the visible stretch is distinguished from the hidden one. (If you do not likepgfplot, you could also use this answer.)
– marmot
27 mins ago
I guess the issue is rather basic: you need to specify the plane in which the circle is in. Your plane has a nontrivial normal vector but you draw the circle in the
xy plane, which is why it does not match up.– marmot
32 mins ago
I guess the issue is rather basic: you need to specify the plane in which the circle is in. Your plane has a nontrivial normal vector but you draw the circle in the
xy plane, which is why it does not match up.– marmot
32 mins ago
The plane has normal vector is (2,-2,1).
– minhthien_2016
30 mins ago
The plane has normal vector is (2,-2,1).
– minhthien_2016
30 mins ago
Yes, I know. Naively I would think that it is better to switch to a local coordinate system in which the center of the sphere is at
(0,0,0) and the normal goes in the z direction, and then just rotate the view. Do your know this nice answer. It will allow you to draw the intersection in such a way that the visible stretch is distinguished from the hidden one. (If you do not like pgfplot, you could also use this answer.)– marmot
27 mins ago
Yes, I know. Naively I would think that it is better to switch to a local coordinate system in which the center of the sphere is at
(0,0,0) and the normal goes in the z direction, and then just rotate the view. Do your know this nice answer. It will allow you to draw the intersection in such a way that the visible stretch is distinguished from the hidden one. (If you do not like pgfplot, you could also use this answer.)– marmot
27 mins ago
add a comment |
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I guess the issue is rather basic: you need to specify the plane in which the circle is in. Your plane has a nontrivial normal vector but you draw the circle in the
xyplane, which is why it does not match up.– marmot
32 mins ago
The plane has normal vector is (2,-2,1).
– minhthien_2016
30 mins ago
Yes, I know. Naively I would think that it is better to switch to a local coordinate system in which the center of the sphere is at
(0,0,0)and the normal goes in the z direction, and then just rotate the view. Do your know this nice answer. It will allow you to draw the intersection in such a way that the visible stretch is distinguished from the hidden one. (If you do not likepgfplot, you could also use this answer.)– marmot
27 mins ago