How to draw a circle (sphere) passing through four points?
1
I am trying to draw a circle (sphere) passing through four points B, C, E, F like this picture 
I tried with tikz-3dplot and my code
documentclass[border=3mm,12pt]{standalone}
usepackage{fouriernc}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
usetikzlibrary{intersections,calc,backgrounds}
begin{document}
tdplotsetmaincoords{70}{110}
%tdplotsetmaincoords{80}{100}
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 (0,b,0)
coordinate (S) at (0,0,h)
coordinate (E) at ({a*h^2/(a*a + h*h)},0,{(a*a*h)/(a*a + h*h)})
coordinate (F) at (0,{(b*h*h)/(b*b + h*h)},{(b*b*h)/(b*b + h*h)});
draw[dashed,thick]
(A) -- (B) (A) -- (C) (A) -- (E) (S)--(A) (F)--(A);
draw[thick]
(S) -- (B) -- (C) -- cycle;
draw[thick]
(F) -- (B) (C)--(E) (F)--(E);
tkzMarkRightAngle(S,E,A);
tkzMarkRightAngle(S,F,A);
foreach point/position in {A/below,B/left,C/below,S/above,E/left,F/above}
{
fill (point) circle (.8pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
and got
How can I draw a circle (sphere) passing through four points B, C, E, F?
3d tikz-3dplot
asked 1 hour ago
minhthien_2016minhthien_2016
1,102815
|
show 1 more comment
1
I am trying to draw a circle (sphere) passing through four points B, C, E, F like this picture
I tried with tikz-3dplot and my code
documentclass[border=3mm,12pt]{standalone}
usepackage{fouriernc}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
usetikzlibrary{intersections,calc,backgrounds}
begin{document}
tdplotsetmaincoords{70}{110}
%tdplotsetmaincoords{80}{100}
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 (0,b,0)
coordinate (S) at (0,0,h)
coordinate (E) at ({a*h^2/(a*a + h*h)},0,{(a*a*h)/(a*a + h*h)})
coordinate (F) at (0,{(b*h*h)/(b*b + h*h)},{(b*b*h)/(b*b + h*h)});
draw[dashed,thick]
(A) -- (B) (A) -- (C) (A) -- (E) (S)--(A) (F)--(A);
draw[thick]
(S) -- (B) -- (C) -- cycle;
draw[thick]
(F) -- (B) (C)--(E) (F)--(E);
tkzMarkRightAngle(S,E,A);
tkzMarkRightAngle(S,F,A);
foreach point/position in {A/below,B/left,C/below,S/above,E/left,F/above}
{
fill (point) circle (.8pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
and got
How can I draw a circle (sphere) passing through four points B, C, E, F?
3d tikz-3dplot
asked 1 hour ago
minhthien_2016minhthien_2016
1,102815
A circle is already uniquely fixed by 3 (noncollinear) points. There exist answers that show you how to find such a circle. E.g. tex.stackexchange.com/questions/461161/… (Sorry for advertising;-)
– marmot
58 mins ago
@marmot Is it true in 3D?
– minhthien_2016
44 mins ago
I believe that an orthographic projection of a sphere is a circle. The subtle point is whether the projected circle runs through the points you indicate, something that I cannot decide without more information on how the sphere is determined.
– marmot
40 mins ago
The sphere has centre is midpoint of the segment EC.
– minhthien_2016
37 mins ago
OK this tells you already where the center of the circle will be. If you know that E and C are on the boundary, this completely fixes the circle. If you load the call library, you could do draw let p1=($(E)-(C)$), n1={veclen(x1,y1)/2} in ($(E)!0.5!(C)$) circle (n1);
– marmot
30 mins ago
|
show 1 more comment
1
1
1
I am trying to draw a circle (sphere) passing through four points B, C, E, F like this picture
I tried with tikz-3dplot and my code
documentclass[border=3mm,12pt]{standalone}
usepackage{fouriernc}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
usetikzlibrary{intersections,calc,backgrounds}
begin{document}
tdplotsetmaincoords{70}{110}
%tdplotsetmaincoords{80}{100}
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 (0,b,0)
coordinate (S) at (0,0,h)
coordinate (E) at ({a*h^2/(a*a + h*h)},0,{(a*a*h)/(a*a + h*h)})
coordinate (F) at (0,{(b*h*h)/(b*b + h*h)},{(b*b*h)/(b*b + h*h)});
draw[dashed,thick]
(A) -- (B) (A) -- (C) (A) -- (E) (S)--(A) (F)--(A);
draw[thick]
(S) -- (B) -- (C) -- cycle;
draw[thick]
(F) -- (B) (C)--(E) (F)--(E);
tkzMarkRightAngle(S,E,A);
tkzMarkRightAngle(S,F,A);
foreach point/position in {A/below,B/left,C/below,S/above,E/left,F/above}
{
fill (point) circle (.8pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
and got
How can I draw a circle (sphere) passing through four points B, C, E, F?
3d tikz-3dplot
asked 1 hour ago
minhthien_2016minhthien_2016
1,102815
I am trying to draw a circle (sphere) passing through four points B, C, E, F like this picture
I tried with tikz-3dplot and my code
documentclass[border=3mm,12pt]{standalone}
usepackage{fouriernc}
usepackage{tikz,tikz-3dplot}
usepackage{tkz-euclide}
usetkzobj{all}
usetikzlibrary{intersections,calc,backgrounds}
begin{document}
tdplotsetmaincoords{70}{110}
%tdplotsetmaincoords{80}{100}
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 (0,b,0)
coordinate (S) at (0,0,h)
coordinate (E) at ({a*h^2/(a*a + h*h)},0,{(a*a*h)/(a*a + h*h)})
coordinate (F) at (0,{(b*h*h)/(b*b + h*h)},{(b*b*h)/(b*b + h*h)});
draw[dashed,thick]
(A) -- (B) (A) -- (C) (A) -- (E) (S)--(A) (F)--(A);
draw[thick]
(S) -- (B) -- (C) -- cycle;
draw[thick]
(F) -- (B) (C)--(E) (F)--(E);
tkzMarkRightAngle(S,E,A);
tkzMarkRightAngle(S,F,A);
foreach point/position in {A/below,B/left,C/below,S/above,E/left,F/above}
{
fill (point) circle (.8pt);
node[position=3pt] at (point) {$point$};
}
end{tikzpicture}
end{document}
and got
How can I draw a circle (sphere) passing through four points B, C, E, F?
3d tikz-3dplot
3d tikz-3dplot
asked 1 hour ago
minhthien_2016minhthien_2016
1,102815
asked 1 hour ago
minhthien_2016minhthien_2016
1,102815
asked 1 hour ago
minhthien_2016minhthien_2016
1,102815
asked 1 hour ago
minhthien_2016minhthien_2016
1,102815
asked 1 hour ago
minhthien_2016minhthien_2016
1,102815
1,102815
A circle is already uniquely fixed by 3 (noncollinear) points. There exist answers that show you how to find such a circle. E.g. tex.stackexchange.com/questions/461161/… (Sorry for advertising;-)
– marmot
58 mins ago
@marmot Is it true in 3D?
– minhthien_2016
44 mins ago
I believe that an orthographic projection of a sphere is a circle. The subtle point is whether the projected circle runs through the points you indicate, something that I cannot decide without more information on how the sphere is determined.
– marmot
40 mins ago
The sphere has centre is midpoint of the segment EC.
– minhthien_2016
37 mins ago
OK this tells you already where the center of the circle will be. If you know that E and C are on the boundary, this completely fixes the circle. If you load the call library, you could do draw let p1=($(E)-(C)$), n1={veclen(x1,y1)/2} in ($(E)!0.5!(C)$) circle (n1);
– marmot
30 mins ago
|
show 1 more comment
A circle is already uniquely fixed by 3 (noncollinear) points. There exist answers that show you how to find such a circle. E.g. tex.stackexchange.com/questions/461161/… (Sorry for advertising;-)
– marmot
58 mins ago
@marmot Is it true in 3D?
– minhthien_2016
44 mins ago
I believe that an orthographic projection of a sphere is a circle. The subtle point is whether the projected circle runs through the points you indicate, something that I cannot decide without more information on how the sphere is determined.
– marmot
40 mins ago
The sphere has centre is midpoint of the segment EC.
– minhthien_2016
37 mins ago
OK this tells you already where the center of the circle will be. If you know that E and C are on the boundary, this completely fixes the circle. If you load the call library, you could do draw let p1=($(E)-(C)$), n1={veclen(x1,y1)/2} in ($(E)!0.5!(C)$) circle (n1);
– marmot
30 mins ago
A circle is already uniquely fixed by 3 (noncollinear) points. There exist answers that show you how to find such a circle. E.g. tex.stackexchange.com/questions/461161/… (Sorry for advertising;-)
– marmot
58 mins ago
A circle is already uniquely fixed by 3 (noncollinear) points. There exist answers that show you how to find such a circle. E.g. tex.stackexchange.com/questions/461161/… (Sorry for advertising;-)
– marmot
58 mins ago
@marmot Is it true in 3D?
– minhthien_2016
44 mins ago
@marmot Is it true in 3D?
– minhthien_2016
44 mins ago
I believe that an orthographic projection of a sphere is a circle. The subtle point is whether the projected circle runs through the points you indicate, something that I cannot decide without more information on how the sphere is determined.
– marmot
40 mins ago
I believe that an orthographic projection of a sphere is a circle. The subtle point is whether the projected circle runs through the points you indicate, something that I cannot decide without more information on how the sphere is determined.
– marmot
40 mins ago
The sphere has centre is midpoint of the segment EC.
– minhthien_2016
37 mins ago
The sphere has centre is midpoint of the segment EC.
– minhthien_2016
37 mins ago
OK this tells you already where the center of the circle will be. If you know that E and C are on the boundary, this completely fixes the circle. If you load the call library, you could do draw let p1=($(E)-(C)$), n1={veclen(x1,y1)/2} in ($(E)!0.5!(C)$) circle (n1);
– marmot
30 mins ago
OK this tells you already where the center of the circle will be. If you know that E and C are on the boundary, this completely fixes the circle. If you load the call library, you could do draw let p1=($(E)-(C)$), n1={veclen(x1,y1)/2} in ($(E)!0.5!(C)$) circle (n1);
– marmot
30 mins ago
|
show 1 more comment
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A circle is already uniquely fixed by 3 (noncollinear) points. There exist answers that show you how to find such a circle. E.g. tex.stackexchange.com/questions/461161/… (Sorry for advertising;-)
– marmot
58 mins ago
@marmot Is it true in 3D?
– minhthien_2016
44 mins ago
I believe that an orthographic projection of a sphere is a circle. The subtle point is whether the projected circle runs through the points you indicate, something that I cannot decide without more information on how the sphere is determined.
– marmot
40 mins ago
The sphere has centre is midpoint of the segment EC.
– minhthien_2016
37 mins ago
OK this tells you already where the center of the circle will be. If you know that E and C are on the boundary, this completely fixes the circle. If you load the call library, you could do draw let p1=($(E)-(C)$), n1={veclen(x1,y1)/2} in ($(E)!0.5!(C)$) circle (n1);
– marmot
30 mins ago