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 enter image description here



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



enter image description here



How can I draw a circle (sphere) passing through four points B, C, E, F?






3d tikz-3dplot







share|improve this question























  • 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
















1















I am trying to draw a circle (sphere) passing through four points B, C, E, F like this picture enter image description here



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



enter image description here



How can I draw a circle (sphere) passing through four points B, C, E, F?






3d tikz-3dplot







share|improve this question























  • 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














1












1








1








I am trying to draw a circle (sphere) passing through four points B, C, E, F like this picture enter image description here



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



enter image description here



How can I draw a circle (sphere) passing through four points B, C, E, F?






3d tikz-3dplot







share|improve this question














I am trying to draw a circle (sphere) passing through four points B, C, E, F like this picture enter image description here



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



enter image description here



How can I draw a circle (sphere) passing through four points B, C, E, F?






3d tikz-3dplot




3d tikz-3dplot






share|improve this question













share|improve this question











share|improve this question




share|improve this question










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



















  • 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










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