How to draw the angle between two intersecting 3D circles












3















I'm new to TikZ and I'm trying to label the angle between two intersecting circles, as seen in red in the following picture,
enter image description here



Below is my code so far which makes the following diagram,
enter image description here



documentclass[border=5pt]{standalone}
usepackage{tikz,tikz-3dplot}
begin{document}
tdplotsetmaincoords{70}{110}
begin{tikzpicture}[tdplot_main_coords,scale=5]
pgfmathsetmacro{r}{1}
pgfmathsetmacro{O}{60}
pgfmathsetmacro{i}{45}

coordinate (O) at (0,0,0);
tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE

tdplotsetrotatedcoords{-O}{i}{0}
tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO
end{tikzpicture}
end{document}


I appreciate the help!










share|improve this question







New contributor




Fatema Farag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

























    3















    I'm new to TikZ and I'm trying to label the angle between two intersecting circles, as seen in red in the following picture,
    enter image description here



    Below is my code so far which makes the following diagram,
    enter image description here



    documentclass[border=5pt]{standalone}
    usepackage{tikz,tikz-3dplot}
    begin{document}
    tdplotsetmaincoords{70}{110}
    begin{tikzpicture}[tdplot_main_coords,scale=5]
    pgfmathsetmacro{r}{1}
    pgfmathsetmacro{O}{60}
    pgfmathsetmacro{i}{45}

    coordinate (O) at (0,0,0);
    tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE

    tdplotsetrotatedcoords{-O}{i}{0}
    tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO
    end{tikzpicture}
    end{document}


    I appreciate the help!










    share|improve this question







    New contributor




    Fatema Farag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.























      3












      3








      3








      I'm new to TikZ and I'm trying to label the angle between two intersecting circles, as seen in red in the following picture,
      enter image description here



      Below is my code so far which makes the following diagram,
      enter image description here



      documentclass[border=5pt]{standalone}
      usepackage{tikz,tikz-3dplot}
      begin{document}
      tdplotsetmaincoords{70}{110}
      begin{tikzpicture}[tdplot_main_coords,scale=5]
      pgfmathsetmacro{r}{1}
      pgfmathsetmacro{O}{60}
      pgfmathsetmacro{i}{45}

      coordinate (O) at (0,0,0);
      tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE

      tdplotsetrotatedcoords{-O}{i}{0}
      tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO
      end{tikzpicture}
      end{document}


      I appreciate the help!










      share|improve this question







      New contributor




      Fatema Farag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.












      I'm new to TikZ and I'm trying to label the angle between two intersecting circles, as seen in red in the following picture,
      enter image description here



      Below is my code so far which makes the following diagram,
      enter image description here



      documentclass[border=5pt]{standalone}
      usepackage{tikz,tikz-3dplot}
      begin{document}
      tdplotsetmaincoords{70}{110}
      begin{tikzpicture}[tdplot_main_coords,scale=5]
      pgfmathsetmacro{r}{1}
      pgfmathsetmacro{O}{60}
      pgfmathsetmacro{i}{45}

      coordinate (O) at (0,0,0);
      tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE

      tdplotsetrotatedcoords{-O}{i}{0}
      tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO
      end{tikzpicture}
      end{document}


      I appreciate the help!







      tikz-pgf tikz-3dplot






      share|improve this question







      New contributor




      Fatema Farag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|improve this question







      New contributor




      Fatema Farag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|improve this question




      share|improve this question






      New contributor




      Fatema Farag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      asked 3 hours ago









      Fatema FaragFatema Farag

      161




      161




      New contributor




      Fatema Farag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.





      New contributor





      Fatema Farag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      Fatema Farag is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






















          1 Answer
          1






          active

          oldest

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          3














          Welcome to TeX.SE! Here is a proposal. I do not know what the absolutely correct way is. I do, of course, know how to indicate an angle between two lines on a plane. But here we deal with an angle line between two curves. Is it supposed to run on the sphere? If so, on a great circle? In the limit of an infinitely large sphere this prescription will not reproduce our standard conventions in the plane, rather it will yield a straight line. Since this seems not to be well-defined, I just computed the intersection, I, of the two circles and points on the two circles that are away from the intersection by the same amount, I1 and I2. And then I connected those with an arc that "looks right".



          documentclass[border=5pt]{standalone}
          usepackage{tikz,tikz-3dplot}
          begin{document}
          tdplotsetmaincoords{70}{110}
          begin{tikzpicture}[tdplot_main_coords,scale=5]
          pgfmathsetmacro{r}{1}
          pgfmathsetmacro{O}{60}
          pgfmathsetmacro{i}{45}
          pgfmathsetmacro{dang}{-30}

          coordinate (O) at (0,0,0);
          tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE

          tdplotsetrotatedcoords{-O}{i}{0}
          tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO

          path ({sin(O)},{cos(O)},{0}) coordinate (I);
          path ({sin(O+dang)},{cos(O+dang)},{0}) coordinate (I1);
          path[tdplot_rotated_coords] ({sin(dang)},{cos(dang)},{0})
          coordinate (I2);
          draw (I1) to[out=95,in=-50] node[pos=0.5,right] {$i^circ$} (I2);
          end{tikzpicture}
          end{document}


          enter image description here






          share|improve this answer


























          • ... of course there is a well-defined way to define such arcs: draw an ordinary arc in the plane that runs through I, I1 and I2. Perhaps this is the "correct" way?

            – marmot
            1 hour ago











          Your Answer








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          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          3














          Welcome to TeX.SE! Here is a proposal. I do not know what the absolutely correct way is. I do, of course, know how to indicate an angle between two lines on a plane. But here we deal with an angle line between two curves. Is it supposed to run on the sphere? If so, on a great circle? In the limit of an infinitely large sphere this prescription will not reproduce our standard conventions in the plane, rather it will yield a straight line. Since this seems not to be well-defined, I just computed the intersection, I, of the two circles and points on the two circles that are away from the intersection by the same amount, I1 and I2. And then I connected those with an arc that "looks right".



          documentclass[border=5pt]{standalone}
          usepackage{tikz,tikz-3dplot}
          begin{document}
          tdplotsetmaincoords{70}{110}
          begin{tikzpicture}[tdplot_main_coords,scale=5]
          pgfmathsetmacro{r}{1}
          pgfmathsetmacro{O}{60}
          pgfmathsetmacro{i}{45}
          pgfmathsetmacro{dang}{-30}

          coordinate (O) at (0,0,0);
          tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE

          tdplotsetrotatedcoords{-O}{i}{0}
          tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO

          path ({sin(O)},{cos(O)},{0}) coordinate (I);
          path ({sin(O+dang)},{cos(O+dang)},{0}) coordinate (I1);
          path[tdplot_rotated_coords] ({sin(dang)},{cos(dang)},{0})
          coordinate (I2);
          draw (I1) to[out=95,in=-50] node[pos=0.5,right] {$i^circ$} (I2);
          end{tikzpicture}
          end{document}


          enter image description here






          share|improve this answer


























          • ... of course there is a well-defined way to define such arcs: draw an ordinary arc in the plane that runs through I, I1 and I2. Perhaps this is the "correct" way?

            – marmot
            1 hour ago
















          3














          Welcome to TeX.SE! Here is a proposal. I do not know what the absolutely correct way is. I do, of course, know how to indicate an angle between two lines on a plane. But here we deal with an angle line between two curves. Is it supposed to run on the sphere? If so, on a great circle? In the limit of an infinitely large sphere this prescription will not reproduce our standard conventions in the plane, rather it will yield a straight line. Since this seems not to be well-defined, I just computed the intersection, I, of the two circles and points on the two circles that are away from the intersection by the same amount, I1 and I2. And then I connected those with an arc that "looks right".



          documentclass[border=5pt]{standalone}
          usepackage{tikz,tikz-3dplot}
          begin{document}
          tdplotsetmaincoords{70}{110}
          begin{tikzpicture}[tdplot_main_coords,scale=5]
          pgfmathsetmacro{r}{1}
          pgfmathsetmacro{O}{60}
          pgfmathsetmacro{i}{45}
          pgfmathsetmacro{dang}{-30}

          coordinate (O) at (0,0,0);
          tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE

          tdplotsetrotatedcoords{-O}{i}{0}
          tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO

          path ({sin(O)},{cos(O)},{0}) coordinate (I);
          path ({sin(O+dang)},{cos(O+dang)},{0}) coordinate (I1);
          path[tdplot_rotated_coords] ({sin(dang)},{cos(dang)},{0})
          coordinate (I2);
          draw (I1) to[out=95,in=-50] node[pos=0.5,right] {$i^circ$} (I2);
          end{tikzpicture}
          end{document}


          enter image description here






          share|improve this answer


























          • ... of course there is a well-defined way to define such arcs: draw an ordinary arc in the plane that runs through I, I1 and I2. Perhaps this is the "correct" way?

            – marmot
            1 hour ago














          3












          3








          3







          Welcome to TeX.SE! Here is a proposal. I do not know what the absolutely correct way is. I do, of course, know how to indicate an angle between two lines on a plane. But here we deal with an angle line between two curves. Is it supposed to run on the sphere? If so, on a great circle? In the limit of an infinitely large sphere this prescription will not reproduce our standard conventions in the plane, rather it will yield a straight line. Since this seems not to be well-defined, I just computed the intersection, I, of the two circles and points on the two circles that are away from the intersection by the same amount, I1 and I2. And then I connected those with an arc that "looks right".



          documentclass[border=5pt]{standalone}
          usepackage{tikz,tikz-3dplot}
          begin{document}
          tdplotsetmaincoords{70}{110}
          begin{tikzpicture}[tdplot_main_coords,scale=5]
          pgfmathsetmacro{r}{1}
          pgfmathsetmacro{O}{60}
          pgfmathsetmacro{i}{45}
          pgfmathsetmacro{dang}{-30}

          coordinate (O) at (0,0,0);
          tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE

          tdplotsetrotatedcoords{-O}{i}{0}
          tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO

          path ({sin(O)},{cos(O)},{0}) coordinate (I);
          path ({sin(O+dang)},{cos(O+dang)},{0}) coordinate (I1);
          path[tdplot_rotated_coords] ({sin(dang)},{cos(dang)},{0})
          coordinate (I2);
          draw (I1) to[out=95,in=-50] node[pos=0.5,right] {$i^circ$} (I2);
          end{tikzpicture}
          end{document}


          enter image description here






          share|improve this answer















          Welcome to TeX.SE! Here is a proposal. I do not know what the absolutely correct way is. I do, of course, know how to indicate an angle between two lines on a plane. But here we deal with an angle line between two curves. Is it supposed to run on the sphere? If so, on a great circle? In the limit of an infinitely large sphere this prescription will not reproduce our standard conventions in the plane, rather it will yield a straight line. Since this seems not to be well-defined, I just computed the intersection, I, of the two circles and points on the two circles that are away from the intersection by the same amount, I1 and I2. And then I connected those with an arc that "looks right".



          documentclass[border=5pt]{standalone}
          usepackage{tikz,tikz-3dplot}
          begin{document}
          tdplotsetmaincoords{70}{110}
          begin{tikzpicture}[tdplot_main_coords,scale=5]
          pgfmathsetmacro{r}{1}
          pgfmathsetmacro{O}{60}
          pgfmathsetmacro{i}{45}
          pgfmathsetmacro{dang}{-30}

          coordinate (O) at (0,0,0);
          tdplotdrawarc[dashed]{(O)}{r}{0}{360}{}{} %CIRCLE ONE

          tdplotsetrotatedcoords{-O}{i}{0}
          tdplotdrawarc[tdplot_rotated_coords]{(O)}{r}{0}{360}{}{} %CIRCLE TWO

          path ({sin(O)},{cos(O)},{0}) coordinate (I);
          path ({sin(O+dang)},{cos(O+dang)},{0}) coordinate (I1);
          path[tdplot_rotated_coords] ({sin(dang)},{cos(dang)},{0})
          coordinate (I2);
          draw (I1) to[out=95,in=-50] node[pos=0.5,right] {$i^circ$} (I2);
          end{tikzpicture}
          end{document}


          enter image description here







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 1 hour ago

























          answered 2 hours ago









          marmotmarmot

          98.9k4113219




          98.9k4113219













          • ... of course there is a well-defined way to define such arcs: draw an ordinary arc in the plane that runs through I, I1 and I2. Perhaps this is the "correct" way?

            – marmot
            1 hour ago



















          • ... of course there is a well-defined way to define such arcs: draw an ordinary arc in the plane that runs through I, I1 and I2. Perhaps this is the "correct" way?

            – marmot
            1 hour ago

















          ... of course there is a well-defined way to define such arcs: draw an ordinary arc in the plane that runs through I, I1 and I2. Perhaps this is the "correct" way?

          – marmot
          1 hour ago





          ... of course there is a well-defined way to define such arcs: draw an ordinary arc in the plane that runs through I, I1 and I2. Perhaps this is the "correct" way?

          – marmot
          1 hour ago










          Fatema Farag is a new contributor. Be nice, and check out our Code of Conduct.










          draft saved

          draft discarded


















          Fatema Farag is a new contributor. Be nice, and check out our Code of Conduct.













          Fatema Farag is a new contributor. Be nice, and check out our Code of Conduct.












          Fatema Farag is a new contributor. Be nice, and check out our Code of Conduct.
















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