Drawing a curve tangent to a line












3















I'd like to draw a set of curves, each tangent to a different point on a given line. The requirement is that the curves are convex and downward sloping.



In the following MWE, I use the to[out=<x>,in=<y>] operation to manually adjust the slope of the curves so that they appear to be tangent at the desired point. This requires a lot of trial-and-errors and the result is not ideal. Is there a better way to draw such curves?



MWE



documentclass[border=2pt,tikz]{standalone}

begin{document}

begin{tikzpicture}

  foreach i in {1,2,3,4}{

    draw[thick](0,4.5)--(7,0)coordinate[pos=i/5](i);

    fill(i)circle[radius=2pt]node[below left]{pt i};

    draw[red](i)to[out=140,in=-80]++(-1,1.5) (i)to[out=-25,in=170]++(1.25,-.4);

  }

  draw[<->](0,5)node[left]{$y$}--(0,0)--(8,0)node[below]{$x$};

end{tikzpicture}

end{document}


enter image description here






tikz-pgf







share|improve this question



























    3















    I'd like to draw a set of curves, each tangent to a different point on a given line. The requirement is that the curves are convex and downward sloping.



    In the following MWE, I use the to[out=<x>,in=<y>] operation to manually adjust the slope of the curves so that they appear to be tangent at the desired point. This requires a lot of trial-and-errors and the result is not ideal. Is there a better way to draw such curves?



    MWE



    documentclass[border=2pt,tikz]{standalone}
    
begin{document}
    
begin{tikzpicture}
    
  foreach i in {1,2,3,4}{
    
    draw[thick](0,4.5)--(7,0)coordinate[pos=i/5](i);
    
    fill(i)circle[radius=2pt]node[below left]{pt i};
    
    draw[red](i)to[out=140,in=-80]++(-1,1.5) (i)to[out=-25,in=170]++(1.25,-.4);
    
  }
    
  draw[<->](0,5)node[left]{$y$}--(0,0)--(8,0)node[below]{$x$};
    
end{tikzpicture}
    
end{document}


    enter image description here






    tikz-pgf







    share|improve this question

























      3












      3








      3


      1






      I'd like to draw a set of curves, each tangent to a different point on a given line. The requirement is that the curves are convex and downward sloping.



      In the following MWE, I use the to[out=<x>,in=<y>] operation to manually adjust the slope of the curves so that they appear to be tangent at the desired point. This requires a lot of trial-and-errors and the result is not ideal. Is there a better way to draw such curves?



      MWE



      documentclass[border=2pt,tikz]{standalone}
      
begin{document}
      
begin{tikzpicture}
      
  foreach i in {1,2,3,4}{
      
    draw[thick](0,4.5)--(7,0)coordinate[pos=i/5](i);
      
    fill(i)circle[radius=2pt]node[below left]{pt i};
      
    draw[red](i)to[out=140,in=-80]++(-1,1.5) (i)to[out=-25,in=170]++(1.25,-.4);
      
  }
      
  draw[<->](0,5)node[left]{$y$}--(0,0)--(8,0)node[below]{$x$};
      
end{tikzpicture}
      
end{document}


      enter image description here






      tikz-pgf







      share|improve this question














      I'd like to draw a set of curves, each tangent to a different point on a given line. The requirement is that the curves are convex and downward sloping.



      In the following MWE, I use the to[out=<x>,in=<y>] operation to manually adjust the slope of the curves so that they appear to be tangent at the desired point. This requires a lot of trial-and-errors and the result is not ideal. Is there a better way to draw such curves?



      MWE



      documentclass[border=2pt,tikz]{standalone}
      
begin{document}
      
begin{tikzpicture}
      
  foreach i in {1,2,3,4}{
      
    draw[thick](0,4.5)--(7,0)coordinate[pos=i/5](i);
      
    fill(i)circle[radius=2pt]node[below left]{pt i};
      
    draw[red](i)to[out=140,in=-80]++(-1,1.5) (i)to[out=-25,in=170]++(1.25,-.4);
      
  }
      
  draw[<->](0,5)node[left]{$y$}--(0,0)--(8,0)node[below]{$x$};
      
end{tikzpicture}
      
end{document}


      enter image description here






      tikz-pgf




      tikz-pgf






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 4 hours ago









      Herr K.Herr K.

      14k43483




      14k43483






















          1 Answer
          1






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          oldest

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          5














          You could use decorations.marking, which transforms you automatically in tangent space. Then you just need to draw a curve which has slope 0 at (0,0).



          documentclass[border=2pt,tikz]{standalone}
          
usetikzlibrary{decorations.markings}
          
begin{document}
          
begin{tikzpicture}[touching curve at/.style={postaction=decorate,
          
decoration={markings,mark=at position #1 with 
          
{draw[touching] (-1,0.5) to[out=-45,in=180] (0,0) to[out=0,in=-135] (1,0.5);}}},
          
touching/.style={red}]
          
  draw[thick,touching curve at/.list={1/5,2/5,3/5,4/5}](0,4.5)--(7,0);
          
  draw[<->](0,5)node[left]{$y$}--(0,0)--(8,0)node[below]{$x$};
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer



















          • 2





            Awesome! Thank you very much!

            – Herr K.
            4 hours ago











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          1 Answer
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          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          5














          You could use decorations.marking, which transforms you automatically in tangent space. Then you just need to draw a curve which has slope 0 at (0,0).



          documentclass[border=2pt,tikz]{standalone}
          
usetikzlibrary{decorations.markings}
          
begin{document}
          
begin{tikzpicture}[touching curve at/.style={postaction=decorate,
          
decoration={markings,mark=at position #1 with 
          
{draw[touching] (-1,0.5) to[out=-45,in=180] (0,0) to[out=0,in=-135] (1,0.5);}}},
          
touching/.style={red}]
          
  draw[thick,touching curve at/.list={1/5,2/5,3/5,4/5}](0,4.5)--(7,0);
          
  draw[<->](0,5)node[left]{$y$}--(0,0)--(8,0)node[below]{$x$};
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer



















          • 2





            Awesome! Thank you very much!

            – Herr K.
            4 hours ago
















          5














          You could use decorations.marking, which transforms you automatically in tangent space. Then you just need to draw a curve which has slope 0 at (0,0).



          documentclass[border=2pt,tikz]{standalone}
          
usetikzlibrary{decorations.markings}
          
begin{document}
          
begin{tikzpicture}[touching curve at/.style={postaction=decorate,
          
decoration={markings,mark=at position #1 with 
          
{draw[touching] (-1,0.5) to[out=-45,in=180] (0,0) to[out=0,in=-135] (1,0.5);}}},
          
touching/.style={red}]
          
  draw[thick,touching curve at/.list={1/5,2/5,3/5,4/5}](0,4.5)--(7,0);
          
  draw[<->](0,5)node[left]{$y$}--(0,0)--(8,0)node[below]{$x$};
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer



















          • 2





            Awesome! Thank you very much!

            – Herr K.
            4 hours ago














          5












          5








          5







          You could use decorations.marking, which transforms you automatically in tangent space. Then you just need to draw a curve which has slope 0 at (0,0).



          documentclass[border=2pt,tikz]{standalone}
          
usetikzlibrary{decorations.markings}
          
begin{document}
          
begin{tikzpicture}[touching curve at/.style={postaction=decorate,
          
decoration={markings,mark=at position #1 with 
          
{draw[touching] (-1,0.5) to[out=-45,in=180] (0,0) to[out=0,in=-135] (1,0.5);}}},
          
touching/.style={red}]
          
  draw[thick,touching curve at/.list={1/5,2/5,3/5,4/5}](0,4.5)--(7,0);
          
  draw[<->](0,5)node[left]{$y$}--(0,0)--(8,0)node[below]{$x$};
          
end{tikzpicture}
          
end{document}


          enter image description here






          share|improve this answer













          You could use decorations.marking, which transforms you automatically in tangent space. Then you just need to draw a curve which has slope 0 at (0,0).



          documentclass[border=2pt,tikz]{standalone}
          
usetikzlibrary{decorations.markings}
          
begin{document}
          
begin{tikzpicture}[touching curve at/.style={postaction=decorate,
          
decoration={markings,mark=at position #1 with 
          
{draw[touching] (-1,0.5) to[out=-45,in=180] (0,0) to[out=0,in=-135] (1,0.5);}}},
          
touching/.style={red}]
          
  draw[thick,touching curve at/.list={1/5,2/5,3/5,4/5}](0,4.5)--(7,0);
          
  draw[<->](0,5)node[left]{$y$}--(0,0)--(8,0)node[below]{$x$};
          
end{tikzpicture}
          
end{document}


          enter image description here







          share|improve this answer












          share|improve this answer



          share|improve this answer










          answered 4 hours ago









          marmotmarmot

          100k4116223




          100k4116223








          • 2





            Awesome! Thank you very much!

            – Herr K.
            4 hours ago














          • 2





            Awesome! Thank you very much!

            – Herr K.
            4 hours ago








          2




          2





          Awesome! Thank you very much!

          – Herr K.
          4 hours ago





          Awesome! Thank you very much!

          – Herr K.
          4 hours ago


















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