tikz: not so precise graphic

Question

Do you see the point (0.78951,1.38506) is slightly below the previous one, while it should be above?

\documentclass{standalone}

    \usepackage[T1]{fontenc}
    \usepackage[utf8]{inputenc}
    \usepackage{amsmath,amssymb,amsfonts,systeme} % Typical maths resource packages
    \usepackage{color}                    % For creating coloured text and background
    \usepackage{array}
    \usepackage{tikz}
    \usepackage{tkz-euclide}
    \usetkzobj{all}
    \usetikzlibrary{arrows.meta}
    \usepackage{siunitx}
    \usepackage{pgfplots}
    \usepackage{filecontents}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[
  grid, grid style=dashed,
  xticklabel style={rotate=90},
  ymin=1.33,ymax=1.39,
  extra y ticks={1.33,1.35,1.37},            % <---
  xmax=1,xmin=0,
  extra x ticks={0},            % <---
  xtick={0,0.20594,0.38019,0.62664,0.78951,1},
  minor tick num=1,
  axis lines = middle,
  set layers,                   % <---
  %axis on top,                  % <---
  xlabel=$x_1$,ylabel=$n_D$,
  x label style={at={(1,0)},right},
  y label style={at={(0,1)},above},
  x tick label style={/pgf/number format/.cd,
                      fixed relative,
                      /pgf/number format/precision=5
                     },
  style={thick}
               ]
  \addplot+[color=red,mark=*,mark options={draw=red,fill=green},thick,smooth]
    coordinates {
    (0.00000, 1.33300)(0.20594,1.37003)(0.38019,1.37944)(0.62664,1.38502)(0.78951,1.38506)(1.00000,1.38511)
    };
  \end{axis}
\end{tikzpicture}
\end{document}

Is it just me, or is it really like that? In this case, do you have any suggestions?

Thank you in advance

Answer 1

It's a optical effect because the slope of the red curve at point (0.65664, 1.38502) is too big relative to the (real) slope between the points (0.65664, 1.38502) and (0.78951,1.38506). You can see in this magnified screenshot (with the blue horizontal line) that the point (0.78951,1.38506) is really above the previous one.

Note the adding of the line \pgfplotsset{compat=1.16} in the code:

\documentclass{standalone}

    \usepackage[T1]{fontenc}
    \usepackage[utf8]{inputenc}
    \usepackage{amsmath,amssymb,amsfonts,systeme} % Typical maths resource packages
    \usepackage{color}                    % For creating coloured text and background
    \usepackage{array}
    \usepackage{tikz}
    \usepackage{tkz-euclide}
    \usetkzobj{all}
    \usetikzlibrary{arrows.meta}
    \usepackage{siunitx}
    \usepackage{pgfplots}
    \usepackage{filecontents}
    \pgfplotsset{compat=1.16}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[
  grid, grid style=dashed,
  xticklabel style={rotate=90},
  ymin=1.33,ymax=1.39,
  extra y ticks={1.33,1.35,1.37},            % <---
  xmax=1,xmin=0,
  extra x ticks={0},            % <---
  xtick={0,0.20594,0.38019,0.62664,0.78951,1},
  minor tick num=1,
  axis lines = middle,
  set layers,                   % <---
  %axis on top,                  % <---
  xlabel=$x_1$,ylabel=$n_D$,
  x label style={at={(1,0)},right},
  y label style={at={(0,1)},above},
  x tick label style={/pgf/number format/.cd,
                      fixed relative,
                      /pgf/number format/precision=5
                     },
  style={thick}
               ]
  \addplot+[color=red,mark=*,mark options={draw=red,fill=green},thick,smooth]
    coordinates {
    (0.00000, 1.33300)(0.20594,1.37003)(0.38019,1.37944)(0.62664,1.38502)(0.78951,1.38506)(1.00000,1.38511)
    };
    \draw[ultra thin, blue] (0.62,1.38410)--(0.8,1.38410) ;
    \draw[ultra thin, violet] (0.62664,1.38502) -- (0.70,1.38570);
  \end{axis}

\end{tikzpicture}
\end{document}

You could reduce this effect by reducing the tension (by default, it is 0.55): \addplot+[color=red,mark=*,mark options={draw=red,fill=green},thick,smooth,tension=0.25]

give:

Answer 2

The point at 0.79 is not actually lower. Rather the interpolated graph keeps increasing after the point at 0.62 and this makes it look as if the point as 0.79 is lower. You can see that this is the case by magnifying the graph and just looking at these two points. The image below shows that the point at 0.79, on the right, is indeed slightly higher than the point at 0.62:

[This is really an extended comment, except that you can't put images into comments...]