[Tex/LaTex] Smoother curves

pgfplots

With the attached code I have the result in picture. In the range 0-20 it is very clear that the curve has sharp changes and this is not aesthetically good.

Is there a way to make curves smoother? Thanks

\begin{tikzpicture}
\begin{axis}[
    width=\textwidth, height=10cm,
    xlabel=$Pressure~(m~water)$,
    ylabel={$Water~content~(v/v)$},
    legend style={draw=none, legend columns=2, at={(.9,.9)}}]
    \addplot+[blue,no marks,domain=0.001:160] {.508-1.52398*exp(-(13702.2/x)^0.13266)};
    \addplot+[violet,no marks,domain=0.001:160] {.445-0.34900*exp(-(30.0706/x)^0.23650)};
    \addplot+[red,no marks,domain=0.001:160] {.503-0.41288*exp(-(1.56530/x)^0.66572)};
    \addplot+[orange,no marks,domain=0.001:160] {.465-0.39848*exp(-(0.67406/x)^0.84737)};
    \addplot+[green,no marks,domain=0.001:160] {.350-0.31765*exp(-(0.53648/x)^1.21892)};
    \addplot+[brown,no marks,domain=0.001:160] {.395-0.38594*exp(-(0.07439/x)^0.92067)};
    \legend{Silty clay, Clay loam, Loam, Sandy loam, Medium fine loam, Coarsesand};
\end{axis}
\end{tikzpicture}

Best Answer

While the option smooth makes the curve smoother, it also results in off shooting at the edges thereby making the graph inaccurate. It is better to use samples key and increase the number of samples. More the samples, more finer is the curve. Here only the limiting factor is the time taken for compilation and the memory. Below is an example with samples=500.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
  \begin{tikzpicture}
    \begin{axis}[
        width=\textwidth, height=10cm,
        xlabel=$Pressure~(m~water)$,
        ylabel={$Water~content~(v/v)$},
        legend style={draw=none, legend columns=2, at={(.9,.9)}}]
        \addplot+[blue,no marks,domain=0.001:160,samples=500] {.508-1.52398*exp(-(13702.2/x)^0.13266)};
        \addplot+[violet,no marks,domain=0.001:160,samples=500] {.445-0.34900*exp(-(30.0706/x)^0.23650)};
        \addplot+[red,no marks,domain=0.001:160,samples=500] {.503-0.41288*exp(-(1.56530/x)^0.66572)};
        \addplot+[orange,no marks,domain=0.001:160,samples=500] {.465-0.39848*exp(-(0.67406/x)^0.84737)};
        \addplot+[green,no marks,domain=0.001:160,samples=500] {.350-0.31765*exp(-(0.53648/x)^1.21892)};
        \addplot+[brown,no marks,domain=0.001:160,samples=500] {.395-0.38594*exp(-(0.07439/x)^0.92067)};
        \legend{Silty clay, Clay loam, Loam, Sandy loam, Medium fine loam, Coarsesand};
    \end{axis}
\end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] Fill area between curves

The question didn't contain the functions or coordinates needed to produce the graphs showed in the image, so I used some dummy coordinates, but the idea is the same. Two customizable filling patterns were also defined:

\documentclass[8pt]{beamer}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{pgfplots}

% New customizable pattern
\tikzset{
  hatch distance/.store in=\hatchdistance,
  hatch distance=8pt,
  hatch thickness/.store in=\hatchthickness,
  hatch thickness=5pt,
  hatch color/.store in=\hatchcolor,
  hatch color=gray!20
}

\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{thick vlines}
  {\pgfpointorigin}{\pgfqpoint{\hatchthickness}{100pt}}{\pgfqpoint{\hatchdistance}{100pt}}%
  {
  \pgfsetlinewidth{\hatchthickness}
  \pgfpathmoveto{\pgfqpoint{0.5pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{0.5pt}{100pt}}
  \pgfusepath{stroke}
  }
\pgfdeclarepatterninherentlycolored[\hatchcolor]{crosshatch dots color}
{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}
{\pgfpoint{8pt}{8pt}}
{
  \pgfsetfillcolor{\hatchcolor}
  \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}
  \pgfusepath{fill}
  \pgfsetfillcolor{\hatchcolor}
  \pgfpathcircle{\pgfpoint{2pt}{1.75pt}}{20pt}
  \pgfpathcircle{\pgfpoint{6pt}{5.75pt}}{20pt}
  \pgfusepath{fill}
  \pgfsetfillcolor{pgf@darklightsteelblue!70}
  \pgfpathcircle{\pgfpoint{2pt}{2.25pt}}{0.4pt}
  \pgfpathcircle{\pgfpoint{6pt}{6.25pt}}{0.4pt}
  \pgfusepath{fill}
}

\begin{document}

\begin{frame}
  \begin{tikzpicture}
  \begin{axis}[domain=0:1,
   width=10cm,
  minor tick num=3,
   height=8cm,
  ymin=0,
  ymax=1.2,
  xmin=0,
  xmax=1,
  xticklabel=\empty,
  yticklabel=\empty,
  samples=50,
  smooth,
  xlabel=$r_{k}$,
  ylabel=$s_{k}$,
  extra x ticks={0,1},
  extra y ticks={1},
  extra x tick style={grid=major,thick},
  extra y tick style={grid=major,thick},
  extra x tick labels={$0$,$1$},
  extra y tick labels={$1$},
  legend pos=north east]

\draw[pattern=crosshatch dots color]
  (axis cs:0,0) -- (axis cs:0.12,1) -- (axis cs:1,1) -- (axis cs:0,0);
\addplot+[
  id=mod,
  color=black,
  domain=0:1,
  samples=50,
  pattern=thick vlines,
  hatch thickness=3pt
] coordinates {(0,0) (0.2,0.45) (0.5,0.8) (0.75,0.92) (1,1)};
\addplot[id=naive,color=black,domain=0:1,samples=50] {x} ;

\node (a) at (axis cs:0.2,0.8)  {$a_{P}$};
\node[draw,fill=gray!30] (b) at (axis cs:0.45,0.6)  {$a_{R}$};

\begin{scope}[
  every pin edge/.style={<-,>=latex},
  pin distance=1.5cm
]
\node[pin=-30:{Rating model},] at (axis cs:0.5,0.8) {};
\node[pin=-30:{Random model},] at (axis cs:0.3,0.3) {};
\node[pin=15:{Perfect model},] at (axis cs:0.4,1.01) {};
\end{scope}
\end{axis}
\end{tikzpicture}
\end{frame}

\end{document}

enter image description here

And using x^0.45 to produce the curved path:

\documentclass[8pt]{beamer}
\usepackage{tikz}
\usetikzlibrary{patterns}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

% New customizable pattern
\tikzset{
  hatch distance/.store in=\hatchdistance,
  hatch distance=8pt,
  hatch thickness/.store in=\hatchthickness,
  hatch thickness=5pt,
  hatch color/.store in=\hatchcolor,
  hatch color=gray!20
}

\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{thick vlines}
  {\pgfpointorigin}{\pgfqpoint{\hatchthickness}{100pt}}{\pgfqpoint{\hatchdistance}{100pt}}%
  {
  \pgfsetlinewidth{\hatchthickness}
  \pgfpathmoveto{\pgfqpoint{0.5pt}{0pt}}
  \pgfpathlineto{\pgfqpoint{0.5pt}{100pt}}
  \pgfusepath{stroke}
  }
\pgfdeclarepatterninherentlycolored[\hatchcolor]{crosshatch dots color}
{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}
{\pgfpoint{8pt}{8pt}}
{
  \pgfsetfillcolor{\hatchcolor}
  \pgfpathrectangle{\pgfpointorigin}{\pgfpoint{8pt}{8pt}}
  \pgfusepath{fill}
  \pgfsetfillcolor{\hatchcolor}
  \pgfpathcircle{\pgfpoint{2pt}{1.75pt}}{20pt}
  \pgfpathcircle{\pgfpoint{6pt}{5.75pt}}{20pt}
  \pgfusepath{fill}
  \pgfsetfillcolor{pgf@darklightsteelblue!70}
  \pgfpathcircle{\pgfpoint{2pt}{2.25pt}}{0.4pt}
  \pgfpathcircle{\pgfpoint{6pt}{6.25pt}}{0.4pt}
  \pgfusepath{fill}
}

\begin{document}

\begin{frame}
  \begin{tikzpicture}
  \begin{axis}[domain=0:1,
   width=10cm,
  minor tick num=3,
   height=8cm,
  ymin=0,
  ymax=1.2,
  xmin=0,
  xmax=1,
  xticklabel=\empty,
  yticklabel=\empty,
  samples=50,
  smooth,
  xlabel=$r_{k}$,
  ylabel=$s_{k}$,
  extra x ticks={0,1},
  extra y ticks={1},
  extra x tick style={grid=major,thick},
  extra y tick style={grid=major,thick},
  extra x tick labels={$0$,$1$},
  extra y tick labels={$1$},
  legend pos=north east]

\draw[pattern=crosshatch dots color]
  (axis cs:0,0) -- (axis cs:0.05,1) -- (axis cs:1,1) -- (axis cs:0,0);
\addplot[
  id=mod,
  color=black,
  domain=0:1,
  samples=100,
  pattern=thick vlines,
  hatch thickness=3pt
] {(x^(0.45))};
\addplot[id=naive,color=black,domain=0:1,samples=50] {x} ;

\node (a) at (axis cs:0.2,0.8)  {$a_{P}$};
\node[draw,fill=gray!30] (b) at (axis cs:0.45,0.6)  {$a_{R}$};

\begin{scope}[
  every pin edge/.style={<-,>=latex},
  pin distance=1.5cm
]
\node[pin=-30:{Rating model},] at (axis cs:0.5,0.8) {};
\node[pin=-30:{Random model},] at (axis cs:0.3,0.3) {};
\node[pin=15:{Perfect model},] at (axis cs:0.4,1.01) {};
\end{scope}
\end{axis}
\end{tikzpicture}
\end{frame}

\end{document}

enter image description here

In general, the following code can be used to fill the area between the graph of two functions f and g:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\pgfplotsset{compat=newest}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
  domain=-2:9,
  samples=60,
  stack plots=y
]
% draw graph for the first function f
\addplot+[mark=none] {(x-3)^2};
% draw graph of max(g-f, 0) and stack
\addplot+[mark=none,fill=green!40,draw=red] {max(x+2-((x-3)^2),0)} \closedcycle;
% draw graph of min(g-f, 0) and stack
\addplot+[mark=none,fill=none,draw=red] {min(x+2-((x-3)^2),0)};
\end{axis}
\end{tikzpicture}

\end{document}

enter image description here

[Tex/LaTex] Make plot smoother in pgfplots

The default surface plot of pgfplots uses two triangles for each rectangular patch segment. Usually, the diagonal does not matter much -- but in this case, it really matters and the result is unsuitable.

Note that shader=interp appears to select the other diagonal (unintentionally, but it does). A simple solution would be to add shader=interp, unless you really need the grid lines.

\documentclass{standalone}

\usepackage{pgfplots}
\usepgfplotslibrary{patchplots}
\pgfplotsset{compat = 1.12}

\newcommand{\param}{2.0}

\begin{document}
        \begin{tikzpicture}
          \begin{axis}[view={40}{50}]
            \addplot3[surf, domain = 0:1, y domain = 0:1, unbounded coords=jump,
                shader=interp,
                samples = 25]
            {x^(-\param-1)*y^(-\param-1)*(x^(-\param)+y^(-\param)-1)^(-1/\param-2)+\param*x^(-\param-1)*y^(-\param-1)*(x^(-\param)+y^(-\param)-1)^(-1/\param-2)};
        \end{axis}
      \end{tikzpicture}
\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Fill area between curves

[Tex/LaTex] Make plot smoother in pgfplots

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