The first code:

documentclass[pstricks]{standalone}

usepackage{pst-plot}

defm{1/((x-1)^2)^(1/3)}



begin{document}    

begin{pspicture}(-1,-1)(3.5,3.5)

 psaxes[labelFontSize=scriptstyle]{->}(0,0)(3,3)[$x$,-90][$y$,0]

 psplot[ algebraic,

         % plotstyle=curve,

            plotpoints=1000, <<-- notice

            yMaxValue=3,

            linewidth=1.5pt,

            linecolor=red]{0}{3}{m}

psline[linestyle=dashed](1,0)(1,3)

end{pspicture} 

end{document}

The second code:

documentclass[pstricks]{standalone}

usepackage{pst-plot}

defm{1/((x-1)^2)^(1/3)}



begin{document}    

begin{pspicture}(-1,-1)(3.5,3.5)

psaxes[labelFontSize=scriptstyle]{->}(0,0)(3,3)[$x$,-90][$y$,0]

psplot[ algebraic,

         plotstyle=curve,

         %plotpoints=1000,

          yMaxValue=3,

         linewidth=1.5pt,

         linecolor=red]{0}{3}{m}

psline[linestyle=dashed](1,0)(1,3)

end{pspicture} 

end{document}

The result of compiling is frustrating.

1. What is the difference between them?


2. Can you fix the picture to make it become equal?

The best way to explain is showing the animations, right?

With curve plotstyle

It needs at least 3 points. When N=2 there is no graph.

documentclass[12pt,pstricks]{standalone}

usepackage{pst-plot}

defm{1/((x-1)^2)^(1/3)}

defxl{3 -1.5 exp neg 1 add}

defxr{3 -1.5 exp 1 add}

begin{document}

multido{i=2+1}{20}{%

begin{pspicture}[algebraic,showpoints,plotstyle=curve](-1,-1)(3.5,4)

    psaxes[labelFontSize=scriptstyle]{->}(0,0)(3,3.5)[$x$,-90][$y$,0]

    psplot[linecolor=red,plotpoints=i]{0}{xl}{m}

    psplot[linecolor=red,plotpoints=i]{xr}{3}{m}

    psline[linestyle=dashed](1,0)(1,3)

    rput[t](2,3){$N=i$}

end{pspicture}} 

end{document}

With line plotstyle

It needs at least 2 points.

documentclass[12pt,pstricks]{standalone}

usepackage{pst-plot}

defm{1/((x-1)^2)^(1/3)}

defxl{3 -1.5 exp neg 1 add}

defxr{3 -1.5 exp 1 add}

begin{document}

multido{i=2+1}{20}{%

begin{pspicture}[algebraic,showpoints,plotstyle=line](-1,-1)(3.5,4)

    psaxes[labelFontSize=scriptstyle]{->}(0,0)(3,3.5)[$x$,-90][$y$,0]

    psplot[linecolor=red,plotpoints=i]{0}{xl}{m}

    psplot[linecolor=red,plotpoints=i]{xr}{3}{m}

    psline[linestyle=dashed](1,0)(1,3)

    rput[t](2,3){$N=i$}

end{pspicture}} 

end{document}

Final output

documentclass[12pt,pstricks]{standalone}

usepackage{pst-plot}

defm{1/((x-1)^2)^(1/3)}

defxl{3 -1.5 exp neg 1 add}

defxr{3 -1.5 exp 1 add}

begin{document}

begin{pspicture}[algebraic](-.5,-.6)(4,4)

    psaxes[labelFontSize=scriptstyle]{->}(0,0)(3.5,3.5)[$x$,0][$y$,90]

    psplot[linecolor=red]{0}{xl}{m}

    psplot[linecolor=red]{xr}{3}{m}

    psline[linestyle=dashed](1,0)(1,3)

end{pspicture}

end{document}

My best practices

• Split the graph into two or more invocation of psplot when there are discontinuities in a single plot.


• Increasing plotpoints blindly will waste more storage because the size of PDF (or SVG) increases as well.


• You don't need to change plotstyle most of the time.

Explanation

• 
  defxl{3 -1.5 exp neg 1 add} is the value of xl<1 such that f(xl)=3.



• defxr{3 -1.5 exp 1 add} is the value of xr>1 such that f(xr)=3.




• plotstyle represents the type of curves is used to connect points.



• 
  plotpoints represents the number of points used to draw the curve.

documentclass[pstricks]{standalone}

usepackage{pst-plot}

begin{document}    



begin{pspicture}(-1,-1)(3.5,3.5)

psaxes[labelFontSize=scriptstyle]{->}(0,0)(3,3)[$x$,-90][$y$,0]

psclip{psframe[linestyle=none](3,3)}

  psplot[ algebraic,linewidth=1.5pt,linecolor=red]{0}{3}{1/((x-1)^2)^(1/3)}

endpsclip

psline[linestyle=dashed](1,0)(1,3)

end{pspicture} 



end{document}