problem at drawing 3D square for right angle with tikz, pgfplots

Question

I'm drawing a 3D square for right angle following https://tex.stackexchange.com/a/163384/14423. That works fine, but I try filling that square and the results isn't the spected:

\documentclass{memoir}
\usepackage{tikz,pgfplots}
\usetikzlibrary{calc}

\pgfplotsset{ /pgfplots/area style/.style={%
 area cycle list,
 area legend,
 axis on top,
 }}

\newcommand{\RightAngle}[4][5pt]{%
    \draw[fill] ($#3!#1!#2$)
    --($ #3!2!($($#3!#1!#2$)!.5!($#3!#1!#4$)$) $)
    --($#3!#1!#4$) ;
    }

\begin{document}    
\begin{tikzpicture}
 \begin{axis}[scale=0.65,view={130}{30},axis equal,axis on top,axis lines=center,xlabel=$x(t)$,ylabel=$y(t)$,zlabel=$z(t)$,xtick=\empty,ytick=\empty,ztick=\empty]
  \addplot3[thick,->,black,samples y=0] coordinates {(0.261,1.047,1) (0.511,2.047,1)};
  \addlegendentryexpanded{$T(t)$}
  \addplot3[thick,->,color=green,samples y=0] coordinates {(0.261,1.047,1) (0.261,1.047,-0.5)};
 \addlegendentryexpanded{$T'(t)$}
 \addplot3[thick,->,color=red,samples y=0] coordinates {(0.261,1.047,1) (0.261,1.047,-0.125)};
 \addlegendentryexpanded{$N(t)$}
 \addplot3[blue,domain=0:pi,samples y=0] ({x/4},{x},{sin(deg(1.5*x))});
 %\addlegendentryexpanded{$\Ce$}
 \addplot3[mark=*,mark size=1.5pt] coordinates{(0.261,1.047,1)} node{};
 \coordinate (P) at (0.261,1.047,1);
 \coordinate (T) at (0.511,2.047,1);
 \coordinate (N) at (0.261,1.047,-0.125);
 \RightAngle{(T)}{(P)}{(N)};
\end{axis}
\end{tikzpicture}

\end{document}

As you can see there is a dotted node and the square for right angle is not filled completely. What am I doing wrong? and how get square filled with dashed lines?

Answer 1

Because you are using something optimised for an older version of pgfplots which gave wrong output, you need to specify a version to get the correct output. At least, that is how I roughly understood the console warnings. Adding the compatibility option newest gave me the output posted in the question. So, with advice from Alenanno, this could be set to e.g. 1.12 which seems to be the version I get if I ask for newest.

When you specify the right angle, you specify from left to right of the bottom and then up to the top right and nothing else. TikZ completes the path using the shortest possible route i.e. from top right to bottom left of the square and fills the result i.e. half of the square. You need to specify that the path goes through P before returning to the start point in order to fill the square.

\newcommand{\RightAngle}[4][5pt]{%
  \draw[fill] ($#3!#1!#2$) -- ($ #3!2!($($#3!#1!#2$)!.5!($#3!#1!#4$)$) $) -- ($#3!#1!#4$) -- #3  -- cycle;
}

I also moved the legend a bit so I could see what I was doing.

To fill the square with lines, try the patterns library and use pattern rather than fill for the path. For example:

\newcommand{\RightAngle}[4][5pt]{%
  \draw[pattern=north east lines] ($#3!#1!#2$) -- ($ #3!2!($($#3!#1!#2$)!.5!($#3!#1!#4$)$) $) -- ($#3!#1!#4$) -- #3  -- cycle;
}

Complete code:

\documentclass[tikz,border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\usetikzlibrary{calc,patterns}

\pgfplotsset{ /pgfplots/area style/.style={%
    area cycle list,
    area legend,
    axis on top,
  }}

\newcommand{\RightAngle}[4][5pt]{%
  \draw[pattern=north east lines] ($#3!#1!#2$) -- ($ #3!2!($($#3!#1!#2$)!.5!($#3!#1!#4$)$) $) -- ($#3!#1!#4$) -- #3  -- cycle;
}
\begin{document}
\begin{tikzpicture}
  \begin{axis}
    [
      scale=0.65,
      view={130}{30},
      axis equal,
      axis on top,
      axis lines=center,
      xlabel=$x(t)$,
      ylabel=$y(t)$,
      zlabel=$z(t)$,
      xtick=\empty,
      ytick=\empty,
      ztick=\empty,
      legend style={anchor=east}
    ]
    \addplot3[thick,->,black,samples y=0] coordinates {(0.261,1.047,1) (0.511,2.047,1)};
    \addlegendentryexpanded{$T(t)$}
    \addplot3[thick,->,color=green,samples y=0] coordinates {(0.261,1.047,1) (0.261,1.047,-0.5)};
    \addlegendentryexpanded{$T'(t)$}
    \addplot3[thick,->,color=red,samples y=0] coordinates {(0.261,1.047,1) (0.261,1.047,-0.125)};
    \addlegendentryexpanded{$N(t)$}
    \addplot3[blue,domain=0:pi,samples y=0] ({x/4},{x},{sin(deg(1.5*x))});
    %\addlegendentryexpanded{$\Ce$}
    \addplot3[mark=*,mark size=1.5pt] coordinates{(0.261,1.047,1)} node{};
    \coordinate (P) at (0.261,1.047,1);
    \coordinate (T) at (0.511,2.047,1);
    \coordinate (N) at (0.261,1.047,-0.125);
    \RightAngle{(T)}{(P)}{(N)};
  \end{axis}
\end{tikzpicture}
\end{document}