Color gradient in a polygon along a specified direction

Question

This code:

\documentclass[tikz,border=1mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{backgrounds}

\begin{document}
    \begin{tikzpicture}[scale=4]
        \begin{scope}[on background layer]
            \draw[fill, top color=black, bottom color=white, shading=axis, shading angle=-33.02] 
            (1,1) -- (-1,1) -- (-1,0.8) -- (1,-0.5) -- cycle;
        \end{scope}
    \end{tikzpicture}
\end{document}

produces the following polygon with a color gradient orthogonal to the diagonal line.

I have two problems:

1) The gradient should always be orthogonal to the diagonal line. How can I compute automatically the right angle? Is there another way to define the direction of the gradient / shading?

2) The shading does not really go from white to black. I want the shading to be white at the diagonal line and black in the upper right corner. What is the right way to do that?

Answer 1

Only for comparism. Run with xelatex:

\documentclass[pstricks,border=1mm]{standalone}
\usepackage{pst-grad}

\begin{document}
\psset{unit=4}
\begin{pspicture}(-1,-0.5)(1,1)
\psclip{\pspolygon[linestyle=none](1,1)(-1,1)(-1,0.8)(1,-0.5)}
  \pspolygon[linestyle=none,fillstyle=gradient,gradbegin=black,
  gradangle=-33,gradend=white,gradmidpoint=0.47](-1.5,1)(1,1)(1,-0.5)
\endpsclip
\pspolygon(1,1)(-1,1)(-1,0.8)(1,-0.5)
\end{pspicture}

\end{document}

Answer 2

You definitely do not have to hardcode the shading angle. This answer comes with a style that can be used as

shading angle from={line from (-1,0.8) to (1,-0.5)}

which then inserts the appropriate shading angle

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{backgrounds,calc}

\begin{document}
    \begin{tikzpicture}[scale=4,shading angle from/.style args={line from #1 to #2}{
    insert path={let \p1=($#2-#1$),\n1={atan2(\y1,\x1)} in},
    shading angle=\n1}]
        \begin{scope}[on background layer]
            \draw[fill, top color=black, bottom color=white,
            shading angle from={line from (-1,0.8) to (1,-0.5)}] 
            (1,1) -- (-1,1) -- (-1,0.8) -- (1,-0.5) -- cycle;
        \end{scope}
    \end{tikzpicture}
\end{document}