Shadings in TikZ due to vertices

Question

I have this particular problem with shadings in TikZ. I want to convert quadrilateral patch plot to TikZ.

What I know - vector of vertices coordinates and connectivity list of patches.
What I do not know - order of vertices in connectivity list.

I have managed to get correct clockwise order for rectangular shapes. However in case of arbitrary shaped quadrilaterals, I have a problem to determine which particular vertex is in upper right corner, upper left corner etc.

\documentclass[tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{shadings}

\begin{document}
\begin{tikzpicture}
    \fill [fill,
           upper right=red, 
           upper left=blue, 
           lower left=green,
           lower right=yellow]
          (-1,-1) -- (-1,1) -- (1,1) -- (1,-1) -- cycle;
    % coordinates description was added in picture below 
\end{tikzpicture}
\end{document}

I need to get something like on the image but with assigning colours to particular vertex (a, b, ...) rather then to particular corner.

Do anyone please know how to achieve this?

Answer 1

Here is a proposal and the syntax is up for negotiation. The basic points are that the shading can be rotated using a shading angle. This shading angle can be computed with calc. The syntax is something like

\path[shaded quadrilateral={(-1,-1)--(-1,1)--(1,1)--(1,-1)}];

where the first color is associated to the first vertex, the second color to the second vertex and so on. The colors are stored in pgf keys, which is illustrated by the following MWE. The restriction is that the shape needs to have 4 corners.

\documentclass[tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{shadings,calc}

\begin{document}
\begin{tikzpicture}[font=\sffamily,
  shaded quadrilateral/.style args={#1--#2--#3--#4}{
  insert path={($0.25*#1+0.25*#2+0.25*#3+0.25*#4$) coordinate (auxsq)
  let \p1=($#1-(auxsq)$),\n1={atan2(\y1,\x1)},
  \p2=($#2-(auxsq)$),\n2={atan2(\y2,\x2)-\n1)}
   in [/utils/exec=\pgfmathtruncatemacro{\itest}{sign(sin(\n2-\n1))}]
    \ifnum\itest=1 
            [upper right=\pgfkeysvalueof{/tikz/sq/color 1}, 
             upper left=\pgfkeysvalueof{/tikz/sq/color 2}, 
             lower left=\pgfkeysvalueof{/tikz/sq/color 3},
             lower right=\pgfkeysvalueof{/tikz/sq/color 4},shading angle=\n1-45] 
      \else
             [upper right=\pgfkeysvalueof{/tikz/sq/color 1}, 
             upper left=\pgfkeysvalueof{/tikz/sq/color 4}, 
             lower left=\pgfkeysvalueof{/tikz/sq/color 3},
             lower right=\pgfkeysvalueof{/tikz/sq/color 2},shading angle=\n1-45] 
       \fi               
      #1--#2--#3--#4-- cycle
  }},sq/.cd,color 1/.initial=red,color 2/.initial=blue,color 3/.initial=green,
  color 4/.initial=yellow]
 \begin{scope}[local bounding box=normal]
  \path[shaded quadrilateral={(-1,-1)--(-1,1)--(1,1)--(1,-1)}];
 \end{scope}
 \node[above] at (normal.north) {normal use};
 %
 \begin{scope}[xshift=3cm,local bounding box=perm]
  \path[shaded quadrilateral={(1,1)--(1,-1)--(-1,-1)--(-1,1)}];
 \end{scope}
 \node[above,align=center] at (perm.north) {permutations\\ of the vertices};
 %
 \begin{scope}[yshift=-3cm,local bounding box=cols,
  sq/.cd,color 1=magenta,color 2=red,color 3=cyan,color 4=black]
  \path[shaded quadrilateral={(1,1)--(1,-1)--(-1,-1)--(-1,1)}];
 \end{scope}
 \node[above] at (cols.north) {color change};
 %
 \begin{scope}[xshift=3cm,yshift=-3cm,local bounding box=rot]
  \path[shaded quadrilateral={(30:{sqrt(2)})--(120:{sqrt(2)})--(210:{sqrt(2)})--(300:{sqrt(2)})}];
 \end{scope}
 \node[above,align=center] at (rot.north) {rotated};
 %
 \pgfmathsetseed{2019}
 \begin{scope}[yshift=-6.5cm,local bounding box=rand1,
  sq/.cd,color 1=magenta,color 2=red,color 3=cyan,color 4=black]
  \path[shaded quadrilateral={(90*rnd:1+0.7*rnd)--(90+90*rnd:1+0.7*rnd)--(180+90*rnd:1+0.7*rnd)--(270+90*rnd:1+0.7*rnd)}];
 \end{scope}
 \node[above] at (rand1.north) {random 1};
 %
 \begin{scope}[xshift=3cm,yshift=-6.5cm,local bounding box=orientation]
  \path[shaded quadrilateral={(-1,-1)--(1,-1)--(1,1)--(-1,1)}];
 \end{scope}
 \node[above,align=center] at (orientation.north) {orientation\\ change};
\end{tikzpicture}
\end{document}