corners.sty

\NeedsTeXFormat{LaTeX2e}[1994/06/01]
\ProvidesPackage{custom}[2018/07/02 Joined up polygon corners in tikz]

\RequirePackage{tikz,xparse}
\usetikzlibrary{math,calc,intersections}

\providecommand{\len}{0.8pt}
\DeclareDocumentCommand{\tikzcorner}{O{black} O{black} m m m}{
    \coordinate (AAAA) at #3;
    \coordinate (BBBB) at #4;
    \coordinate (CCCC) at #5;

\coordinate[rotate around = {90:(AAAA)}] (BBBB') at (BBBB);
\coordinate[rotate around = {90:(CCCC)}] (BBBB'') at (BBBB);
\path[name path=upper AAAA,dashed] (AAAA) 
let \p1 = ($ (AAAA) - (BBBB)$),
    \p2 = ($ (BBBB') - (AAAA)$)
in 
	++ ($(0,0)!\len!(\p2)$) node[coordinate](AAAA'){AAAA'}  --++ ($(\p1)!{3*veclen(\p1)}!(0,0)$);
\path[name path=lower AAAA,dashed] (AAAA) 
let \p1 = ($ (AAAA) - (BBBB)$),
    \p2 = ($ (BBBB') - (AAAA)$)
in 
	++ ($(0,0)!-\len!(\p2)$) node[coordinate](AAAA''){AAAA''} --++ ($(\p1)!{3*veclen(\p1)}!(0,0)$);
\path[name path=upper CCCC,dashed] (CCCC) 
let \p1 = ($ (CCCC) - (BBBB)$),
    \p2 = ($ (BBBB'') - (CCCC)$)
in 
	++ ($(0,0)!-\len!(\p2)$) node[coordinate](CCCC'){CCCC'} --++ ($(\p1)!{3*veclen(\p1)}!(0,0)$);
\path[name path=lower CCCC,dashed] (CCCC) 
let \p1 = ($ (CCCC) - (BBBB)$),
    \p2 = ($ (BBBB'') - (CCCC)$)
in 
++ ($(0,0)!\len!(\p2)$)node[coordinate](CCCC''){CCCC''}  --++ ($(\p1)!{3*veclen(\p1)}!(0,0)$);
    \path [name intersections={of=upper AAAA and upper CCCC,by=XXXX}] (XXXX) node[coordinate] {XXXX};
	\path [name intersections={of=lower AAAA and lower CCCC,by=YYYY}] (YYYY) node[coordinate] {YYYY};
    \path (AAAA')  -- (XXXX) node [pos=0.2,coordinate] (AAAA*) {AAAA*};
    \path (AAAA'') -- (XXXX) node[pos=0.2,coordinate] (AAAA**) {AAAA**};
    \path (CCCC')  -- (YYYY) node [pos=0.2,coordinate] (CCCC*) {CCCC*};
    \path (CCCC'') -- (YYYY) node[pos=0.2,coordinate] (CCCC**) {CCCC**};
	\fill[#1] (AAAA**) -- (AAAA*) -- (XXXX) -- (YYYY) -- (AAAA**);
	\fill[#2] (CCCC**) -- (CCCC*) -- (XXXX) -- (YYYY) -- (CCCC**);
}