daleif2-loopspace.tex

\documentclass[png]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}

% See http://tex.stackexchange.com/questions/276935/tikz-projection-parallel-to-given-line

\makeatletter
\tikzset{/tikz/parallel cs/.cd,
    to line initial coordinate/.store in=\tikz@parallelcs@toA,
    to line final coordinate/.store in=\tikz@parallelcs@toB,
    on line initial coordinate/.store in=\tikz@parallelcs@onA,
    on line final coordinate/.store in=\tikz@parallelcs@onB,
    from coordinate/.store in=\tikz@parallelcs@from,
    to/.style args={#1--#2}{
        to line initial coordinate=#1,
        to line final coordinate=#2,
    },
    on/.style args={#1--#2}{
        on line initial coordinate=#1,
        on line final coordinate=#2,
    },
    from/.style={
        from coordinate=#1
    }
}
  \tikzdeclarecoordinatesystem{parallel}{
    \tikzset{/tikz/parallel cs/.cd,#1}
    \tikz@scan@one@point\pgfutil@firstofone%
    (intersection of \tikz@parallelcs@from --$(\tikz@parallelcs@toA)!(\tikz@parallelcs@from)!90:(\tikz@parallelcs@toB)$ and \tikz@parallelcs@onA--\tikz@parallelcs@onB)%
    \relax
  }
\makeatother


\begin{document}
%\begin{tikzpicture}
%  \node[point,label=$P$] (P) at (3,3) {};
%  \draw[blue] (1.75,0) node[point,label=$A$] (A) {} -- (3,1) node[point,label=$B$] (B) {};
%  \draw       (0,1) node[point,label=$C$] (C) {} -- (2,3) node[point,label=$D$] (D) {};
%  \draw[red] (P) -- (parallel cs:from=P,to=A--B,on=C--D) node [point,label=$Q$] (Q) {};
%  \draw[black!30!white] (Q) -- (C) 
%      (D) -- (intersection of C--D and current bounding box.north west--current bounding box.north east);
%  \draw[blue!30!white] 
%      (intersection of A--B and current bounding box.south west--current bounding box.south east) -- (A)
%      (B) -- (intersection of A--B and current bounding box.north east--current bounding box.south east);
%\end{tikzpicture}
\begin{tikzpicture}
    \tikzset{point/.style={draw,circle,inner sep=0pt,outer sep=0pt,minimum width=1pt,fill}}
    \coordinate (P) at (0,4);
    \coordinate (B-0) at (1,0);
    \coordinate (A-1) at (2,0);
    \coordinate (B-1) at (intersection of P--B-0 and 0,1--1,1);
    \draw (P) -- (B-0) (P) -- (A-1);
    \foreach[remember=\i as \lasti (initially 1)] \i in {2,...,15} {
        \draw (B-\lasti) 
            -- (parallel cs:from=B-\lasti,to=B-0--A-1,on=P--A-1)
               node[point] (A-\i) {}
            -- (parallel cs:from=A-\i,to=A-1--B-1,on=P--B-0)
               node[point] (B-\i) {};
    }
\end{tikzpicture}
\end{document}