TikZ intersection problem with PWM signal generation

Question

Consider the MWE of a PWM signal generation based on this question.

\documentclass[tikz, border=6mm]{standalone}

\usetikzlibrary{intersections}

\begin{document}
\newcommand{\step}{.25}
  \begin{tikzpicture}[>=latex]
    \draw [->] (0,-1.4) -- ++(8,0) node [right] {$t$};
    \draw [->] (0,-1.4) node [left] {$0$} -- ++(0,3) ;
    \draw [name path=sawtooth, line width=0.1pt,line join=miter] 
      \foreach \x in {0,\step,...,6} {
        % (\x,1.0) -- ++(0,-2.0) -- ++(\step,2.0) % y domain = -1.0 -- 1.0
        (\x,1.4) -- ++(0,-2.8) -- ++(\step,2.8) % y domain = -1.4 -- 1.4
      };

      \draw [red,smooth, domain=0:2*pi, name path global=wave-1,line width=0.1pt] plot ({\x},{sin((\x+0) r)}) node [below right, font=\scriptsize] {$sig_1$};
      \draw [blue,name intersections={of={wave-1} and sawtooth, total=\n}]
        \foreach \i [remember=\i as \lasti (initially 1)] in {2,...,\n} {
         \ifodd\i {}
          \else
            (intersection-\lasti |- 0,-2*1) rectangle (intersection-\i |- 0,-3)  
          \fi
        };
      \draw [->] (0,-3) -- ++(8,0) node [right] {$t$};
      \draw [->] (0,-3) node [left] {0} -- ++(0,1.2) ;      

  \end{tikzpicture}
\end{document}

This MWE compiles correct and the generated PWM signal is also correct. Of course, I want the sawtooth signal to be in the y domain (-1.0,1.0) so that the PWM signal is maximal and minimal. But if I compile the MWE with that y domain, Tikz fails to determine the intersections correctly. I made the sawtooth and sine wave with ultra thin lines but no success. Can someone shed a light on the capabilities of the determination of the intersections in this particular case?

Answer 1

If the red signal is very close to the outer ends of the sawtooth signal at an intersection, TikZ finds only one instead of two intersections. Therefore, you may want to split the sawtooth path into two, a vertical and a diagonal one. (BTW, it is sometimes safer to work with "fake straight lines" when one wants to sort intersections, see this answer.)

\documentclass[tikz, border=6mm]{standalone}

\usetikzlibrary{intersections}

\begin{document}
\newcommand{\step}{.25}
  \begin{tikzpicture}[>=latex]
    \draw [->] (0,-1.4) -- ++(8,0) node [right] {$t$};
    \draw [->] (0,-1.4) node [left] {$0$} -- ++(0,3) ;
    \draw [name path=sawtooth vert, line width=0.1pt,line join=miter] 
      \foreach \x in {0,\step,...,6} {
        (\x,1.0) to[bend left=0] ++(0,-2.0)  % y domain = -1.0 -- 1.0
        %(\x,1.4) -- ++(0,-2.8) -- ++(\step,2.8) % y domain = -1.4 -- 1.4
      };
     \draw [name path=sawtooth diag, line width=0.1pt,line join=miter]   
      \foreach \x in {0,\step,...,6} {
       (\x,-1.0) to[bend left=0] ++(\step,2.0)};
      \draw [red,smooth, domain=0:2*pi, name path global=wave-1,line width=0.1pt] plot ({\x},{sin((\x+0) r)}) node [below right, font=\scriptsize] {$sig_1$};
      \path  [name intersections={of={wave-1} and {sawtooth diag}, name=x, total=\n}]
         \pgfextra{\typeout{\n\space intersections\space in\space vert}};
      \draw [blue,name intersections={of={wave-1} and {sawtooth vert}, total=\n}]
      \pgfextra{\typeout{\n\space intersections}}
        \foreach \i [remember=\i as \lasti (initially 1)] in {2,...,\n} {
%          \ifodd\i {}
%           \else
            (x-\lasti |- 0,-2*1) rectangle (intersection-\i |- 0,-3)  
%          \fi
        };
      \draw [->] (0,-3) -- ++(8,0) node [right] {$t$};
      \draw [->] (0,-3) node [left] {0} -- ++(0,1.2) ;      

  \end{tikzpicture}
\end{document}