An undesirable path occurs when I intersect two paths

Question

There is an undesirable path in my result.

However, if I comment out the path intersection code (the fourth line from below), the undesirable path disappears.

One of the paths involved in the intersection is a closed path (that is, \path [name path=Part2] (BRM1) -- (BR1) -- (BM1) -- (BL1) -- (BLM1) -- (BLM2) -- (BL2) -- (BM2) -- (BR2) -- (BRM2) -- cycle in my code). I cannot figure out why an intersection involving a closed path can generate some path outside the closed path. What I want to produce is as follows.

I would appreciate your help with this situation.

\documentclass[12pt,a4paper]{article}
\usepackage{amssymb, amsmath, amsthm}
\usepackage{tikz}
\usetikzlibrary{angles,calc,intersections,quotes}
\begin{document}
\begin{center}
\begin{tikzpicture}
\coordinate (A) at (3,1.5);
\coordinate (BLM) at (0.5,-2);  %below leftmost
\coordinate (BRM) at (6,-1.5);  %below rightmost
\coordinate (BM) at (3.5,-1.8); %below middle 
\coordinate (BL) at (2,-2.1);

\coordinate (BR) at (5,-2.5);

\draw (BR) -- (BRM) -- (A) -- (BLM) -- (BL) -- (BM) -- cycle;
\foreach \pt in {BL,BM,BR}
    \draw (A) -- (\pt);
\foreach \pt/\xshift/\yshift in {BLM/-0.5cm/-0.7cm, BL/-0.2cm/-0.72cm, BM/0.1cm/-0.66cm, BR/0.4cm/-0.8cm, BRM/0.6cm/-0.6cm}
{
    \foreach \i in {1,2,3,4}
        \coordinate (\pt\i) at ($(A)+\i*(\xshift,\yshift)$);
}
\foreach \i in {1,2,3,4}
    \draw (BLM\i) -- (BL\i) -- (BM\i) -- (BR\i) -- (BRM\i);
\path [name path=Part2] (BRM1) -- (BR1) -- (BM1) -- (BL1) -- (BLM1) -- (BLM2) -- (BL2) -- (BM2) -- (BR2) -- (BRM2) -- cycle;
\foreach \x in {0,0.25,...,2.5}
{
    \path [overlay,name path=slashpath\x,draw] ($(BLM2)+(\x,0)-(0.35,0.2)$) -- +(50:1.5cm);
    \draw [name intersections={of=Part2 and slashpath\x},very thin] (intersection-1) -- (intersection-2);
}
\end{tikzpicture}
\end{center}
\end{document}

Answer 1

I've placed % <---- this to highlight each change in your code.

Update 2: Clean up of the code

When performing the clip operation, the search for intersections is useless since the clip does this natively. The clip transforms the path you called name path=Part2 into a pochoir (stencil) and therefore everything that is hatched is colored inside this pochoir (clip area or stencil). So there's no need to search for intersections like you do.

The simplified code is now (same result):

\documentclass[12pt,a4paper]{article}
\usepackage{amssymb, amsmath, amsthm}
\usepackage{tikz}
\usetikzlibrary{angles,calc,intersections,quotes,patterns}
\begin{document}
\begin{center}
\begin{tikzpicture}
\coordinate (A) at (3,1.5);
\coordinate (BLM) at (0.5,-2);  %below leftmost
\coordinate (BRM) at (6,-1.5);  %below rightmost
\coordinate (BM) at (3.5,-1.8); %below middle 
\coordinate (BL) at (2,-2.1);

\coordinate (BR) at (5,-2.5);

\draw (BR) -- (BRM) -- (A) -- (BLM) -- (BL) -- (BM) -- cycle;
\foreach \pt in {BL,BM,BR}
    \draw (A) -- (\pt);
\foreach \pt/\xshift/\yshift in {BLM/-0.5cm/-0.7cm, BL/-0.2cm/-0.72cm, BM/0.1cm/-0.66cm, BR/0.4cm/-0.8cm, BRM/0.6cm/-0.6cm}
{
    \foreach \i in {1,2,3,4}
        \coordinate (\pt\i) at ($(A)+\i*(\xshift,\yshift)$);
}
\foreach \i in {1,2,3,4}
    \draw (BLM\i) -- (BL\i) -- (BM\i) -- (BR\i) -- (BRM\i);
    \begin{scope}% <---- add scope here
\path [clip%,name path=Part2 <-- add clip delete useless name path
] (BRM1) -- (BR1) -- (BM1) -- (BL1) -- (BLM1) -- (BLM2) -- (BL2) -- (BM2) -- (BR2) -- (BRM2) -- cycle;%<----- add clip here
\foreach \x in {0.25,.5,...,2.5}%<----- delete 0 here
%{ <-- useless group with only one TikZ command
    \path [%name path=slashpath\x, <-- useless name path
    draw] ($(BLM2)+(\x,0)-(0.35,0.2)$) -- +(50:1.5cm);
    %\draw [name intersections={of=Part2 and slashpath\x},very thin] (intersection-1) -- (intersection-2); <--- useless intersections
%}
    \end{scope}%<----- end of scope
\end{tikzpicture}
\end{center}
\end{document}

Update 1: Explanations about clip et scope

What is important here is the clip action. clip makes it possible to virtually cut out the figure as one would do with scissors. Clip acts like a pochoir (in french) (stencil in english). It is like a mask that hides everything that is not cut out. It only leaves the inner part of the clip (pochoir) visible. Once clipped, everything that is drawn only appears within the clip (pochoir).

Everything that is drawn after the clip remains inside this pochoir. Everything else is hidden, the constructions and drawings made remain inside the pochoir.

This scope environment is useful here because it limits the cutting when you want to work on a piece of the figure, but not on the whole figure.

It delimits a part of the figure. Here, it limits the pochoir within this scope environment.

When you get out of this scope, you can draw on the complete figure again.

In the case of your figure, the scope environment is not useful because you don't build anything more after this clip.

\documentclass[12pt,a4paper]{article}
\usepackage{amssymb, amsmath, amsthm}
\usepackage{tikz}
\usetikzlibrary{angles,calc,intersections,quotes,patterns}
\begin{document}
\begin{center}
\begin{tikzpicture}
\coordinate (A) at (3,1.5);
\coordinate (BLM) at (0.5,-2);  %below leftmost
\coordinate (BRM) at (6,-1.5);  %below rightmost
\coordinate (BM) at (3.5,-1.8); %below middle 
\coordinate (BL) at (2,-2.1);

\coordinate (BR) at (5,-2.5);

\draw (BR) -- (BRM) -- (A) -- (BLM) -- (BL) -- (BM) -- cycle;
\foreach \pt in {BL,BM,BR}
    \draw (A) -- (\pt);
\foreach \pt/\xshift/\yshift in {BLM/-0.5cm/-0.7cm, BL/-0.2cm/-0.72cm, BM/0.1cm/-0.66cm, BR/0.4cm/-0.8cm, BRM/0.6cm/-0.6cm}
{
    \foreach \i in {1,2,3,4}
        \coordinate (\pt\i) at ($(A)+\i*(\xshift,\yshift)$);
}
\foreach \i in {1,2,3,4}
    \draw (BLM\i) -- (BL\i) -- (BM\i) -- (BR\i) -- (BRM\i);
    \begin{scope}% <---- add scope here
\path [clip,name path=Part2] (BRM1) -- (BR1) -- (BM1) -- (BL1) -- (BLM1) -- (BLM2) -- (BL2) -- (BM2) -- (BR2) -- (BRM2) -- cycle;%<----- add clip here
\foreach \x in {0.25,.5,...,2.5}%<----- delete 0 here
{
    \path [overlay,name path=slashpath\x,draw] ($(BLM2)+(\x,0)-(0.35,0.2)$) -- +(50:1.5cm);
    \draw [name intersections={of=Part2 and slashpath\x},very thin] (intersection-1) -- (intersection-2);
}
    \end{scope}%<----- end of scope
\end{tikzpicture}
\end{center}
\end{document}

Answer 2

To fill an area by slashing lines in tikz, using pattern is easier than intersections.

Here

• tikz library patterns.meta is loaded and
• \path [name path=Part2] is replaced with pattern={Lines[angle=50, distance=5pt]}.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc, patterns.meta}
\begin{document}
\begin{tikzpicture}
  \coordinate (A) at (3,1.5);
  \coordinate (BLM) at (0.5,-2);  %below leftmost
  \coordinate (BRM) at (6,-1.5);  %below rightmost
  \coordinate (BM) at (3.5,-1.8); %below middle 
  \coordinate (BL) at (2,-2.1);

  \coordinate (BR) at (5,-2.5);
\draw (BR) -- (BRM) -- (A) -- (BLM) -- (BL) -- (BM) -- cycle;
  \foreach \pt in {BL,BM,BR}
      \draw (A) -- (\pt);
  \foreach \pt/\xshift/\yshift in {BLM/-0.5cm/-0.7cm, BL/-0.2cm/-0.72cm, BM/0.1cm/-0.66cm, BR/0.4cm/-0.8cm, BRM/0.6cm/-0.6cm}
  {
      \foreach \i in {1,2,3,4}
          \coordinate (\pt\i) at ($(A)+\i*(\xshift,\yshift)$);
  }
\foreach \i in {1,2,3,4}
      \draw (BLM\i) -- (BL\i) -- (BM\i) -- (BR\i) -- (BRM\i);
% draw pattern
  \path[pattern={Lines[angle=50, distance=5pt]}] 
    (BRM1) -- (BR1) -- (BM1) -- (BL1) -- (BLM1) -- (BLM2) -- (BL2) -- (BM2) -- (BR2) -- (BRM2) -- cycle;
\end{tikzpicture}
\end{document}

tikz library patterns.meta is documented in pgfmanual v3.1.5b, sec. 63.3. You can learn docs and examples of pattern Lines and its options in that subsection.

PS: pattern Lines is newly added in pgf/tikz v3.1.5, see corresponding release notes.