Named paths inside a tikz/pic

Question

I am trying to understand the naming behavior of paths inside a pic definition. Consider the following

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections}

\tikzset{%
    path1/.pic={%
        \coordinate (-p) at (-0.5,-0.5);
        \draw[red, name path=-horz-fails] (-1,0.5) to (1,0.5);
        \draw[black, name path=-vert] (0,-1) to (0,1);
    };
}
\tikzset{%
    path2/.pic={%
        \draw[blue, name path=-horz] (-1,0) to (1,0);
    };
}

\begin{document}
\begin{tikzpicture}
    \pic [name=p1] at (0, 0) {path1};
    \pic (p2) at (0, 0) {path2};
    \draw [name intersections={of=-vert and -horz}]
        (intersection-1) circle (2pt) to (p1-p);
    %\draw [name intersections={of=-vert and -horz-fails}]
    %    (intersection-1) circle (2pt);
\end{tikzpicture}
\end{document}

In this example, all four lines are correctly drawn. Further, the uncommented intersection is correctly drawn; however, if I uncomment the second intersection, I get get the compiler error

! Package tikz Error: I do not know the path named `-horz-works'. Perhaps you 
 misspelt it.

From my searches, I came across this question and the associated bug report from the answer. As with that answer, the last path named in the pic is available outside the definition. I thought this might be related, but I cloned the repository and tried compiling with the fix, but I still get the same result. I also tried to use name path .., but that did not make the path available in the main picture environment.

My question is: Is this a manifestation of the same bug? If not, what are the naming rules for paths inside a pic definition?

I notice that the coordinate (-p here) inherits the pic name outside scope of the pic as I expected and I would like to reference the path in the same manner.

---

Motivation

My ultimate goal is to draw a line to the intersection of two paths defined inside a generated pic. I have some Python code that generates the lines of latitude and longitude along a sphere. I would like to use the pic multiple times within a single picture; thus, I would like to refer to the paths with the parent pic name to compute only those intersections that will further what I am trying to show. Since I am computing the paths, I could define the coordinates of the intersections, but I would like to let TikZ do the job and that seems like overkill to me.

Answer 1

Use name path global, which is made for this: "broadcast" paths outside environments such as scopes or pics.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections}

\tikzset{%
    path1/.pic={%
        \coordinate (-p) at (-0.5,-0.5);
        \draw[red, name path global=-horz-fails] (-1,0.5) to (1,0.5);
        \draw[black, name path global=-vert] (0,-1) to (0,1);
    };
}
\tikzset{%
    path2/.pic={%
        \draw[blue, name path global=-horz] (-1,0) to (1,0);
    };
}

\begin{document}
\begin{tikzpicture}
    \pic [name=p1] at (0, 0) {path1};
    \pic (p2) at (0, 0) {path2};
    \draw [name intersections={of=-vert and -horz}]
        (intersection-1) circle (2pt) to (p1-p);
    \draw [name intersections={of=-vert and -horz-fails}]
        (intersection-1) circle (2pt);
\end{tikzpicture}
\end{document}

If you want to have unique names, just prepend the names of the paths by the name of the pic.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections}
\makeatletter
\newcommand{\figname}[1]{\edef#1{\tikz@fig@name}}
\makeatother

\tikzset{%
    path1/.pic={%
        \figname{\myname}
        \coordinate (-p) at (-0.5,-0.5);
        \draw[red, name path global=\myname-horz-fails] (-1,0.5) to (1,0.5);
        \draw[black, name path global=\myname-vert] (0,-1) to (0,1);
    };
}
\tikzset{%
    path2/.pic={%
        \figname{\myname}
        \draw[blue, name path global=\myname-horz] (-1,0) to (1,0);
    };
}

\begin{document}
\begin{tikzpicture}
    \pic (p1) at (0, 0) {path1};
    \pic (p2) at (0, 0) {path2};
    \draw [name intersections={of=p1-vert and p2-horz}]
        (intersection-1) circle (2pt) to (p1-p);
    \draw [name intersections={of=p1-vert and p1-horz-fails}]
        (intersection-1) circle (2pt);
\end{tikzpicture}
\end{document}

(same output)

Answer 2

Here a quick hack by simply put every path in a single pic.

This does not answer your question but ensures that you no longer have any mistakes.

\documentclass[tikz,border=5mm]{standalone}
%\usepackage{tikz}
\usetikzlibrary{intersections}

\tikzset{%
    path1/.pic={%
        \coordinate (-p) at (-0.5,-0.5);
        \draw[red, name path=-horz-fails] (-1,0.5) to (1,0.5);
       % \draw[black, name path=-vert] (0,-1) to (0,1);
    },
        path3/.pic={%
        \coordinate (-p) at (-0.5,-0.5);
        %\draw[red, name path=-horz-fails] (-1,0.5) to (1,0.5);
        \draw[black, name path=-vert] (0,-1) to (0,1);
    },
    path2/.pic={%
        \draw[blue, name path=-horz] (-1,0) to (1,0);
    };
}

\begin{document}
\begin{tikzpicture}
    \pic [name=p1] at (0, 0) {path1};
    \pic (p2) at (0, 0) {path2};
    \pic (p3) at (0,0) {path3};
    \draw [name intersections={of=-vert and -horz}]
        (intersection-1) circle (2pt) to (p1-p);
    \draw [name intersections={of=-vert and -horz-fails}]
        (intersection-1) circle (2pt);
\end{tikzpicture}
\end{document}