[Tex/LaTex] How to create a new extensible symbol

Question

Given an arbitrary thin vertical symbol, can I create a new math delimiter from it (and if so, how)?

Edit: Ideally, I would like to be able to create an extensible symbol, either built out an existing normal symbol, or even made from scratch.

Edit 2: I am pretty sure that what I am after is an explanation of how to create a .tfm file for an extensible symbol (which Werner's answer describes the general structure of, but not how to make one).

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For example, let's say I wanted to use the \dagger () or \wr () symbol as a delimiter, and write expressions like

\[\left\ldagger \sum_{n=1}^\infty a_n \right\rdagger\]

where the symbol scaled appropriately. Would there be any distinction between declaring a symmetric delimiter (like \vert), as opposed to one that has inherently different "left" and "right" versions like [ and ]?

Now, even being unaware of the inner workings of TeX, I imagine that there has to be lots of information in the fonts for how a delimiter is to be scaled in different situations, and if I try to make my own delimiter, this information won't be present. Would I need to get deep into FontForge or equivalent to achieve my custom delimiters, or is there an easier way?

Answer 1

Scott Pakin's Comprehensive LaTeX Symbol List identifies the structure of extensible delimiters in section 8.2 Resizing symbols (p 100-102):

All variable-sized delimiters are defined (by the corresponding .tfm file) in terms of up to five segments, as illustrated by Figure 1 on page 102. The top, middle, and bottom segments are of a fixed size. The top-middle and middle-bottom segments (which are constrained to be the same character) are repeated as many times as necessary to achieve the desired height.

This is merely informative since I am unfamiliar with the procedure of how to create these things in a .tfm file.

Conveniently, scalerel provides \scaleleftright[<max width>]{<left obj>}{<stuff>}{<right obj>} (and a comparable \stretchleftright) for scaling/stretching both <left obj> and <right obj> to the height of <stuff> (constrained, if required and optional, to a width of <max width>). Here's a quick example:

\documentclass{article}
\usepackage{scalerel}% http://ctan.org/pkg/scalerel
\begin{document}
\[ \stretchleftright{\dagger}{\displaystyle\sum_{i=1}^n i}{\dagger} \]
\[ \scaleleftright{\dagger}{\displaystyle\sum_{i=1}^n i}{\dagger} \]
\end{document}