I wish to display and print mathematical formulae not using one of the existing TeX distributions and not via a web browser, but using my own code so that the display is integrated into my packages as part of its user interface. At present I use the BaKoMa versions if cmr, cmmi, cmsy and cmex, but I might like to move to using Latin Modern (Math) for the benefit of its broader Unicode coverage.
I can find (almost) all the symbols from the original TeX fonts there and so just by adjusting lookup tables I can adapt my existing code to display most stuff. However (checking latinmodern math using fontforge) many of the symbols from cmex10 are present but with codes outside the Unicode range. As a concrete example there is a range of sizes of radical marks starting at U+110790, and a bit before that the various gradually larger and larger parentheses, brackets and braces. Etc Etc.
My problem is that because I can only see these symbols with codes beyond U+10ffff I do not know how to get my C++ code to display them. wxWidgets rejects codepoints above the Unicode range, and native calls on Windows are based on UTF16 which also only covers the Unicode range. I am uncertain why these have been given "extended" codepoints not just ones of the broad private use areas! But I need a pointer - please - to how I can write C++ code that will get them rendered on my screen or page. It may be obvious if I just knew which web page to read, but so far my searches have proved unsuccessful.
This related to TeX in that my first test program is my own dvi viewer (it behaves OK with old style fonts - but again I want to know if I am locked to them for ever or if I can update to use Unicode fonts and code-mapping). I intended to end up with my own TeX-like layout code but using TeX compatible fonts seems a very good idea both for quality and so I have an easy source of files of metric information.
So please can somebody point me either to information that will let me render the cmex10-like characters from Latin Modern Math from my own C++ code, or redirect me to an alternative place where this question might better be asked.