> Does gmsh script support custom functions? I cannot find any guides to 
> writing custom functions in gmsh manual

Not really, no.  There is 'Macro' (which I think used to be called 'Function'), 
but no.

    http://gmsh.info/dev/doc/texinfo/gmsh.html#User_002ddefined-macros

But there is the Gmsh API which can be used instead of writing a GEO file

    http://gmsh.info/dev/doc/texinfo/gmsh.html#Gmsh-API

Before that came along, the best approach was generating the GEO file in an 
external script, e.g. Python.  A formalization of this which I still use myself 
is pygmsh.

    https://github.com/nschloe/pygmsh/
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