LuaTeX: How to slant, extend or embolden only some characters of a font, NOT the whole font?

Question

In luaotfload we can slant, extend or embolden a whole font by writing something like \font\x="xxx.otf:+slant=a;+extend=b;+embolden=c" at d pt. But what can I do when I would like to apply such changes only to one character or a range of characters?

Example: Let's get a slanted ∑ (\sum) as under the following link:

How do I get a slanted \sum symbol?

MWE:

\input luaotfload.sty
\font\mathfont="latinmodern-math.otf:mode=base;script=math;slant=.25" at 60 pt
\textfont1=\mathfont
\Umathcode∑="1"1∑     \let\sum=∑
$∑ab$% How to apply the slant only to the sum?
\bye

As mentioned this will slant the whole math font. What has to be done so that the slant is only applied to the \sum?

If yes, can this be written as a new OTF feature as in this question?:

How to manipulate selected letters in LuaTeX?

Edit: I found out that I can add PDF commands to tfmdata.characters[...].commands but it does not work as expected. The width of the glyph ist set to 0 (overprinting) and the spacing in the following paragraphs is wrong. What is happening here?

How to write the comamnds properly? Please help me.

MWE 2:

\input luaotfload.sty
\directlua{
    local function slantedsum(tfmdata)
      tfmdata.characters[8721].commands = {
        {'pdf', 'origin', 'q 1.04 0 .2 1 0 0 cm'},
        {'char', 8721},
        {'pdf', 'origin', 'Q'},
      }
    end
    fonts.constructors.features.otf.register{
    name = 'ssum',
    description = 'Slant sum symbol',
    manipulators = {
        base = slantedsum,
    },
}
}
\font\mathfont="latinmodern-math.otf:mode=base;script=math;+ssum" at 10 pt
\textfont1=\mathfont
\font\1="lmroman10-regular.otf" at 10 pt
\1
\Umathcode∑="1"1∑     \let\sum=∑
abcd
$∑ab$% How to apply the slant only to the sum?
abcd
abcd
\bye

Answer 1

To understand what is happening, we should start with a short note about "origin" mode for PDF literals: It allows you to act as if the origin of the PDF coordinate system is at the current point you are working on. This is done by applying a coordinate transform which moves the current coordinates (from TeX's point of view) to (0, 0) before your literal and by applying a transform which moves (0, 0) back to the current TeX point afterwards. Normally these two transforms cancel each other out, so except for your literal nothing else is affected by them. If you insert q in one 'origin' literal and Q in another, all transforms between them get discarded, so it's your responsibility that this cancelling out still works. This only works if both literals (from TeX's point of view) appear at the same position. If you use \pdfextension save and \pdfextension restore LuaTeX will warn you if this isn't the case, but for direct literals you are on your own.

Here this condition isn't satisfied since the char command moves you right by the width of your char. Now the width of the char is not set by zero but still has the right size, but after the glyph the coordinate system for the rest of the page (or until the next Q) is shifted left by the width of the glyph.

You can fix this by telling LuaTeX to put both your PDF literals at the same coordinates:

\input luaotfload.sty
\directlua{
    local function slantedsum(tfmdata)
      tfmdata.characters[8721].commands = {
        {'pdf', 'origin', 'q 1.04 0 .2 1 0 0 cm'},
        {'push'}, % Remember where we are
        {'char', 8721},
        {'pop'}, % Move back there
        {'pdf', 'origin', 'Q'},
      }
    end
    fonts.constructors.features.otf.register{
    name = 'ssum',
    description = 'Slant sum symbol',
    manipulators = {
        base = slantedsum,
    },
}
}
\font\mathfont="latinmodern-math.otf:mode=base;script=math;+ssum" at 10 pt
\textfont1=\mathfont
\font\1="lmroman10-regular.otf" at 10 pt
\1
\Umathcode∑="1"1∑     \let\sum=∑
abcd
$∑ab$% How to apply the slant only to the sum?
abcd
abcd
\bye