How to extract Bezier curve equation from font with no "thickness"?

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I am working on a path-following problem where the path is letters from a font. Bezier curves will solve my problem of a predefined geometric path in terms of an equation, but I can't seem to find a tool that enables me to generate Bezier curves of each letter from a font, with a thickness of 0. The figure below illustrates what I want to achieve.

Thick 'A' to thin 'A':

Tick 'A' to thin 'A'

The red lines surrounding the 'A' on the left represents where the Bezier curves are situated (for example in Fontforge). The 'A' on the right only represents the Bezier curves (no filling/thickness), which will essentially result in 'open' Bezier curves, which I wish to obtain. A partial solution to this problem will also help.

Note: I would like to be able to extract the Bezier curve (point coordinates/equations) from any given font. I am not sure whether this is possible using Fontforge (Windows), and changing the weight attribute of a glyph gives errors.



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