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We are solving How to get intersection point(s) of two glyphs? and if we could find minimum distance between two Bézier curves analytically, it would be computationally effective. It would be much better method than bisection method we quite often use in typography.

A mathematician told me that this approach could lead into a horrible system of equations. That's likely reason we use numerical methods instead.

One of my (poor) ideas is to convert Bézier curves to spiral curves (see application in FontForge), but it might lead us into an even worse situation (from mathematical point of view).

My next idea is to split up Bézier curves into smaller parts, but it's probably not improving a thing. I'm sorry I'm not providing MWE, please feel free to delete/close my question.

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closed as off-topic by Masroor, Martin Thoma, egreg, Thorsten, Werner Jun 4 '14 at 16:42

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not fall within the scope of TeX, LaTeX or related typesetting systems as defined in the help center." – Masroor, Martin Thoma, egreg, Thorsten, Werner
If this question can be reworded to fit the rules in the help center, please edit the question.

    
what is your definition of distance? – percusse Jun 4 '14 at 15:36
    
@percusse Euclidean. – Malipivo Jun 4 '14 at 15:41
2  
This seems to be off-topic for TeX.SE. You might want to ask it at math.SE though (please provide a link, I'm interested in the answers to your question!) – Martin Thoma Jun 4 '14 at 15:47
    
@moose Thank you for your feedback, I posted it there. math.stackexchange.com/questions/821267/… – Malipivo Jun 5 '14 at 4:51

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