Hello Alexei,

> Each curved segment has a large number [...]

I guess this is similar to the Euclidean distance transform algorithm.
http://webstaff.itn.liu.se/~stegu/JFA/Danielsson.pdf

As I said before I will not leave out this option, I will try to implement
this
and then we can compare the performance.

> I am deeply sorry if this mathematical fact offends you in any way.
> Your code is good but please allow me to suggest an alternative,
> perhaps, faster implementation.

Please, don't apologize. I don't find anything offending in your
suggestions.
I realize that we are all in the same boat and we all want to make the
algorithm
as fast as possible. I think we can't comment on which algorithm is better
than the
other without checking the performance and other important factors. So, I
am open to
all of your suggestions and will choose the one that we all can agree on,
same for
`fixed-point' vs `float', same for subdivision or not.

Again Thank you for all of your suggestions,I will require them more in the
future.

Anuj

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