Re: converting svg glyph to path data for use in scheme

[Trevor Daniels]

David Kastrup wrote Monday, December 14, 2015 11:32 AM


> Urs Liska <address@hidden> writes:
> 
>> Am 13.12.2015 um 14:09 schrieb Graham Breed:
>>> On 13/12/15 12:48, N. Andrew Walsh wrote:
>>>> Take a look at conversions.ly (sorry; mround is the equivalend
>>>> function in
>>>> the spreadsheet I use to do the same thing). Those functions will
>>>> convert
>>>> the input (given as a fraction comprising two integers) into Lily's
>>>> semitone values. That should allow you to convert between
>>>> just-intonation
>>>> ratios an the nearest note name. Urs has some comments in there
>>>> explaining
>>>> a bit how it works.
>>>
>>> Converting from ratios to cents is easy.  Converting between ratios
>>> and cents requires a function from cents to ratios.  That's a lot more
>>> difficult because information is lost.  You got us excited by
>>> suggesting that had been solved.
>>
>> Well, this is because conversion from cent to ratio isn't part of the
>> objective currently.
> 
> Guile has
> 
> (rationalize (inexact->exact (atan 0 -1)) #e1e-6)
> 
> so you can try converting irrational numbers to ratios.  However,
> figuring out the precision to use may be tricky and there is no "prefer
> simple ratios" option.  All you have to work with is the eps argument.

One way to approach this would be via continued fractions.
These provide a means to determine the "best" rational approximations
to a real number.

The continued fractions give a list of rational approximations in
which each member is a closer approximation to the real value than
the previous members, and each is also closer than any approximation
with a smaller or equal denominator.

For example, pi = [3;7,15,1,292,1,1,...] as a continued fraction,
which gives the successive "best" rational approximations to pi of 
3/1, 22/7, 333/106, 355/113, ...

Not sure how you'd determine which of the ratios was "correct" when
used for conversion from cent to ratio, though.  Maybe try a few
and see what comes out.

Trevor