[metapost] turningnumber revisited

[Boguslaw Jackowski]

Dear colleagues,

I was nearly sure that the problem of turningnumber has
gone forever... Alas, the simple example below shows that the
implementation of the turningnumber primitive needs fixing:

%%%% BEGIN turnpath.mp
path p;
p=origin .. controls (100,200) and (300,500) ..
   (0,500) .. controls (-300,500) and (-100,200) ..
   origin & cycle;
for i:=0 upto 8: show turningnumber(p rotated 45i); endfor
end.
%%%% END turnpath.mp

A 2-node, 4-control path above should have the turningnumber=1.
And this is the case with MF; with MP, however, the result depends
on the rotation of the path.

MP 1.211 and MP 1.503 produce the result

   >> -1
   >> -1
   >> -1
   >> 1
   >> 1
   >> 1
   >> 1
   >> -1
   >> -1

MF's output is:

   >> 1
   >> 1
   >> 1
   >> 1
   >> 1
   >> 1
   >> 1
   >> 1
   >> 1

Cheers -- Jacko

-- 
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  Bogus\l{}aw Jackowski: B_Jackowski at GUST.ORG.PL
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  Hofstadter's Law: It always takes longer than you expect, even
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