[metapost] turningnumber revisited

[luigi scarso]

2011/6/28 Boguslaw Jackowski <B_Jackowski at gust.org.pl>

>
> Hi,
>
>
>  I'm not surprised because at (0,0)  (1,1) and (2,0) we don't have C1
>> continuity (as Dan said).
>>
>
> A triangle also doesn't have C1 continuity and well-behaves. The problem
> are cusps.
>
> I mean a C1 discontinuity with 180°

>
>  IN
>> -->------------+
>>              |
>>              V
>> OUT           |   -180°
>> --<------------+
>>
>>
>>
>> OUT
>> --<------------+
>>              |
>>              ^ +180°
>> IN            |
>> -->------------+
>>
>
> You've illustrated perfectly the reason, why cusps are "nasty".
>
>
But the interesting point now is:
in

mode_setup;
turningcheck :=0;
path p;
p:=(0,0)..{up}(1,1) & (1,1){down} .. {1,0}(2,0){-1,0} -- cycle ;
 for i:=0 upto 1000: show (1+i/1000,turningnumber (p rotated (1+i/1000) ));
endfor
end.

why the turningnumber jump from 2 to zero  around 1.47 degrees ?

(1.468,2)
(1.469,2)
(1.47,2)
(1.471,0)
(1.472,0)
(1.473,0)

(et similia in other situation)


-- 
luigi
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