# [metapost] turningnumber revisited

luigi scarso luigi.scarso at gmail.com
Mon Jun 27 17:52:45 CEST 2011

```2011/6/27 Boguslaw Jackowski <B_Jackowski at gust.org.pl>:
>
> Luigi:
>>
>> maybe
>> from 0 to 1,1 +90°;
>> then +180° (hence I have 270°)
>> then from 1,1 to 2,0 +90° (hence I have 360°, i.e. turning number = +1)
>> then +180° (hence I have 360°+180°)
>> then from 2,0 to 0,0 go straight
>> then +180° to match the initial position (hence I have 360°+360°
>> turning number = +2)
>
> Hmmm...
>
> Then how you would explain the following pattern of the resulting
> turning numbers for the first path rotated by an angle between
> 0 and 90 degree:
>
> angle range  turningnumber
>  0--1:           2
>  2--9:           0
>  10--29:          2
>  30--36:          0
>  37--44:          2
>  45--52:          0
>     53:          1
>  54--77:          0
>  78--85:         -1
>  86--88:          0
>  89--90:          2
>
> The pattern for the second path is a little bit less complex:
>
>  0--45:          1
>  46--74:          0
>     75:          1
>  76--88:          0
>  89--90:          1
>
> Cheers -- Jacko
>
> Ps. The testing code was:
>
>  p:=(0,0)..{up}(1,1) & (1,1){down} .. (2,0) -- cycle ;
>  for i:=0 upto 90: show (i,turningnumber (p rotated i)); endfor
>
> and
>
>  p:=(0,0)..{up}(1,1) & (1,1){down} .. (0,1/2) -- cycle ;
>  for i:=0 upto 90: show (i,turningnumber (p rotated i)); endfor
>
> respectively.
nice, thank you very much. I need to look into the source now.
I will eventually instrument (i.e. put new sensors into) MFLua for this.

--
luigi

```