Re: [NTG-context] Metapost: directionpoint gives unexpected point(?)

Hi Taco, thanks, from your observation and the way I build the paths, I found out that I can avoid the problem by shortening the paths I join just slightly: cl := (fullcircle scaled 4u) shifted z0; cl := cl cutbefore point (1/6+epsilon) along cl cutafter point (2/6-epsilon) along cl; cs := (fullcircle scaled 16u) shifted z1; cs := cs cutafter point (1/6-epsilon) along cs; and indeed, it works here now, with different values of the scale u, and it seems more stable. /Mikael PS I found out that eps and epsilon both worked, and I do not see in the metafun manual if there is a difference. On Fri, Feb 12, 2021 at 9:35 AM Taco Hoekwater wrote:

Hi,

...

On 11 Feb 2021, at 17:41, Mikael Sundqvist wrote:

Thanks for your investigation and extended example!

So, if I understand it correctly, the problem occurs where the different circles are glued together with the .. construction.

Took me a while to get it, but the problem is the definition of p0:

p[0] := cs .. cl .. (cs rotated 120) .. (cl rotated 120) .. (cs rotated 240) .. (cl rotated 240) .. cycle;

Here are cs and cl after your earlier definition:

cs := (141.73224999999996,-49.097491614210789) ..(75.312386775380347,111.25424516116959) ..(28.347427842053655,147.2925755432174);

cl := (28.346108531095332,147.29283827977969) ..(0,154.88788322842163) ..(-28.346108531095332,147.29283827977969);

Note how the last point of cs and the first point of cl are nearly the same. When you combine these bits into p0, p0 becomes a cyclic path with 18 points (where you really want/need only 12 points).

The micro-segments between these nearly-identical paths are the problem. At smaller u values the differences between the points become zero, and the directionpoint of a path of length zero is mathematically undefined.

I do not know a quick generic solution off hand, but that is what the issue is.

Best wishes, Taco

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