Re: MetaPost: Confusion with `function()` and `xyscaled`

[Peter Rolf <indiego@gmx.net>]

Am 21.10.2011 17:26, schrieb Paul Menzel:
> Dear Peter,
> 
> 
> thank you for your answer.
> 
> Am Freitag, den 21.10.2011, 17:02 +0200 schrieb Peter Rolf:
> 
>> I agree, this is confusing on the first sight. But scaling is not meant
>> as 'scaling to' a dimension. In fact is is just a simple multiplication.
>> The reason why it seems to work this way with
>> 'fullsquare' and such predefined paths is, that they have a 'neutral'
>> size/scale (bounding box size of filled path is (1pt,1pt)).
> 
> So how can I find out what the dimension of the path of a function is?
> Not scaling it, it also looked pretty small, so I am guessing (1pt,1pt).

I guess in this case its size is (10,log(10)) + pen size when drawn.

> 
>> Multiplying such a path with (x,y) gives an object with size (1*x,1*y).
>> In general: if the bounding box of an object has the size (a,b) and you
>> scale it with (x,y), the resulting object has a size of (ax,by). That's
>> all the magic.
> 
> but if you use numbers with a unit than it should not be multiplied but
> expanded to that value, should not it? Otherwise I am unsure how
> multiplication works with a unit.
>
1pt is the base unit in MP (used if no dimension is given; probably
stored as 65536sp (scaled point) units).

Now if you use pure numerics for scale, such as 'xscaled 2', this is
interpreted as '2pt' (or 2*65536sp). If you use any dimension, it is
also converted into scaled points. All the same for MP.

If I'm right this should all be the same (untested)

xscaled 2
xscaled 2pt
xscaled (2*65536sp)

1 = 1pt = 65536sp


>> I must admit that this wasn't clear to me before you came up with your
>> question. So thanks for that. :-)
> 
> Thank you for your answer. As written above it is still not entirely
> clear to me. I hope you can remedy my last confusion.
> 
> 
> Thanks a lot,
> 
> Paul
> 
> 
> 
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