Am Freitag, den 21.10.2011, 18:08 +0200 schrieb Peter Rolf:
> Am 21.10.2011 17:26, schrieb Paul Menzel:

> > 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.

That was it kind of. Probably the most of my confusion resulting from
the use of the inverse function.

So all in all the width is 1 – the x-coordinates seem to be scaled to
the width of 1 – and the height is 10, as ten is the highest value.
Therefore the width has to be multiplied with 10cm to get it to 10cm and
since the height it 10 already multiplying it with 2cm gets it to 20cm.

> >> 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).

In the manual I only found bp for »big point«, which equal PostScript
points equaling 1/72 of an inch.

> 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

This gives the same result.

> xscaled (2*65536sp)

I could not test the above because the numbers got too big and MetaPost
complained.

> 1 = 1pt = 65536sp

[…]


Thanks,

Paul