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

[Peter Rolf <indiego@gmx.net>]

Am 23.10.2011 16:12, schrieb Paul Menzel:
> 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.
>
I see. I must admit that I haven't looked deeper into function (never
used it).

If I want to test the bounding box of a graphic, I normally use a small
debugging macro (last code line of nearly all of my graphics). It simply
draws a small red frame at the bounding box borders. You can use the
'Measuring Tool' in Acrobat (also Reader?) or even better the 'Object
Inspector' to get the exact size.

minlinewidth:= .143pt;

def wirepen= pencircle scaled minlinewidth enddef ;

def drawbb =
    drawoptions() ;
    interim linejoin:= mitered;
    draw (llcorner currentpicture) shifted ( .5minlinewidth,
.5minlinewidth)
    --   (lrcorner currentpicture) shifted (-.5minlinewidth,
.5minlinewidth)
    --   (urcorner currentpicture) shifted
(-.5minlinewidth,-.5minlinewidth)
    --   (ulcorner currentpicture) shifted (
.5minlinewidth,-.5minlinewidth)
    --   cycle
    withpen wirepen withcolor red;
%  draw boundingbox currentpicture withpen wirepen withcolor red ; % was
not neutral!
enddef ;


>>>> 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.

It can't be helped, I always mix this up. :-D
It's 'bp' for MP and for Adobe products, and 'pt' for TeX. Ask me in a
few weeks and I can't give the correct answer.

> 
>> 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.
>
My fault. In the meantime I have checked it and 'sp' is not a predefined
constant in MP (couldn't find it in the manual). Also never used it in MP.

>> 1 = 1pt = 65536sp
> 
> […]
> 
> 
> Thanks,
> 
> Paul
> 
> 
> 
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