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

[Peter Rolf <indiego@gmx.net>]

Hi Paul,

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)).
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.

I must admit that this wasn't clear to me before you came up with your
question. So thanks for that. :-)

Best wishes,  Peter


Am 21.10.2011 13:38, schrieb Paul Menzel:
> Am Freitag, den 21.10.2011, 01:14 +0200 schrieb Paul Menzel:
>> Dear ConTeXt/MetaFun folks,
>>
>>
>> looking at the example for grid and functions in the MetaFun manual [1]
>> section 9.3
>>
>>         drawoptions(withpen pencircle scaled .25pt withcolor .5white) ;
>>         draw hlingrid(0, 20, .2, 20cm, 10cm) ;
>>         draw vloggrid(0, 10, .5, 10cm, 20cm) ;
>>         drawoptions(withpen pencircle scaled .50pt) ;
>>         draw hlingrid(0, 20, 1, 20cm, 10cm) ;
>>         draw vloggrid(0, 10, 1, 10cm, 20cm) ;
>>         
>>         fmt_pictures := false ; % use TeX as formatting engine
>>         textextoffset := ExHeight ; % a variable set by ConTeXt
>>         draw hlintext.lft(0, 20, 5, 20cm, "@3e") ;
>>         draw vlogtext.bot(0, 10, 9, 10cm, "@3e") ;
>>         
>>         draw
>>         function(1,"log(x)","x",1,10,1) xyscaled (10cm,2cm)
>>         withpen pencircle scaled 5mm withcolor transparent(1,.5,yellow) ;
>>
>> I am confused how the resulting function is scaled correctly. The
>> resulting dimensions seem to be 10cm and 18 cm. So I guess the 2 cm mean
>> to shift it up some how.
>>
>> Could someone please explain to me how `xyscaled` works in this case
>> please. I though `xyscaled (αcm, ζcm)` would set the object/path to a
>> width of α cm and a height of ζ cm.
> 
> Looking up the definition of the macro `xyscaled` it is indeed just a
> short version of `xscaled αcm yscaled ζcm`.
> 
>         $ more mp-tool.mp
>         […]
>         %D More robust:
>         
>         % let  normalscaled =  scaled ;
>         % let normalxscaled = xscaled ;
>         % let normalyscaled = yscaled ;
>         %
>         % def  scaled expr s =  normalscaled (s) enddef ;
>         % def xscaled expr s = normalxscaled (s) enddef ;
>         % def yscaled expr s = normalyscaled (s) enddef ;
>         
>         %D Shorter
>         
>         primarydef p xyscaled q =
>           begingroup ; save qq ; pair qq ; qq = paired(q) ;
>             ( p
>               if xpart qq<>0 : xscaled (xpart qq) fi
>               if ypart qq<>0 : yscaled (ypart qq) fi )
>           endgroup
>         enddef ;
>         […]
> 
> I am still confused though what happens in the above example scaling the
> path of the function.
> 
> Trying
> 
>         \starttext
>         \startMPcode
>           draw fullsquare xscaled 10cm yscaled 2cm;
>         \stopMPcode
>         \stoptext
> 
> the resulting rectangle has the dimensions of 10 cm width and 2 cm
> height but the path of the function above does not.
> 
> 
> Thanks,
> 
> Paul
> 
> 
>> [1] http://www.pragma-ade.com/general/manuals/metafun-s.pdf
>>
>>
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