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

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

[Paul Menzel]

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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.


Thanks,

Paul


[1] http://www.pragma-ade.com/general/manuals/metafun-s.pdf

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\starttext
\startMPcode
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) ;
draw fullsquare xyscaled (10cm,2cm);
\stopMPcode

\startMPcode
draw fullsquare xyscaled (1cm,1cm);
\stopMPcode
\startMPcode
draw fullsquare xyscaled (2cm,1cm);
\stopMPcode
\startMPcode
draw fullsquare xyscaled (1cm,2cm);
\stopMPcode
\startMPcode
draw fullsquare xyscaled (1,2);
\stopMPcode
\stoptext

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

[Paul Menzel]

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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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___________________________________________________________________________________

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

[Peter Rolf]

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
>>
>>
>> ___________________________________________________________________________________
>> If your question is of interest to others as well, please add an entry to the Wiki!
>>
>> maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context
>> webpage  : http://www.pragma-ade.nl / http://tex.aanhet.net
>> archive  : http://foundry.supelec.fr/projects/contextrev/
>> wiki     : http://contextgarden.net
>> ___________________________________________________________________________________

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___________________________________________________________________________________

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

[Paul Menzel]

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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).

> 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.

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

[Peter Rolf]

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
> 
> 
> 
> ___________________________________________________________________________________
> If your question is of interest to others as well, please add an entry to the Wiki!
> 
> maillist : ntg-context@ntg.nl / http://www.ntg.nl/mailman/listinfo/ntg-context
> webpage  : http://www.pragma-ade.nl / http://tex.aanhet.net
> archive  : http://foundry.supelec.fr/projects/contextrev/
> wiki     : http://contextgarden.net
> ___________________________________________________________________________________

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___________________________________________________________________________________

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

[Aditya Mahajan]

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> 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.

IIRC, xysized does that. (I am usually confused between ..sized and 
..scaled, but one of them scales to the given dimensions).

Aditya

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

[Hans Hagen]

On 21-10-2011 22:53, Aditya Mahajan wrote:
>> 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.
>
> IIRC, xysized does that. (I am usually confused between ..sized and
> ..scaled, but one of them scales to the given dimensions).

scaled is just multiplication so x scaled 1cm is x * 1 * cm which can be 
pretty large

Hans


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MetaFun manual: Incorrect label of ordinate axis on page 382, section 9.3 drawing functions (was: Confusion with `function()` and `xyscaled`)

[Paul Menzel]

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Dear MetaFun folks,


Am Freitag, den 21.10.2011, 01:14 +0200 schrieb Paul Menzel:

> 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) ;

the labeling of the vertical axis (y-coordinate) is not incorrect.

The maximum value is 10 and therefore it should probably be corrected as
follows.

- draw hlingrid(0, 20, 1, 20cm, 10cm) ;
+ draw hlingrid(0, 20, 2, 20cm, 10cm) ;

- draw hlintext.lft(0, 20, 5, 20cm, "@3e") ;
+ draw hlintext.lft(0, 10, 5, 20cm, "@3e") ;

Furthermore on the bottom labels seem to be incorrect in the figure, it
goes from 1 to 0, but this seems to be a bug in the used ConTeXt
version, since I do not have that problem when compiling(?) that example
locally.

Please find the corrected example attached.

[…]


Thanks and I hope I did not mess up,

Paul


> [1] http://www.pragma-ade.com/general/manuals/metafun-s.pdf

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\starttext
\startMPcode
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, 2, 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, 10, 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) ;
\stopMPcode
\stoptext

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

[Paul Menzel]

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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

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

[Peter Rolf]

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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> 
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If your question is of interest to others as well, please add an entry to the Wiki!

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

[Hans Hagen]

On 23-10-2011 17:17, Peter Rolf wrote:
> 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 ;

draw boundingbox currentpicture enlarged -.5minlinewidth withpen wirepen 
withcolor red ;

> 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

sp's would overflow anyway

Hans

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