Metafun: how to draw a straight line past the end points

Metafun: how to draw a straight line past the end points

[Otared Kavian]

Hi,

I have a silly question: given two points in the plane
	z1 = (1cm,3cm) ;
	z2 = (5cm, 9cm) ;
the command
	draw z1 -- z2 withpen pencircle scaled .5pt ;
draws the line segment joining z1 and z2. How could I draw the line segment which goes a little further (say 1cm) than both the end points of this segment (that is in this example, a point before z1 and a point after z2 on the straight line) .
Indeed it is possible to write the equation of the line and then compute by hand the coordinates of the new end points, but I think there is a simpler way in Metafun to do this.

Thanks for any help: Otared


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Re: Metafun: how to draw a straight line past the end points

[Fabrice L]

Hi,

> Le 9 déc. 2020 à 10:57, Otared Kavian <otared@gmail.com> a écrit :
> 
> Hi,
> 
> I have a silly question: given two points in the plane
> 	z1 = (1cm,3cm) ;
> 	z2 = (5cm, 9cm) ;
> the command
> 	draw z1 -- z2 withpen pencircle scaled .5pt ;
> draws the line segment joining z1 and z2. How could I draw the line segment which goes a little further (say 1cm) than both the end points of this segment (that is in this example, a point before z1 and a point after z2 on the straight line) .
> Indeed it is possible to write the equation of the line and then compute by hand the coordinates of the new end points, but I think there is a simpler way in Metafun to do this.

The shortened operation is the solution ! See MetaFun manual section 1.18

\starttext
\startMPpage
z1 = (1cm,3cm) ;
z2 = (5cm, 9cm) ;
draw (z1--z2) shortened -1cm  withcolor blue ;
draw (z1--z2) withcolor red ;

\stopMPpage
\stoptext
	
Fabrice.

> 
> Thanks for any help: Otared
> 
> 
> ___________________________________________________________________________________
> 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
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> wiki     : http://contextgarden.net
> ___________________________________________________________________________________

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Re: Metafun: how to draw a straight line past the end points

[Otared Kavian]

Hi Fabrice,

Thanks a lot ! Indeed that does the job, which shows how wonderful Metafun is !

Best regards: Otared

> On 9 Dec 2020, at 17:19, Fabrice L <fabrice.alpha@gmail.com> wrote:
> 
> Hi,
> 
>> Le 9 déc. 2020 à 10:57, Otared Kavian <otared@gmail.com> a écrit :
>> 
>> Hi,
>> 
>> I have a silly question: given two points in the plane
>> 	z1 = (1cm,3cm) ;
>> 	z2 = (5cm, 9cm) ;
>> the command
>> 	draw z1 -- z2 withpen pencircle scaled .5pt ;
>> draws the line segment joining z1 and z2. How could I draw the line segment which goes a little further (say 1cm) than both the end points of this segment (that is in this example, a point before z1 and a point after z2 on the straight line) .
>> Indeed it is possible to write the equation of the line and then compute by hand the coordinates of the new end points, but I think there is a simpler way in Metafun to do this.
> 
> The shortened operation is the solution ! See MetaFun manual section 1.18
> 
> \starttext
> \startMPpage
> z1 = (1cm,3cm) ;
> z2 = (5cm, 9cm) ;
> draw (z1--z2) shortened -1cm  withcolor blue ;
> draw (z1--z2) withcolor red ;
> 
> \stopMPpage
> \stoptext
> 	
> Fabrice.
> 
>> 
>> Thanks for any help: Otared
>> 
>> 
>> ___________________________________________________________________________________
>> 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://context.aanhet.net
>> archive  : https://bitbucket.org/phg/context-mirror/commits/
>> wiki     : http://contextgarden.net
>> ___________________________________________________________________________________
> 
> ___________________________________________________________________________________
> 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://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : http://contextgarden.net
> ___________________________________________________________________________________

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___________________________________________________________________________________

Re: Metafun: how to draw a straight line past the end points

[Aditya Mahajan]

On Wed, 9 Dec 2020, Otared Kavian wrote:

> Thanks a lot ! Indeed that does the job, which shows how wonderful Metafun is !

Or, if you want to use high school algebra:

\starttext
\startMPcode
    z1 = (1cm,3cm) ;
    z2 = (5cm, 9cm) ;
    z3 = 1cm * dir(angle (z2 - z1)) shifted z2;
    draw z1 -- z3 ; 
    draw z1 -- z2 withcolor red;
\stopMPcode
\stoptext

Aditya
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Re: Metafun: how to draw a straight line past the end points

[Otared Kavian]

Hi Aditya,

Thanks for the alternative method, which comes handy if one wishes to extend the straight line by a different amount at either end:

\starttext
\startMPcode
   z1 = (1cm,3cm) ;
   z2 = (5cm, 9cm) ;
   z3 = 1cm * dir(angle (z2 - z1)) shifted z2 ;
   z4 = -.5cm*dir(angle(z2 - z1)) shifted z1 ;
   draw z1 -- z3 ; 
   draw z4 -- z1 ;
   draw z1 -- z2 withcolor red ;
\stopMPcode
\stoptext

Best regards: Otared

> On 9 Dec 2020, at 18:37, Aditya Mahajan <adityam@umich.edu> wrote:
> 
> On Wed, 9 Dec 2020, Otared Kavian wrote:
> 
>> Thanks a lot ! Indeed that does the job, which shows how wonderful Metafun is !
> 
> Or, if you want to use high school algebra:
> 
> \starttext
> \startMPcode
>    z1 = (1cm,3cm) ;
>    z2 = (5cm, 9cm) ;
>    z3 = 1cm * dir(angle (z2 - z1)) shifted z2;
>    draw z1 -- z3 ; 
>    draw z1 -- z2 withcolor red;
> \stopMPcode
> \stoptext
> 
> Aditya
> ___________________________________________________________________________________
> 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://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : http://contextgarden.net
> ___________________________________________________________________________________

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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
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___________________________________________________________________________________

Re: Metafun: how to draw a straight line past the end points

[Aditya Mahajan]

On Wed, 9 Dec 2020, Otared Kavian wrote:

> Hi Aditya,
> 
> Thanks for the alternative method, which comes handy if one wishes to extend the straight line by a different amount at either end:
> 
> \starttext
> \startMPcode
>    z1 = (1cm,3cm) ;
>    z2 = (5cm, 9cm) ;
>    z3 = 1cm * dir(angle (z2 - z1)) shifted z2 ;
>    z4 = -.5cm*dir(angle(z2 - z1)) shifted z1 ;
>    draw z1 -- z3 ; 
>    draw z4 -- z1 ;
>    draw z1 -- z2 withcolor red ;
> \stopMPcode
> \stoptext

Or just redefine shortened to accept a pair! 

\startMPdefinitions
primarydef p shortened d =
    reverse ( ( reverse (p enlonged -xpart paired(d)) ) enlonged -ypart paired(d) )
enddef ;
\stopMPdefinitions



\starttext
\startMPpage
z1 = (1cm,3cm) ;
z2 = (5cm, 9cm) ;
draw (z1--z2) shortened (-1cm,-2cm)  withcolor blue ;
draw (z1--z2) withcolor red ;

\stopMPpage
\stoptext

Now that if you really want to shorten a path, then cutends works better than shortened

\startMPdefinitions
primarydef p shortened d =
    reverse ( ( reverse (p enlonged -xpart paired(d)) ) enlonged -ypart paired(d) )
enddef ;
\stopMPdefinitions


\starttext
\startMPpage
z1 = (1cm,3cm) ;
z2 = (5cm, 9cm) ;
path p, q;
p := z1 {up} .. {right} z2;
q := p shifted (6cm, 0);

draw p withcolor red ;
draw p shortened (1cm,2cm)  withcolor blue ;

draw q withcolor green ;
draw q cutends (1cm,2cm)  withcolor blue ;

\stopMPpage
\stoptext

Aditya
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Re: Metafun: how to draw a straight line past the end points

[Otared Kavian]

Thanks Aditya!
One can learn a lot with your answers !
In the Metafun manual I see enlonged but I did not know to use it.

Best regards: Otared

> On 9 Dec 2020, at 21:38, Aditya Mahajan <adityam@umich.edu> wrote:
> 
> On Wed, 9 Dec 2020, Otared Kavian wrote:
> 
>> Hi Aditya,
>> 
>> Thanks for the alternative method, which comes handy if one wishes to extend the straight line by a different amount at either end:
>> 
>> \starttext
>> \startMPcode
>>   z1 = (1cm,3cm) ;
>>   z2 = (5cm, 9cm) ;
>>   z3 = 1cm * dir(angle (z2 - z1)) shifted z2 ;
>>   z4 = -.5cm*dir(angle(z2 - z1)) shifted z1 ;
>>   draw z1 -- z3 ; 
>>   draw z4 -- z1 ;
>>   draw z1 -- z2 withcolor red ;
>> \stopMPcode
>> \stoptext
> 
> Or just redefine shortened to accept a pair! 
> 
> \startMPdefinitions
> primarydef p shortened d =
>    reverse ( ( reverse (p enlonged -xpart paired(d)) ) enlonged -ypart paired(d) )
> enddef ;
> \stopMPdefinitions
> 
> 
> 
> \starttext
> \startMPpage
> z1 = (1cm,3cm) ;
> z2 = (5cm, 9cm) ;
> draw (z1--z2) shortened (-1cm,-2cm)  withcolor blue ;
> draw (z1--z2) withcolor red ;
> 
> \stopMPpage
> \stoptext
> 
> Now that if you really want to shorten a path, then cutends works better than shortened
> 
> \startMPdefinitions
> primarydef p shortened d =
>    reverse ( ( reverse (p enlonged -xpart paired(d)) ) enlonged -ypart paired(d) )
> enddef ;
> \stopMPdefinitions
> 
> 
> \starttext
> \startMPpage
> z1 = (1cm,3cm) ;
> z2 = (5cm, 9cm) ;
> path p, q;
> p := z1 {up} .. {right} z2;
> q := p shifted (6cm, 0);
> 
> draw p withcolor red ;
> draw p shortened (1cm,2cm)  withcolor blue ;
> 
> draw q withcolor green ;
> draw q cutends (1cm,2cm)  withcolor blue ;
> 
> \stopMPpage
> \stoptext
> 
> Aditya
> ___________________________________________________________________________________
> 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://context.aanhet.net
> archive  : https://bitbucket.org/phg/context-mirror/commits/
> wiki     : http://contextgarden.net
> ___________________________________________________________________________________

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___________________________________________________________________________________

Re: Metafun: how to draw a straight line past the end points

[Hans Hagen]

On 12/9/2020 9:38 PM, Aditya Mahajan wrote:

> Or just redefine shortened to accept a pair!
> 
> \startMPdefinitions
> primarydef p shortened d =
>      reverse ( ( reverse (p enlonged -xpart paired(d)) ) enlonged -ypart paired(d) )
> enddef ;
> \stopMPdefinitions

patched but then also:

primarydef p enlonged len =
     begingroup
     if len == 0 :
         p
     elseif pair p :
...

in order to save some energy when one is zero

Hans

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