MetaFun: How to draw bent paths?

MetaFun: How to draw bent paths?

[Henri Menke]

Dear list,

I want to draw paths between points which are bent by a certain angle.
The code in the MWE below works well but I was thinking that the expert
here can surely improve it and suggest a nicer syntax.

Cheers, Henri

---

\startMPpage
    vardef bend(expr a,b,phi) =
        a{dir(angle(b-a)+phi)} .. {dir(angle(a-b)+180-phi)}b
    enddef ;

    z1 = (-.5cm,1cm) ;
    z2 = (1cm,3cm) ;

    for phi = 0 step 5 until 360:
        draw bend(z1,z2,phi) withcolor (phi/360)[red,blue] ;
    endfor ;
\stopMPpage

Possible use case:

\startMPpage[offset=1cm]
    vardef bend(expr a,b,phi) =
        a{dir(angle(b-a)+phi)} .. {dir(angle(a-b)+180-phi)}b
    enddef ;

    z1 = (-.5cm,1cm) ;
    z2 = (1cm,3cm) ;
    draw z1 -- z2 ;
    dotlabel.lft("$-$", z1) ;
    dotlabel.lft("$+$", z2) ;

    path p; p := bend(z1,z2,-30) ;
    drawdblarrow p withcolor blue ;
    label.lrt(textext("$\Delta$"),point .5 along p)  withcolor blue ;
\stopMPpage

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Re: MetaFun: How to draw bent paths?

[Hans Hagen]

On 9/16/2018 10:28 AM, Henri Menke wrote:
> Dear list,
> 
> I want to draw paths between points which are bent by a certain angle.
> The code in the MWE below works well but I was thinking that the expert
> here can surely improve it and suggest a nicer syntax.
looks like a challenge for Alan ... isn't it also a bit 3d (2.5d)?

-----------------------------------------------------------------
                                           Hans Hagen | PRAGMA ADE
               Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
        tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
-----------------------------------------------------------------
___________________________________________________________________________________
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
___________________________________________________________________________________

Re: MetaFun: How to draw bent paths?

[Henri Menke]

On 9/18/18 7:57 PM, Hans Hagen wrote:
> On 9/16/2018 10:28 AM, Henri Menke wrote:
>> Dear list,
>>
>> I want to draw paths between points which are bent by a certain angle.
>> The code in the MWE below works well but I was thinking that the expert
>> here can surely improve it and suggest a nicer syntax.
> looks like a challenge for Alan ... isn't it also a bit 3d (2.5d)?

I wasn't thinking about a 3D application here, just a little bend on the
path to go around other elements in my drawing without having to think
about explicit control points (like the second example in my original
post).  In the meantime I have improved the defintion of the macro to
avoid double computation of the angle:

    vardef bend(expr a,b,phi) =
        save x ;
        x := angle(b-a) ;
        a{dir(x+phi)} .. {dir(x-phi)}b
    enddef ;

So currently the applied syntax is

    drawarrow bend(z1, z2, 30) ;

However, I would prefer something like

    drawarrow z1 bend(30) z2 ;

I'm not sure whether this is possible though.  Actually I'm reading the
MetaPost manual right know because my MP skills are rather poor.

> 
> -----------------------------------------------------------------
>                                           Hans Hagen | PRAGMA ADE
>               Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
>        tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
> -----------------------------------------------------------------
> ___________________________________________________________________________________
> 
> 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
___________________________________________________________________________________

Re: MetaFun: How to draw bent paths?

[Henri Menke]

On 18/09/18 21:23, Henri Menke wrote:
> On 9/18/18 7:57 PM, Hans Hagen wrote:
>> On 9/16/2018 10:28 AM, Henri Menke wrote:
>>> Dear list,
>>>
>>> I want to draw paths between points which are bent by a certain angle.
>>> The code in the MWE below works well but I was thinking that the expert
>>> here can surely improve it and suggest a nicer syntax.
>> looks like a challenge for Alan ... isn't it also a bit 3d (2.5d)?
> 
> I wasn't thinking about a 3D application here, just a little bend on the
> path to go around other elements in my drawing without having to think
> about explicit control points (like the second example in my original
> post).  In the meantime I have improved the defintion of the macro to
> avoid double computation of the angle:
> 
>     vardef bend(expr a,b,phi) =
>         save x ;
>         x := angle(b-a) ;
>         a{dir(x+phi)} .. {dir(x-phi)}b
>     enddef ;
> 
> So currently the applied syntax is
> 
>     drawarrow bend(z1, z2, 30) ;
> 
> However, I would prefer something like
> 
>     drawarrow z1 bend(30) z2 ;
> 
> I'm not sure whether this is possible though.  Actually I'm reading the
> MetaPost manual right know because my MP skills are rather poor.

I think I got it now.  Not sure whether “bend” should be primary or
something else.

\startMPdefinitions
    primarydef a bend phi =
        do_bend(a,phi)
    enddef ;

    vardef do_bend(expr a, phi) expr b =
        save x ;
        x := angle(b-a) ;
        a{dir(x+phi)} .. {dir(x-phi)}b
    enddef ;
\stopMPdefinitions

\starttext

\startMPpage
    z1 = (-.5cm,1cm) ;
    z2 = (1cm,3cm) ;

    for phi = 0 step 5 until 360:
        draw z1 bend(phi) z2 withcolor (phi/360)[red,blue] ;
    endfor ;
\stopMPpage

% Possible use case:

\startMPpage[offset=1cm]
    z1 = (-.5cm,1cm) ;
    z2 = (1cm,3cm) ;
    draw z1 -- z2 ;
    dotlabel.lft("$-$", z1) ;
    dotlabel.lft("$+$", z2) ;

    path p; p := z1 bend(-30) z2 ;
    drawdblarrow p withcolor blue ;
    label.lrt(textext("$\Delta$"),point .5 along p)  withcolor blue ;
\stopMPpage

\stoptext


> 
>>
>> -----------------------------------------------------------------
>>                                           Hans Hagen | PRAGMA ADE
>>               Ridderstraat 27 | 8061 GH Hasselt | The Netherlands
>>        tel: 038 477 53 69 | www.pragma-ade.nl | www.pragma-pod.nl
>> -----------------------------------------------------------------
>> ___________________________________________________________________________________
>>
>> 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
___________________________________________________________________________________

Re: MetaFun: How to draw bent paths?

[Alan Braslau]

On Wed, 19 Sep 2018 11:18:30 +1200
Henri Menke <henrimenke@gmail.com> wrote:

> On 18/09/18 21:23, Henri Menke wrote:
> > On 9/18/18 7:57 PM, Hans Hagen wrote:  
> >> On 9/16/2018 10:28 AM, Henri Menke wrote:  
> >>> Dear list,
> >>>
> >>> I want to draw paths between points which are bent by a certain angle.
> >>> The code in the MWE below works well but I was thinking that the expert
> >>> here can surely improve it and suggest a nicer syntax.  
> >> looks like a challenge for Alan ... isn't it also a bit 3d (2.5d)?  
> > 
> > I wasn't thinking about a 3D application here, just a little bend on the
> > path to go around other elements in my drawing without having to think
> > about explicit control points (like the second example in my original
> > post).  In the meantime I have improved the defintion of the macro to
> > avoid double computation of the angle:
> > 
> >     vardef bend(expr a,b,phi) =
> >         save x ;
> >         x := angle(b-a) ;
> >         a{dir(x+phi)} .. {dir(x-phi)}b
> >     enddef ;
> > 
> > So currently the applied syntax is
> > 
> >     drawarrow bend(z1, z2, 30) ;
> > 
> > However, I would prefer something like
> > 
> >     drawarrow z1 bend(30) z2 ;
> > 
> > I'm not sure whether this is possible though.  Actually I'm reading the
> > MetaPost manual right know because my MP skills are rather poor.  
> 
> I think I got it now.  Not sure whether “bend” should be primary or
> something else.
> 
> \startMPdefinitions
>     primarydef a bend phi =
>         do_bend(a,phi)
>     enddef ;
> 
>     vardef do_bend(expr a, phi) expr b =
>         save x ;
>         x := angle(b-a) ;
>         a{dir(x+phi)} .. {dir(x-phi)}b
>     enddef ;
> \stopMPdefinitions
> 
> \starttext
> 
> \startMPpage
>     z1 = (-.5cm,1cm) ;
>     z2 = (1cm,3cm) ;
> 
>     for phi = 0 step 5 until 360:
>         draw z1 bend(phi) z2 withcolor (phi/360)[red,blue] ;
>     endfor ;
> \stopMPpage
> 
> % Possible use case:
> 
> \startMPpage[offset=1cm]
>     z1 = (-.5cm,1cm) ;
>     z2 = (1cm,3cm) ;
>     draw z1 -- z2 ;
>     dotlabel.lft("$-$", z1) ;
>     dotlabel.lft("$+$", z2) ;
> 
>     path p; p := z1 bend(-30) z2 ;
>     drawdblarrow p withcolor blue ;
>     label.lrt(textext("$\Delta$"),point .5 along p)  withcolor blue ;
> \stopMPpage
> 
> \stoptext


Henri,

1. I added a sanity test (angle(origin) is undefined);
2. it is probably more efficient to calculate the angle twice than to allocate storage;
3. primary b;

4. then I created the variant arc (as in a bow) taking a delta (the tangent of
   an angle).

Alan


\startMPdefinitions
    primarydef a bend phi =
        do_bend(a,phi)
    enddef ;

    vardef do_bend(expr a, phi) primary b =
        if abs(a-b)=0 :
            a
        else :
            (a{dir(angle(b-a)+phi)} .. {dir(angle(b-a)-phi)}b)
        fi
    enddef ;

    primarydef a arc delta =
        do_arc(a,delta)
    enddef ;

    vardef do_arc(expr a,delta) primary b =
        if abs(a-b)=0 :
            a
        else :
            (a .. unitvector direction .5 of (a--b) rotated 90
                 scaled delta * arclength (a--b)
                 shifted .5[a,b]
               .. b)
        fi
    enddef ;
\stopMPdefinitions

\starttext

\startMPpage
    z1 = (-.5cm,1cm) ;
    z2 = (1cm,3cm) ;

    for phi = 0 step 5 until 360:
        draw z1 bend phi z2 withcolor (phi/360)[red,blue] ;
    endfor ;
\stopMPpage

\startMPpage
    z1 = (-.5cm,1cm) ;
    z2 = (1cm,3cm) ;

    for delta = -1 step .1 until 1:
        draw z1 arc delta z2 withcolor ((delta+1)/2)[red,blue] ;
    endfor ;
\stopMPpage

% Possible use case:

\startMPpage[offset=1cm]
    z1 = (-.5cm,1cm) ;
    z2 = (1cm,3cm) ;
    draw z1 -- z2 ;
    dotlabel.lft("$-$", z1) ;
    dotlabel.lft("$+$", z2) ;

    path p; p := z1 bend(-30) z2 ;
    drawdblarrow p withcolor blue ;
    label.lrt(textext("$\Delta$"),point .5 along p)  withcolor blue ;
\stopMPpage

\stoptext
___________________________________________________________________________________
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
___________________________________________________________________________________