[Jprogramming] A plane rotation

Fri Feb 19 07:19:30 UTC 2016

Ah, I see. I was somehow thinking that these were parametric curves.

Thanks,

-- 
Raul

On Fri, Feb 19, 2016 at 1:16 AM, Kip Murray <thekipmurray at gmail.com> wrote:
> In your example, 0 1 is the polynomial coefficients for the straight line
> being rotated.  In usual math notation this is the line y = x = 0 + 1 x .
> When you rotate this line by 1p1 radians about the origin 0 0 you get the
> same straight line, described by 0 1 which is the answer given.  (I am
> "cleaning", of course.)
>
> Also when you consider the straight line y = 1 + 2x (described by 1 2) you
> notice the point 0 1 is on this line so when you rotate this line by 1p1
> radians about the point 0 1 you get the same line, described by the answer
> 1 2 .
>
> It helps to draw pictures of the indicated straight lines.  Hope this helps.
>
> --Kip
>
> On Thursday, February 18, 2016, Raul Miller <rauldmiller at gmail.com> wrote:
>
>> Changing the center of rotation to 0 0 doesn't seem to make a difference.
>>
>>    0 1 linrot 1p1;0 0
>> 1.11022e_16 1
>>
>> But presumably this means I am not understanding what it means to
>> "rotate a linear polynomial"?
>>
>> --
>> Raul
>>
>> On Thu, Feb 18, 2016 at 11:46 PM, Kip Murray <thekipmurray at gmail.com
>> <javascript:;>> wrote:
>> > No, because his center of rotation is not 0 0 .  In his first two
>> examples
>> > the center of rotation is 0 1 and in the third it is 1 1 .  --Kip
>> >
>> > On Thursday, February 18, 2016, Raul Miller <rauldmiller at gmail.com
>> <javascript:;>> wrote:
>> >
>> >> I'm not quite sure I follow what you are doing here.
>> >>
>> >> Shouldn't 2p1 be a neutral rotation, with 1p1 being a reversal of
>> >> direction?
>> >>
>> >> Thanks,
>> >>
>> >> --
>> >> Raul
>> >>
>> >>
>> >> On Thu, Feb 18, 2016 at 10:23 PM, Louis de Forcrand <olius at bluewin.ch
>> <javascript:;>
>> >> <javascript:;>> wrote:
>> >> > To continue with the rotation challenges, write a verb that rotates a
>> >> linear
>> >> > polynomial (coeffs in x) by 0 {:: y with a centre of 1 {:: y:
>> >> >
>> >> >    1 2 linrot 1p1 ; 0 1
>> >> > 1 2
>> >> >    1 2 linrot 1r2p1 ; 0 1
>> >> > 1 _0.5
>> >> >    1 2 linrot 1p1;1 1
>> >> > _3 2
>> >> >
>> >> > My take:
>> >> > linrot=: ({: %. 1 ,. {.)@rotposmat
>> >> >  rotposmat=: centre + j./@posmat |:@:+.@:* r. at angle
>> >> >   centre=: 1&({::)@]
>> >> >   posmat=: (] ,: p.)&0 1@[ - centre
>> >> >   angle=: 0&({::)@]
>> >> >
>> >> > It uses matrix division on a rotated set of two points from the
>> original
>> >> > polynomial. Not very elegant, but I’m pretty sure it works.
>> >> >
>> >> > Best regards,
>> >> > Louis
>> >> >
>> >> >> On 17 Feb 2016, at 06:40, Kip Murray <thekipmurray at gmail.com
>> <javascript:;>
>> >> <javascript:;>> wrote:
>> >> >>
>> >> >> Not bad.  I didn't know about r.  .  For clean I use
>> >> >>
>> >> >> clean =: (* *!.1e_14@|)"0&.+.
>> >> >>
>> >> >> --Kip
>> >> >>
>> >> >> On Tuesday, February 16, 2016, Raul Miller <rauldmiller at gmail.com
>> <javascript:;>
>> >> <javascript:;> <mailto:rauldmiller at gmail.com <javascript:;>
>> <javascript:;>>> wrote:
>> >> >>
>> >> >>> Well...
>> >> >>>
>> >> >>>   rottheta=: (rot~ r.)~
>> >> >>>   1r2p1 rottheta 3 4
>> >> >>> _4 3
>> >> >>>   1r4p1 rottheta _1 1
>> >> >>> _1.41421 1.11022e_16
>> >> >>>
>> >> >>> I remember there being a concise phrase to clean irrelevant bits
>> near
>> >> >>> zero in a complex number, but I can't remember what I need to search
>> >> >>> on to find it, and my foggy memory of how to write it is failing me
>> at
>> >> >>> the moment.
>> >> >>>
>> >> >>> Still, this gets you close.
>> >> >>>
>> >> >>> --
>> >> >>> Raul
>> >> >>>
>> >> >>>
>> >> >>> On Tue, Feb 16, 2016 at 11:50 PM, Kip Murray <
>> thekipmurray at gmail.com <javascript:;>
>> >> <javascript:;>
>> >> >>> <javascript:;>> wrote:
>> >> >>>> I'm retired with time to "fool around".  Finding an old rot90 verb
>> >> that
>> >> >>>> used multiplication by a 2 by 2 matrix, I sought a more direct way
>> >> using
>> >> >>>> complex numbers and found one of the solutions that was posted.  I
>> >> also
>> >> >>>> learned a lot from the other solutions posted, thanks everyone!
>> >> >>>>
>> >> >>>> New puzzle: find a complex analysis way to do a rotation given its
>> >> angle
>> >> >>> in
>> >> >>>> radians, examples:
>> >> >>>>
>> >> >>>>    1r2p1 rottheta 3 4
>> >> >>>> _4 3
>> >> >>>>
>> >> >>>>    1r4p1 rottheta _1 1
>> >> >>>> _1.414213562 0
>> >> >>>>
>> >> >>>> --Kip
>> >> >>>>
>> >> >>>> I'm also a former math professor!
>> >> >>>>
>> >> >>>> On Tuesday, February 16, 2016, David Lambert <b49p23tivg at gmail.com
>> <javascript:;>
>> >> <javascript:;>
>> >> >>> <javascript:;>> wrote:
>> >> >>>>
>> >> >>>>>
>> >> >>>>> what's your agenda, are you writing a book? Isn't there a
>> homogeneous
>> >> >>>>> coordinate system/transformation lab?
>> >> >>>>>
>> >> >>>>>>
>> >> >>>>>> On 02/16/2016 06:16 PM, programming-request at forums.jsoftware.com
>> <javascript:;>
>> >> <javascript:;>
>> >> >>> <javascript:;> wrote:
>> >> >>>>>>
>> >> >>>>>>> Date: Tue, 16 Feb 2016 15:18:43 -0600
>> >> >>>>>>> From: Kip Murray<thekipmurray at gmail.com <javascript:;>
>> <javascript:;>
>> >> <javascript:;>>
>> >> >>>>>>> To:"programming at jsoftware.com <javascript:;> <javascript:;>
>> <javascript:;>" <
>> >> >>> programming at jsoftware.com <javascript:;> <javascript:;>
>> <javascript:;>>
>> >> >>>>>>> Subject: [Jprogramming] A plane rotation
>> >> >>>>>>> Message-ID:
>> >> >>>>>>>    <
>> >> >>> CAOfWorgVyDB1NmJwXkB0WOSYFnLUBXCDZ20sV11ukSFCfay5sA at mail.gmail.com
>> <javascript:;>
>> >> <javascript:;>
>> >> >>> <javascript:;>>
>> >> >>>>>>> Content-Type: text/plain; charset=UTF-8
>> >> >>>>>>>
>> >> >>>>>>> Fairly easy: write a verb that rotates a point in the plane by
>> the
>> >> >>> angle
>> >> >>>>>>> of
>> >> >>>>>>> a given complex number.  For example
>> >> >>>>>>>
>> >> >>>>>>>     1j1 rot 1 1  NB. Rotate 1 1 counterclockwise 45 degrees
>> >> >>>>>>>  0 1.414213562
>> >> >>>>>>>
>> >> >>>>>>> Background information:  when you multiply two complex numbers
>> the
>> >> >>>>>>> magnitudes are multiplied and the angles are added.
>> >> >>>>>>>
>> >> >>>>>>> --Kip Murray
>> >> >>>>>>>
>> >> >>>>>>>
>> >> >>>>>>
>> >> >>>>>
>> >> ----------------------------------------------------------------------
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>> >> >>>>
>> >> >>>>
>> >> >>>>
>> >> >>>> --
>> >> >>>> Sent from Gmail Mobile
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>> >> >>
>> >> >>
>> >> >> --
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>> >
>> >
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>
>
>
> --
> Sent from Gmail Mobile
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