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.@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 <[email protected]> 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 <[email protected]
> <mailto:[email protected]>> 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 <[email protected]
>> <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 <[email protected]
>> <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, [email protected]
>> <javascript:;> wrote:
>>>>>
>>>>>> Date: Tue, 16 Feb 2016 15:18:43 -0600
>>>>>> From: Kip Murray<[email protected] <javascript:;>>
>>>>>> To:"[email protected] <javascript:;>" <
>> [email protected] <javascript:;>>
>>>>>> Subject: [Jprogramming] A plane rotation
>>>>>> Message-ID:
>>>>>> <
>> caofworgvydb1nmjwxkb0wosyfnlubxcdz20sv11uksfcfay...@mail.gmail.com
>> <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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>>>
>>>
>>>
>>> --
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>
>
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