A question- you give you define the line and the center of rotation but
the results are 3 points on the line. shouldn't the results be shown in
terms of 2 points on the rotated line? While usually the line is
expressed as y=a+bx (a and b real) which is easy if the the rotation
center is on the line at x =0.
new end =. (r.theta) +end as start is not changed.
A bigger challenge is to have a rotation center that is not on the
original line and given points that do not fit the typical y=a+bx
Example: line ends at 2j3j5 and 3j4 to be rotated about 1j2
this involves a rotation of two vectors (1j1 and3j4 ) as seen from
1j2 about "0" and then a translation of 1j2
rotheta=:[: +. ([: r. [) * [: +.^:_1 ]
1j2+ (_1r4p1) rotheta 1j1 2j2
2.41421j2 3.82843j2 which is the location of the
points after rotation
This can then be put into a y=a+bx form with a =2 and b=1.414..
Don
On 2/20/2016 2:14 PM, Kip Murray wrote:
Here after a struggle are my linrot results.
NB. rotate a line in the plane about a point in the plane
NB. here points are complex numbers
NB. below start and direction are complex numbers, could be vectors
NB. (start,direction) line t is start + t * direction
line =: 1 : '({. m) + ({: m) * ]'
mab =: 1 : '( (u 0) , (% 9&o.) (u 1) - u 0 ) line' NB. point slope
version of u
NB. below u rot (theta,center) rotates results of u by theta radians
about the center
NB. it is assumed the results of u and the center are complex numbers
rot =: 2 : '[: r.&({. n)&.(({: n) -~ ]) u'
ff =: 0j1 1j1 line NB. line starts at 0j1 goes in direction of 1j1
ff"0 [ 0 1 2 NB. Notice y = x + 1
0j1 1j2 2j3
gg =: ff rot _1r4p1 0j1 NB. rotates ff results 45 degees clockwise
about 0j1
gg"0 [ 0 1 2 NB. horizontal (y's are all 1)
0j1 1.414213562j1 2.828427125j1
(gg mab)"0 [ 0 1 2. NB. results x j. y from point slope y = 1 +
0*(x - 0)
0j1 1j1 2j1
--Kip
On Thursday, February 18, 2016, Louis de Forcrand <[email protected]> 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.@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]
<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 <[email protected]
<javascript:;> <mailto:[email protected] <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 <[email protected]
<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 <[email protected]
<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, [email protected]
<javascript:;>
<javascript:;> wrote:
Date: Tue, 16 Feb 2016 15:18:43 -0600
From: Kip Murray<[email protected] <javascript:;>
<javascript:;>>
To:"[email protected] <javascript:;> <javascript:;>" <
[email protected] <javascript:;> <javascript:;>>
Subject: [Jprogramming] A plane rotation
Message-ID:
<
caofworgvydb1nmjwxkb0wosyfnlubxcdz20sv11uksfcfay...@mail.gmail.com
<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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