I can express a point direction approach as well as the 2 point approach rotheta=: ([: r. [) * ] pt=:_1j0 dir=:1j1 ctr=:_1j1
( ctr,0)+ (1r4p1) rotheta (pt-ctr),dir _0.292893j0.292893 0j1.41421 which is, I believe , your desired point/direc tion approach. My previous appr oach gave 2 points on the lin e which can give you the A and B and t can be extracted. ( original magnitude of t unchange d but direction giving dy/dx is changed) Old math te acher f orgiven EE prof emeritus (latin for "has been") whose approach to math is as a tool and less pro ficient in J , also ask s for forgiveness Don ----- Original Message ----- From: "Kip Murray" <[email protected]> To: [email protected] Sent: Saturday, March 12, 2016 6:37:28 AM Subject: Re: [Jprogramming] A plane rotation What you are doing is very nice. I call mine a point direction approach. A point on a straight line is described by S + t * D Where t is a real number, and S And D are points in a vector space, the starting point and the direction point. Another approach valid in any vector space is the two-point approach where a point on the straight line through two points A and B is described by ((1-t)*A) + t*B -- this point is " t of the way from A towards B ", for example when t is 1r2 you have the midpoint between A and B, and if t is 2 then B is the midpoint between A and ((1-t)*A) + t*B , and if t is _1 . . . You are establishing a coordinate system on line AB in which A has coordinate 0 and B has coordinate 1. Forgive an old math teacher, Kip Murray On Friday, March 11, 2016, Donald Kelly <[email protected]> wrote: > We are trying to do the same thing- where you concentrate on a point- > slope approach, I tend to a rotation of points -and there can be many- > points on a shape or a curve. With this latest example I use the following. > > > rotheta=:([:r.[)*] > pts=:_1j0 0j1 1j2 > ctr=:_1j1 > > ] s=:ctr+ (1r4p1) rotheta pts-ctr > _0.292893j0.292893 _0.292893j1.70711 _0.292893j3.12132 > > > which are the the rotated positions of the original points -a vertical > line at x=_0.292893 (_1+%:0.5) > > as you have . The distance between adjacent points is % :2 as in the ori > ginal points . > > > > My earlier posted rotheta was m eant to give input and output in (x,y) > form and didn't work for this example. > I realize why you de alt with 3 points although t his wa sn't needed. > > > As far as the verbs themselves are considered- as simple as possible is > the target. > > > Don > > ----- Original Message ----- > > From: "Kip Murray" <[email protected] <javascript:;>> > To: [email protected] <javascript:;> > Sent: Wednesday, March 9, 2016 8:26:09 PM > Subject: Re: [Jprogramming] A plane rotation > > Verbs ff , gg , and (gg mab) below represent straight lines. If one of > them is evaluated at a real number t the result is a point on the > represented line. I calculated three points on each represented line as a > kind of substitute for graphing the line, and to let you see how the > y-coordinates (imaginary parts) were related to the x-coordinates (real > parts). For me the "results" are the verbs themselves, not the points > calculated from them! Here is another example > > hh =: _1j0 1j1 line NB. line with start _1j0 , direction 1j1 > hh"0 [ 0 1 2 NB. three points on the line > _1j0 0j1 1j2 > jj =: hh rot 1r4p1 _1j1 NB. rotate line 1r4p1 radians about _1j1 > jj"0 [ _1 0 1 NB. three points show result is vertical line x = _1 + > %: 0.5 > _0.2928932188j_1.121320344 _0.2928932188j0.2928932188 > _0.2928932188j1.707106781 > > --Kip Murray > > On Wednesday, March 9, 2016, Don Kelly <[email protected] <javascript:;>> > wrote: > > > 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] > <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.@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:;> > >>>> > >>> <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:;> > >>>> > >>> <javascript:;> <mailto:[email protected] <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 <[email protected] > <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 <[email protected] > <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, [email protected] > <javascript:;> > >>>>>>>> > >>>>>>> <javascript:;> > >>> > >>>> <javascript:;> wrote: > >>>>> > >>>>>> Date: Tue, 16 Feb 2016 15:18:43 -0600 > >>>>>>>>> From: Kip Murray<[email protected] <javascript:;> > <javascript:;> > >>>>>>>>> > >>>>>>>> <javascript:;>> > >>> > >>>> To:"[email protected] <javascript:;> <javascript:;> > <javascript:;>" < > >>>>>>>>> > >>>>>>>> [email protected] <javascript:;> <javascript:;> > <javascript:;>> > >>>>> > >>>>>> Subject: [Jprogramming] A plane rotation > >>>>>>>>> Message-ID: > >>>>>>>>> < > >>>>>>>>> > >>>>>>>> > caofworgvydb1nmjwxkb0wosyfnlubxcdz20sv11uksfcfay...@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 > >>>>>>>>> > >>>>>>>>> > >>>>>>>>> > >>>>>>> > ---------------------------------------------------------------------- > >>>>>>> For information about J forums see > >>>>>>> > >>>>>> http://www.jsoftware.com/forums.htm > >>> > >>>> > >>>>>> > >>>>>> -- > >>>>>> Sent from Gmail Mobile > >>>>>> > ---------------------------------------------------------------------- > >>>>>> For information about J forums see > >>>>>> http://www.jsoftware.com/forums.htm > >>>>>> > >>>>> > ---------------------------------------------------------------------- > >>>>> For information about J forums see > http://www.jsoftware.com/forums.htm > >>>>> > >>>> > >>>> > >>>> -- > >>>> Sent from Gmail Mobile > >>>> ---------------------------------------------------------------------- > >>>> For information about J forums see > http://www.jsoftware.com/forums.htm > >>>> < > >>>> > >>> http://www.jsoftware.com/forums.htm> > >>> ---------------------------------------------------------------------- > >>> For information about J forums see http://www.jsoftware.com/forums.htm > >>> > >> > >> > >> > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > > > > -- > Sent from Gmail Mobile > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm -- Sent from Gmail Mobile ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
