| Re: ROT is ROTTEN (a solution) [message #28165 is a reply to message #28075] |
Wed, 21 November 2001 09:34   |
thompson
Messages: 584
Registered: August 1991
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Senior Member |
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"Martin Downing" <martin.downing@ntlworld.com> writes:
> Hi All,
> This was an interesting problem - I certainly hadn't noticed it before. The
> reason for the behaviour is precision error in the arithmatic which works
> out the poly2d coefficients. It can be corrected effectively by modifying
> line 128 of rot.pro:
> from:
> theta = -angle/!radeg ;angle in degrees CLOCKWISE.
> to:
> theta = (-angle MOD 360) *acos(0.0d)/90 ;angle in degrees CLOCKWISE. (mod
> MRD 21/11/2001 to correct for precision error)
As others have said, great job! Can I make one small suggestion, though.
Instead of acos(0.0d)/90, can I suggest !dpi/180?
theta = (-angle MOD 360) * !dpi/180
William Thompson
> This does two things, firstly (-angle MOD 360) ensures that a precision
> error does not propagate due to large angles which contain multiple 360
> degree rotations,
> for instance that 390.45 degree rotation is treated exactly the same as
> 30.45 degrees [i.e. n*360+theta = = theta].
> Secondly, substituting (acos(0.0d)/90) for !radeg gives a full DOUBLE
> precision representation of theta in radians.
> This fixes it completely as far as I can see:
> IDL> a = findgen(5,5)
> IDL> for deg = -720, 720,90 do print, deg, total(rot(a, deg))
> -720 300.000
> -630 300.000
> -540 300.000
> -450 300.000
> -360 300.000
> -270 300.000
> -180 300.000
> -90 300.000
> 0 300.000
> 90 300.000
> 180 300.000
> 270 300.000
> 360 300.000
> 450 300.000
> 540 300.000
> 630 300.000
> 720 300.000
> compared this to previous output:
> IDL> for deg = -720, 720,90 do print, deg, total(rot(a, deg))
> -720 252.000
> -630 250.000
> -540 300.000
> -450 273.000
> -360 237.000
> -270 290.000
> -180 216.000
> -90 244.000
> 0 300.000
> 90 222.000
> 180 221.000
> 270 300.000
> 360 247.000
> 450 249.000
> 540 300.000
> 630 251.000
> 720 242.000
> Quite how RSI had left the code like that for so long who knows.....(but if
> they want to send me a copy of David's 2nd Ed. that would be nice!)
> cheers
> Martin
> ----------------------------------------
> Martin Downing,
> Clinical Research Physicist,
> Grampian Orthopaedic RSA Research Centre,
> Woodend Hospital, Aberdeen, AB15 6LS.
> Tel. 01224 556055 / 07903901612
> Fax. 01224 556662
> m.downing@abdn.ac.uk
> "Bhautik Jitendra Joshi" <bjoshi@cse.unsw.EDU.AU> wrote in message
> news:Pine.GSO.4.21.0111211537260.24363-100000@haydn.orchestra.cse.unsw.EDU.A
> U...
>> Hi all,
>>
>> The question I put to you all today is this: is ROT completely and utterly
>> broken?
>>
>> Lets take a nice and normal 5x5 float array:
>>
>> MOO>a=findgen(5,5) & print, a
>> 0.00000 1.00000 2.00000 3.00000 4.00000
>> 5.00000 6.00000 7.00000 8.00000 9.00000
>> 10.0000 11.0000 12.0000 13.0000 14.0000
>> 15.0000 16.0000 17.0000 18.0000 19.0000
>> 20.0000 21.0000 22.0000 23.0000 24.0000
>>
>> Now, lets do a quick checksum:
>>
>> MOO>print, total(a)
>> 300.000
>>
>> So any 90 degree rotations we perform should maintain this. Lets try it
>> out:
>>
>> MOO>print, total(rot(a,90))
>> 296.000
>>
>> OMG! *world in crisis* How to fix? Use interpolation.
>>
>> MOO>print, total(rot(a,90,/INTERP))
>> 300.000
>>
>> *phew* Lets do a clockwise rotation instead.
>>
>> MOO>print, total(rot(a,-90,/interp))
>> 300.000
>>
>> So, for those who can remember their high school math, -90 degrees is the
>> same as a 270 degree rotation.
>>
>> MOO>print, total(rot(a,270,/interp))
>> 290.000
>>
>> argh! 360 degrees - a complete rotation, no difference, right?
>>
>> MOO>print, total(rot(a,360,/interp))
>> 290.000
>>
>> Perhaps its the interpolation thats stuffing it up. Lets leave it out.
>>
>> MOO>print, total(rot(a,360))
>> 262.000
>>
>> *brain melts*
>>
>> It doesn't make a difference whether you use the interp or cubic keywords,
>> nor if you shift it so that the centre of rotation is set to be the corner
>> of the pixel rather than the centre of the pixel. If it doesn't work for
>> multiples of 90 it certainly is going to have issues with arbitrary
>> angles.
>>
>> ROT is bad. Can it be fixed? Is there a (fast) alternative?
>>
>> Cheers,
>> Bhautik
>>
>> ________________________________________________________
>> / \
>> |bjoshi@geocities.com | phone: 0404032617 |
>> |ICQ #: 2464537 | http://cow.mooh.org |
>> \~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(__)~~~~~~~/
>> (__) |..|--\
>> /--|^^| moo | |--|
>> |--| | \OO/||^
>> ^||\oo/ moo
>>
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