| Re: Least squares fit of a model to a skeleton consisting out of 3D points. [message #64150 is a reply to message #64029] |
Wed, 03 December 2008 06:37   |
pgrigis
Messages: 436
Registered: September 2007
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Senior Member |
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Johan wrote:
> On Nov 27, 1:53�pm, Jeremy Bailin <astroco...@gmail.com> wrote:
>> On Nov 26, 3:40�am, Johan <jo...@jmarais.com> wrote:
>>
>>
>>
>>
>>
>>> On Nov 24, 4:35�pm, Wox <s...@nomail.com> wrote:
>>
>>>> On Mon, 24 Nov 2008 17:22:53 +0100, Wox <s...@nomail.com> wrote:
>>>> >X=[X,Y,Z] ; (you need to extract the seperate X, Y and Z in your user
>>>> >routine)
>>>> >Y=replicate(1,n_elements(X))
>>
>>>> Woops, redefined X :-). I mean Y=replicate(1,n3Dpoints).
>>
>>> Thank you, it seems that krellipsoidfit.pro works rather well. I do
>>> have another question regarding this and will appreciate if can advise
>>> me.
>>
>>> I need to get the 3 angles and axis lengths and use the following code
>>> to get it from the given eigenvalues (evals) and eigenvectors (evec):
>>
>>> � � � � semia = sqrt(evals[0]) * 2.0
>>> � � � � semib = sqrt(evals[1]) * 2.0
>>> � � � � semic = sqrt(evals[2]) * 2.0
>>
>>> � � � � a = semia * 2.0
>>> � � � � b = semib * 2.0
>>> � � � � c = semic * 2.0
>>> � � � � semiAxes = [semia, semib, semic]
>>> � � � � axes = [a, b, c]
>>
>>> � � � � eigenvector �= evec[*,0]
>>> � � � � eigenvector2 = evec[*,1]
>>> � � � � eigenvector3 = evec[*,2]
>>
>>> � � � � �orientation1 = atan(eigenvector1[1], eigenvector1[0])*!RADEG
>>> � � � � orientation2 = atan(eigenvector2[1], eigenvector2[0])*!RADEG
>>> � � � � orientation3 = atan(eigenvector3[1], eigenvector3[0])*!RADEG
>>> � � � � angles = [orientation1, orientation2, orientation3]
>>
>>> Is this correct or do I need made some adjustments, especially to the
>>> orientation?
>>
>>> Thanks
>>> Johan Marais
>>
>> That does indeed give you 3 angles, but it doesn't fully specify the
>> orientation. Which angles are you looking for?
>>
>> Incidentally, I'm not quite sure why you have that factor of 2 in the
>> definition of semia etc., but I suppose it depends what went into the
>> matrix you're diagonalizing...
>>
>> -Jeremy.- Hide quoted text -
>>
>> - Show quoted text -
>
> I tried different ways of getting the angles but it seems I am still
> at a lost. The angles I am looking for is as follow:
> If you have an orthogonal reference framework and the ellipsoid are
> tilted in it. I am looking for the angles that the 3 axes of the
> ellipsoid make with the xy-plane, the yz-plane and yz-plane of the
The angle between vectors a and b in IDL is given by
arccos( total(a*b) / sqrt( total(a*a)*total(b*b) ) )
Paolo
> reference framework. I assume that for each of them you need to use
> all 3 relevant eigenvectors for each axes of the ellipsoid, or it
> could be only 2?
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