Matrix -> Angles

Matrix -> Angles

Post by Cedrick COLLOM » Fri, 25 Sep 1998 04:00:00



for this function :

M(X,Y,Z) =

|   cosYcosZ                              -cosYsinZ             sinY            |
|   sinXsinYcosZ+cosXsinZ     -sinXsinYsinZ+cosXcosZ     -sinXcosY    |
| -cosXsinYcosZ+sinXsinZ       cosXsinYsinZ+sinXcosZ      cosXcosY   |

you can have 2 couples ( X1,Y1,Z1) and ( X2,Y2,Z2 ) which gives you EXACTLY
the same matrix, more generaly M(X,Y,Z) is surjective but not injective so
it is not bijective !!!

it is why the ONLY way to invert is to do : y=Arcsin(m13) etc etc which
gives you ONE of the 2 possible couples ...

the only way to get rid of this and to get bijectivity is to allow Y to be
between -pi/2 and pi/2 for example ... and in this case only ONE couple
will match and you function will be inversible ...

 
 
 

1. Matrix->Matrix Angle Extraction

I should be able to deduce the answer to this problem, given that I
have information on Quaternion's and Matrix Decomposition, but I
cant quite seem to get it right. The problem is:

        I would like to obtain an axis and a rotation angle
        given 2 matrices which define an objects orientation

I guess what I want to know is how to "transform" one matrix onto
another by rotating about a single vector (axis). The matrices are
pure rotation matrices (3x3 or 4x4).

Thanks suhail
____________________________________________
Suhail A Islam
Biomolecular Modelling Laboratory
Imperial Cancer Research Fund, P.O. Box 123
44 Lincoln's Inn Fields, London WC2A 3PX
Tel: (0171) 269 3380, Fax: (0171) 269 3479

http://www.icnet.uk/bmm/
____________________________________________

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