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#ActualParadigm Shifter

Posted 31 May 2013 - 02:29 PM

You might want to remember that when dealing with products of transposed matrices, the following formula applies:

 

(AB)T = BT * AT

 

EDIT: Proof here: http://www.proofwiki.org/wiki/Transpose_of_Matrix_Product

 

And for multiple products of transposes

 

(A1A2...An-1An)T = AnT * An-1T * ... * A2T * A1T

 

Which is very similar to the product of inverses formula too (replace AT with A-1). The inverse formula is trivial to prove.

 

EDIT2: So, since your X, Y, Z rotation matrices are transposed, you should find that XTYTZT = (ZYX)T

 

i.e. your XYZ rotation matrix will be the other library's ZYX rotation matrix, transposed.


#4Paradigm Shifter

Posted 31 May 2013 - 02:00 PM

You might want to remember that when dealing with products of transposed matrices, the following formula applies:

 

(AB)T = BT * AT

 

EDIT: Proof here: http://www.proofwiki.org/wiki/Transpose_of_Matrix_Product

 

And for multiple products of transposes

 

(A1A2...An-1An)T = AnT * An-1T * ... * A2T * A1T

 

Which is very similar to the product of inverses formula too (replace AT with A-1). The inverse formula is trivial to prove.

 

EDIT2: So, since your X, Y, Z rotation matrices are transposed, you should find that XTYTZT = (ZYX)T


#3Paradigm Shifter

Posted 31 May 2013 - 12:06 PM

You might want to remember that when dealing with products of transposed matrices, the following formula applies:

 

(AB)T = BT * AT

 

EDIT: Proof here: http://www.proofwiki.org/wiki/Transpose_of_Matrix_Product

 

And for multiple products of transposes

 

(A1A2...An-1An)T = AnT * An-1T * ... * A2T * A1T

 

Which is very similar to the product of inverses formula too (replace AT with A-1). The inverse formula is trivial to prove.


#2Paradigm Shifter

Posted 31 May 2013 - 12:02 PM

You might want to remember that when dealing with products of transposed matrices, the following formula applies:

 

(AB)T = BT * AT

 

EDIT: Proof here: http://www.proofwiki.org/wiki/Transpose_of_Matrix_Product

 

And for multiple products of transposes

 

(A1A2...An-1An)T = AnT * An-1T * ... * A2T * A1T

 

Which is very similar to the product of inverses formula too (replace AT with A-1)


#1Paradigm Shifter

Posted 31 May 2013 - 12:00 PM

You might want to remember that when dealing with products of transposed matrices, the following formula applies:

 

(AB)T = BT * AT

 

And for multiple products of transposes

 

(A1A2...An-1An)T = AnT * An-1T * ... * A2T * A1T

 

Which is very similar to the product of inverses formula too (replace AT with A-1)


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