Maths - Forum discusion with Hauke

By: Hauke (haukeheibel) - 2007-04-26 00:41
Hi there, 
 
First of all thanks for the nice web-site. Optically it could be nicer but the content rocks! 
 
So here are my minor remarks regarding the conversion between axis angle representation and matrix representation. 
 
a) When substituting the basis vectors of the plane perpendicular to the rotation vector for the first time, you change the order of the cross product between basis2 and the rotation axis without changing the sign. You are writing: 
 
------------- begin cite ------------- 
 
P2 = P1 + (cos(angle) - 1) * basis1 + sin(angle) * basis2 
 
substituting the basis values above gives: 
 
P2 = P1 + (cos(angle) - 1) * (axis × axis × P1) + sin(angle) * axis × P1 
 
-------------- end cite -------------- 
 
whereas the last line should in my humblest opinion be: 
 
P2 = P1 + (cos(angle) - 1) * ((axis × P1) × axis) + sin(angle) * axis × P1 
 
As you can see I also added brackets around the substitution of basis2, since the cross product is not associative. 
 
b) In the diagram where you are visualizing the plane being perpendicular to the rotation vector, the rotation vector and the point to be rotated, basis2 should actually point in the other direction when sticking to the right hand side rule. 
 
As said before. These are minor remarks and I appreciate the work that has been done a lot. 
 
Regards, 
Hauke Heibel


 


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