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July 28th, 2019, 10:20 AM  #1 
Member Joined: Sep 2013 Posts: 93 Thanks: 2  Rotation in n dimension
Hello In 2D, the rotation matrix is 2x2, R(theta), in 3D you have 3 3x3 matrices, Rx(theta), Ry(theta) and Rz(theta), as you can see here: https://en.wikipedia.org/wiki/Rotation_matrix In n dimension, you have n rotation matrices, all of them nxn?If so, how do you construct them? Do they look like this in 4D? https://ksgamedev.files.wordpress.co...rotation2.png 
July 29th, 2019, 05:36 PM  #2 
Member Joined: Feb 2019 From: United Kingdom Posts: 44 Thanks: 3 
Your first example is a rigid rotation in the plane/space or in more formal language a transformation of coordinates. I'm not in a position to answer the n dimensional case because I don't know, but since I've chosen the tensor route (systems independent of coordinates) I know it's going to pay off.

July 30th, 2019, 12:26 AM  #3  
Senior Member Joined: Aug 2012 Posts: 2,409 Thanks: 753  Quote:
Do they look like this in 4D? https://ksgamedev.files.wordpress.co...rotation2.png[/QUOTE] Could be. I only worked out n=3 once. The trick is that the nth column of the matrix is image of the nth standard basis vector (all zeros except 1 in the nth coordinate). Can you say more about this? I know tensor products in abstract algebra, but I don't know much about the practical aspects of tensors.  
July 31st, 2019, 01:34 AM  #4 
Member Joined: Sep 2013 Posts: 93 Thanks: 2  http://wscg.zcu.cz/wscg2004/Papers_2004_Short/N29.pdf worth reading this if you are interested in n dimensional rotations, what I needed is the general matrix for main rotations, it's on the top of the 2nd page took some time to realize what I wanted 
August 2nd, 2019, 08:50 AM  #5 
Member Joined: Feb 2019 From: United Kingdom Posts: 44 Thanks: 3 
What I find most illuminating about this is how does one even depict a geometrical figure in the ndimensional case to be rotated?


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