Matrices transformation

Shivsaransh12

I don't understand rotation for matrices in 3D, how does your perspective make a difference?

Reply 1

username1732133

Original post by Shivsaransh12

I don't understand rotation for matrices in 3D, how does your perspective make a difference?

Would you like to post as question that you're having trouble with?

Reply 2

Shivsaransh12

Original post by Plücker

Would you like to post as question that you're having trouble with?

No, I'm not really troubled with any question its the derivation of the rotation matrices in 3D. I find it weird to just memorize them and then use them.

Reply 3

username1732133

Original post by Shivsaransh12

No, I'm not really troubled with any question its the derivation of the rotation matrices in 3D. I find it weird to just memorize them and then use them.

Are you happy with the 2D rotation matrix?

Reply 4

Shivsaransh12

Original post by Plücker

Are you happy with the 2D rotation matrix?

Yes, it's just the perspective for the 3D matrix rotation that confuses

Reply 5

mqb2766

So take the 3d rotation matrix about the x-axis. The y-z rotation submatrix is the usual 2D rotation matrix. Are you happy with why that is? The rotation matrices about the x, y, z axes follow the right hand rule
https://en.m.wikipedia.org/wiki/Right-hand_rule

(edited 3 years ago)

Reply 6

DFranklin

Original post by Shivsaransh12

Yes, it's just the perspective for the 3D matrix rotation that confuses

I'm unclear what you mean by "perspective" and "the 3D matrix rotation".

3D matrices aren't usually considered to have "perspective". (In computer graphics perspective matrices are used, but they are actually 4D).

And I can't think of any 3D matrix rotation form canonical enough to be considered "the 3D matrix".

It would be helpful to have at least some context of what you're actually doing (what level are you studying? is this actually a purely mathematical question or do you have an application in mind? etc).

Reply 7

username5404246

I think OP means 'I'm having a hard time understanding how to use the 2d rotation matrix to deduce the 3d rotation matrices'?

Reply 8

DFranklin

Original post by anonemoose

I think OP means 'I'm having a hard time understanding how to use the 2d rotation matrix to deduce the 3d rotation matrices'?

Yeah, I still have no real idea what you / they mean by "the rotation matrices".

Having seen from a separate post the OP is doing A-level M/FM I'm now guessing that they're talking about the 3 families of matrices representing rotations around the x-axis, the y-axis and the z-axis. But there are many other potential things they could be meaning - in particular they could be talking about the matrix for an Euler angle representation (which was what I initially assumed), which has the minefield that there are twelve possible choices for the matrix depending on which 3 rotations you combine.

Reply 9

username5404246

Original post by DFranklin

If it was an actual higher math question we'd be on stackexchange :P
I think it's rotations around the axes.

Reply 10

username5404246

Assuming OP is actually asking about how to deduce the rotations around the axes in 3D:

simply go back to a basic definition of a matrix - an ordered list of where your basis gets mapped.
You can then go and fill in where each basis vector would land when rotated around the given axes, then string them together to get the matrix =)