What is the correct matrix for rotation about y-axis? I am seeing different sign for sine(theta) in different sources...

[shivajikobardan]

Look at the basic rotation 2 part. It is showing us -sinBeta
Source:

https://www.ipb.uni-bonn.de/html/teaching/3dcs-wf-2020/03-3D-CS-Bsc-Rotations-Overview-Matrix-and-Euler-Representation.pdf

However I have found sources claiming that it is +sinBeta and the other is opposite instead.

Source: https://www.cs.colostate.edu/~cs410/yr2018fa/more_progress/pdfs/cs410_F18_Lecture04_Trans_part2.pdf
Here different convention is being used.
I suppose this differs based on how we represent the angle. But none of the sources describe about their choice of angle(either it is clockwise or anticlockwise, where it is derived etc)
I wanted to learn this and got confused here. I hope to seek from experts at freemathhelp.

 

[blamocur]

The signs are determined by the direction of the rotation.
The direction of the rotation is counter-clockwise when looking from the complimentary axis:

• from Y to Z when looking from X
• from Z to X when looking from Y
• from X to Y when looking from Z

 

[shivajikobardan]

could you elaborate a bit more? I am weak in 3d mathematics.

 

[shivajikobardan]

I think you just used right hand curl rule to determine the direction of rotation.

 

[blamocur]

I think you just used right hand curl rule to determine the direction of rotation.

True. And the direction of rotation determines the signs of the matrix elements.

Personally, I never remember those signs myself, so every time I just consider coordinate basis vectors ((1,0,0), (0,1,0), (0,0,1)) and see what happens to them after multiplying by the matrix.

 

[blamocur]

could you elaborate a bit more? I am weak in 3d mathematics.

I am not sure what kind of elaboration you need. Maybe you can elaborate on which parts you find confusing.