Understanding 3D Rotation Transformations

[student6587]

Hello,

First time posting to Physics Forums.

I have been thinking about rotation transformations and am a bit confused on how trig works in 3D.

In 2D, convention says the positive x-axis points to the right, the positive y-axis points upward, and positive angles are measured from the positive x-axis in a counter-clockwise fashion. Proper insertion of a third dimension has the positive z-axis pointing toward the viewer.

How do these rules translate to other perspectives of the 3 cartesian axes? For example, if the positive x-axis points to the left, the positive z axis points up, and the positive y-axis points toward the viewer. Is positive rotation still counter-clockwise? What axis is this angle measured from?

I suspect that the convention is arbitrary but there must be some criteria for consistency. A little bit of context: ultimately, I want to use this knowledge to construct matrix transformations to control the orientation of a simple 3D shape. When I try to work these out by hand, I keep getting the signs wrong.

Thanks!

 

[jedishrfu]

Welcome to PF!

This wiki article describes 3D rotations and show the 3x3 matrices that accomplish this:

http://en.wikipedia.org/wiki/Rotation_matrix