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Trig in 3Dby student6587
Tags: trig 
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#1
Jun2114, 06:47 PM

P: 1

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 xaxis points to the right, the positive yaxis points upward, and positive angles are measured from the positive xaxis in a counterclockwise fashion. Proper insertion of a third dimension has the positive zaxis 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 counterclockwise? 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! 


#2
Jun2114, 07:59 PM

P: 2,785

Welcome to PF!
This wiki article describes 3D rotations and show the 3x3 matrices that accomplish this: http://en.wikipedia.org/wiki/Rotation_matrix 


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