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Trig in 3D

  1. Jun 21, 2014 #1

    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.

  2. jcsd
  3. Jun 21, 2014 #2


    Staff: Mentor

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