Register to reply

Trig in 3D

by student6587
Tags: trig
Share this thread:
Jun21-14, 06:47 PM
P: 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.

Phys.Org News Partner Mathematics news on
Math journal puts Rauzy fractcal image on the cover
Heat distributions help researchers to understand curved space
Professor quantifies how 'one thing leads to another'
Jun21-14, 07:59 PM
P: 3,096
Welcome to PF!

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

Register to reply

Related Discussions
Formal definition of derivative: trig vs non trig functions Topology and Analysis 2
Simplifying multiple trig functions into a single trig function for physics II Precalculus Mathematics Homework 3
Trig function of arc trig functions and the reverse General Math 4
One regular trig question and one question on derivative of trig function Calculus & Beyond Homework 13
What does the trig book mean? Need help with trig Precalculus Mathematics Homework 4