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# 3D rotation of a vertex about the origin

Posted on 2006-04-06

I don't want anything overly complicated nor a 500 page web site to read.

I want a mathmatical equation(s) to rotate a given vertex at (x,y,z) with a current angle Theta to the X axis, Phi to the Y axis, and Omega to the Z axis. The defined rotation is about all three axis defined by a rotation of Theta + Theta' about the X axis, Phi + Phi' to the Y axis, and Omega + Omega' to the Z axis. Where Theta', Phi' and Omega' are the user defined rotation to rotate beyond the current rotation about each axis.

The equation should work with no exceptions such as 90 degree rotation about the Z axis. I've been looking at this complex matrix rotation stuff for a while now and honestly do not feel like figuring out the derrived rotation matrix for a rotation on all three axis. Answer should be in the form:

x = something

y = something

z = something

Another question that is not required to be answered is given an arbitrary vector to rotate about how to calculate rotation about that axis. So say given vector (v.x, v.y. v.z) and a rotation about that vector with a measure of the current angle of the point given by the dot product of the y axis and the line (giving a perpendicular line to the Y axis and the given vector) how could I rotate a point in 3D space about that arbitrary line.

Thank you!

~Aqua