View Single Post
Tinyboss
Tinyboss is offline
#4
Mar3-12, 02:44 PM
P: 234

Rotating vectors on a unit sphere


You want all the unit vectors (a circle's worth of them) that make a 120-degree angle with the given one? If your given vector is [itex](1,0,0)[/itex], then the unit vectors with a 120-degree angle to that are parameterized by [itex](-1/2,(\sqrt3/2)\cos\theta,(\sqrt3/2)\sin\theta)[/itex] for [itex]0\le\theta<2\pi[/itex].

If you have a different given vector, just multiply everything by any rotation matrix that takes [itex](0,0,1)[/itex] to the vector you were given.