View Full Version : Extract vector from rotation matrix

10-22-2014, 04:48 AM
Hi everyone,

I'm looking to build a vector pointing in the direction my object is facing; this will be used to move the object in that direction over a time period. I have a 4x4 rotation matrix describing the orientation of the object, and I want to get that orientation as a unit vector (vec3 ideally) from the origin of the object so I can add this times by a deltaTime to simulate a motion. I'm having trouble getting this vector, and also wondering in fact if this is the correct way to go about things. Does have anyone have any thoughts on this?

Agent D
10-22-2014, 05:57 AM
If you multiply an abritrary vector with the upper left 3x3 sub part (the rotation and scaling part) of the object-to-world 4x4 matrix, the object-to-world
rotation is applied to the given vector.

So multiplying (0,0,1,0) with the 4x4 object-to-world matrix of your object, gives you the direction of the object local Z axis in world coordinates.
If you think about it, you realize that this returns the third column of the matrix. If you take a column-major 3x3 matrix, expressing an object-to-world
rotation, the 1st column is the direction of the local X axis in world coordinates, the second the Y-axis and the third the Z axis.