Three.js - Convert mesh velocity to mesh rotation

Question

Suppose I have a three.js mesh, and a velocity vector3.

The velocity is being altered elsewhere, and then added to the mesh.position every frame.

What I want is

Answer 1

You can construct a rotation matrix from the normalized velocity vector. The vector, normalized, is 1 axis. Then you pick a 2nd axis somehow. Then you do a cross product to find the 3rd axis. Finally do a cross product between the first and 3rd to get the final 2nd axis.

Then you construct a 3x3 matrix from the 3 vectors (i can't remember their order at the moment, but something like [x1,y1,z1,x2,y2,z2,x3,y3,z3]).

Another method is the Quaternion class:

.setFromUnitVectors ( vFrom, vTo )

Sets this quaternion to the rotation required to rotate direction vector vFrom to direction vector vTo. Adapted from http://lolengine.net/blog/2013/09/18/beautiful-maths-quaternion-from-vectors. vFrom and vTo are assumed to be normalized.

http://threejs.org/docs/#Reference/Math/Quaternion

Since internally three.js likes to use quaternions, this may be a good method. If your arrow is an upward pointing arrow, you probably want vFrom=[0,1,0], vTo=velocityVector.normalize();