Archived

This topic is now archived and is closed to further replies.

Getting a vector having dimension rotations.

This topic is 5128 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

Well, I want to make a vector out of rotations, for example, if I have RotX = 0 RotY = 90 RotZ = 0 the unit vector that would come out would be(i think) v.x = 0 v.y = 0 v.z = 1 How could I come on accomplishing this? I figured how to do it in 2D angles, since the hypothenus is always a length of 1, then we can get side A and side B with: sin(angle) = A cos(angle) = B this way, i could create a vector like so v.x = cos(angle) v.y = sin(angle) but, when it comes to 3 dimensions, how could i go on accomplishing my objectives?

Share this post


Link to post
Share on other sites
And so the sticking point starts...
There are different ways to play with things in 3d.
The 3rd dimension adds lots of complexity.

There are a few methods: euler rotation, axis-angle, and quaternions.

You can compose a complete 4x4 matrix for rotation, translation, and scaling based on euler rotation I believe.

The code here assumes rotation around a given axis(kind of)
theta is the YZ plane rotation or around the Z axis.
phi is XZ plane rotation or around Y.
phi is YZ plane rotation or around X.

x'' = y * sin(theta) + x * cos(theta)
y'' = y * cos(theta) - x * sin(theta)
z'' = z

x'''' = x'' * sin(phi) + x'' * cos(phi)
y'''' = y''
z'''' = z'' * cos(phi) - z'' * sin(phi)

x'''''' = x''''
y'''''' = y'''' * sin(chi) + y'''' * cos(chi)
z'''''' = z'''' * cos(chi) - z'''' * sin(chi)


This is the easiest method to derive.
It also is somewhat like the OpenGL glRotate() call.

For high-quality code, quaternions are the method of choice for rotations.(Last I checked- its kind of a debate thing)

Hope that helped...



~V''lion

Bugle4d

Share this post


Link to post
Share on other sites