IC Python API:3D Look At
- Main article: RL Python Samples.
This article will discuss one of the pillars of 3D mathematics for solving a very common problem. Specifically, how to face one item in the scene towards another similar to how Look at (O) is implemented for cameras in iClone. Keep in mind that the position of an item is set by its pivot point and will need to be adjusted if it is not in the desired location.
Necessary Modules
The only required module for this code is:
import RLPy
Look At Math
It is a good idea to tuck away complex math algorithms in easy to understand, reusable functions. Better still is to tuck all complex math functions under a unified class like Math3D for example. 3D math is not an easy subject matter but it's not a field you'll need to master in entirety. In fact, many resources exist online which just need some diligence and patience to uncover such as this one: http://www.technologicalutopia.com/sourcecode/xnageometry/matrix.cs.htm
So let's dive into the mathematical function we'll need to pull of a right-handed look at that is compatible with iClone's coordinate system:
def look_at_right_handed(view_position, view_target, view_up_vector):
# Look at takes two positional vectors and calculates the facing direction
forward = view_position - view_target
forward.Normalize()
right = view_up_vector.Cross(forward)
right.Normalize()
up = forward.Cross(right)
# Retun a right-handed look-at rotational matrix
return RLPy.RMatrix3(right.x, right.y, right.z, # X vector
up.x, up.y, up.z, # Y vector
forward.x, forward.y, forward.z) # Z vector
The result of this formula is a rotational 3x3 matrix.
Important Takeaways
- The forward vector is the view position minus the target position normalized.
- Right vector is the cross product of the up vector and the forward vector normalized.
- Up vector is the cross product of the forward vector and the right vector.
- "Normalized" simply means that the magnitude of the vector will always equal to 1 unless it is too small, then a zero vector will be returned.
