1.5 Coordinate systems

Each world object has a position and orientation in space. This transformation can be described by a matrix that represents the object's local coordinate system. The local coordinate system L stored in each world object is given with respect to its parent coordinate system which usually is just the world coordinate system unless you have linked two objects. If you want the local coordinate system with respect to the world system you have to travel up the transformation hierarchy and concatenate all local systems (however, you don't have to do that yourself as a world object already has an attribute worldtransform which does this for you).

The geometry of a world object is given with respect to the local coordinate system L. So this is the matrix that's required during rendering. You get L by calling localTransform() on the respective world object.

So far, if you would apply a rotation to an object it would rotate around the origin or if you would scale the object the center of the scale would lie in the origin. This is not always the desired behavior and that's why you can specify a pivot point, or rather, a pivot transformation or offset transformation P. This transformation is given with respect to L and is the identity by default. You can get and set this transformation using the getOffsetTransform() and setOffsetTransform() methods.

The concatenation of L and P is the transformation T ( $T=L\cdot P$ ). This is what the transform, pos, rot and scale slots of a world object describe. So if you modify the transform slot you also modify L whereas P always remains constant, unless you change it explicitly via setOffsetTransform().

$\includegraphics[width=12cm]{pics/coordsys}$

Here is a simple code example where you can see the effects when modifying the different transformations:

>>> s = Sphere()
>>> s.pos = vec3(1,2,0)
>>> s.pos
<1, 2, 0>
>>> s.setOffsetTransform(mat4().translation(vec3(2,4,7)))
>>> s.pos
<3, 6, 7>
>>> s.pos = vec3(0,0,0)
>>> s.pos
<0, 0, 0>
>>> s.localTransform()
[1, 0, 0, -2]
[0, 1, 0, -4]
[0, 0, 1, -7]
[0, 0, 0, 1]