# Posts tagged ‘rules’

1. In 3d the product of matrix multiplication is always in world space.
2. An objects transform is a product of its target space multiplied by its reference space.

This second part is really vital to understand, (I dont think I’ve phased it myself well enough here even) But basically it means that if your transforming an object by the world, but the object is parented the difference between the object and its target space need to be multiplied by the objects local space.

I’ll try to describe this more with pics.

Here are some notes on natural spine rigging, im not going into details about stretchy spines are most of this stuff wouldn’t apply especially to do with twist.

• Natural spines do not make ‘N’ shapes!, the top chest part never goes below the lower pelvis part. The lowest the mid section can go is 90 degrees perpedicular to the lower part and top part. – This can be easily accomplished to never go below by using simple dot product math. Which beings me on to my next point.
• The spine system i used and still do is three bones: bottom, mid and top with an IK chain running between the mid and top joints – this allowed me to always make good ‘S’ and ‘C’ shapes, with the spine always keeping its length.
• For deformation ride a simple chain with a complex one, the ribbon spine approach is elegant approach to this. It allows for deformation to still happen when controlling the simple chain in FK mode – my approach is similar to this but is grounded in math.
• Do not try and reach the ‘holy’ 360 degrees in all directions, the math is insanely complicated (trust me!) and more pertained to tentacle rigging where by its controlled by deforming a curves control points in position space rather than rotational. A combination of 180 degrees in yaw and pitch, with a twist of -180 to 180 is fine.
• The animation mechanism can should work in Euler rotation space, by the system underneath directly driving the spine can work in quaternions, in fact i strongly recommend riggers learn quaternion math – naturally most of rotations from the shoulder to the wrist work in a hemispherical space. The key is extrapolating the combined rotational systems creating the final deformation.