# Posts tagged ‘Reference’

All object transforms have a reference coordinate system i.e. the space they exist in even if there parented to an object or not. For example if I’m driving a vehicle, I’m relative to the vehicle which in turn is relative to the earth, and in turn the sun.

When we want to find the difference or offset of an objects transform relative to its space – be it’s parent, world or an other object we use whats called the inverse. Now this is where it gets a little tricky so ill go slow – to transform an object by another object or get it transform relative to that object we use matrix multiplication. Matrix multiplication in laymen’s terms is basically addition like 10 + 10, but most importantly is non-communicative.

This means simply that if one matrix is 20 and another matrix is 30, 20 + 30 will equal 50 but 30 + 20 wont. Or simply put its like subtraction. This is due to how matrices are multiplied together.

If we got back to our start matrix – [1,0,0] [0,1,0] [0,0,1] [0,0,0] we can classify each vector as a ‘row’ i.e.

[a,b,c] – row 1

[d,e,f] – row 2

[h,i, j] – row3

[k,l,m] – row 4

With perpendicular values such as a,d,h,k being ‘columns’. In our example above we have 3 columns by 4 rows or a 3×4 matrix. The crucial rule you have to keep in mind when multiplying matrices is that **the initial matrix must have the same amount columns as the matrix your multiplying it against has rows**. For example if our initial matrix looks like this:

[1,2,3]

[4,5,6]

Our multiplying matrix must have the same amount of rows like so,

[a,d]

[b,e]

[c,f]

We multiply a matrix like so: 1 x a, 2 x b, 3 x c and so on and so forth…

When we get the relative transform of one object to another, we multiply its transform by the inverse of our target object, parent or space. Now this is a quite a bit more complex so i’ll discuss it very simply.

If we treat two matrices as single values for example 10 and 20, when we get the relative space of 10 to 20 what we do is 10 + -20. Which gives us -10; in other words **we’re finding the difference we need to go our base objects transform from our target object, parent or space. Were getting the transform ‘offset’ we need to apply to our target object to get our base objects transform. This offset is always in world space – because it’s the difference thats needed.**

http://www.cgplusplus.com/online-reference/maxscript-reference/

This may help you out like me when I need to test my theories, especially when i’m not on a PC.

A simple problem, with your arm out t-pose palm flat (facing down) do this:

- Rotate you arm down to the side, then forward (You’ll notice the bicep faces up)
- Now go back to your arm out. Rotate it forward (the bicep will face to the right or left now)

We have an oddity here, and I think it’s one of the founding principles of biomechanical rotation, it ‘resolves’ itself. When two rotations meet the union causes another plane of freedom to be introduced – i.e the top of the bicep will twist 45 degrees with your arm going forward and -45 going backwards. Looking at this from a math perspective its spherical rotation. (a quaternion)This spherical rotation similar to a quaternion is what stops the arm from twisting itself off its joint. The muscles are are treating its ball and socket joint as a spherical rotation or in other words a quaternion. Now this may not seem interesting but this is before there’s been any rotation of the elbow.I.e the twist of the upper arms is brought on by the constant rotation of the shoulder and its resolution or twist, is brought on by the rotation of the elbow. This is why it can be hard to get a frame of reference for the twist. I’ll see if i can update this with some pics.

**Edit: My last post was more of a hinderance than a help, so i took it out.**

In my last post I discussed a possible way of doing animation pivots – it sadly was just notes in my book and spare of the moment ideas. I think i missed out a vital chunk, and i think in theory I can make it a little cleaner – weak referencing not needed.

So this is still theoretical, but if we examine a standard object matrix3 transform it contains the transform space and its pivot space i.e the offset to keep it in the right position. So if we essentially generalize this idea (i.e making itself over the top of itself) i think we can work it out.

Probably the most important aspect of rigging, infact what we can sum rigging up is relativity – everything relies on. If its the mesh its relative to a skin, the to the bones and the bones to a rig. And even at the finite level the controls of the rig are relative to a other controls – they exist in a space of there own but are relative to something else even if this is the world.

Rigging is relativity and reference – its a bold statement but is the basis for everything needed. Everytime you parent or constrain an object to another you set its relativity and its reference. The key to rigging is a system where both dont fight but work hand in hand with one another. A good example is the spine – the animator wants control of the hip, chest and head. But also wants control of the torso (everything) – they also dont want counterotation and the ability to hold a pose.

Its a lot of systems but if we boil it down to relativity and reference its relatively (pardon the pun) straight forward. The hips are parented to the torso – so we have defined a refence: the torso and a relavity (torso-hip) to work in. The chest is parented to the torso, the same applies here. But the head is different the neck is really a part of the spine and really moves with the chest, but the problem comes in that we want it to move with the head when needed.

So we define 2 references – firstly we set the heads position relative to the chest, but its rotation to the torso. This means when we rotate the chest the head moves with it but crucial stays pointing at a target. But additional if we move the head the neck will follow – this is via an ik system or lookat/pole vector – simple stuff.

So when building a rig really understand whats relative to what, and understand the methods and math of space.