Ive just been reading up on FACs and some about n-space combinations - The math quite frankly is very very hard, not only to implementing it but just the abstraction. Its more akin to matrix transformation and complex geomtric math. But I think im starting to understand it (only took 3 or so months of not thinking) Im trying to understand this method because if broken down into simple terms can be used not only for blend shape type setups but also bone,muscle types too. Many thanks to DPK- this is where most of these ideas are coming from.(the guy’s a genius)

So I’ll start simply, if we have two targets: A and B and two weights associated with them [1,0] and [0,1]. This is not the usual standard blenshape method weight. Infact the weight is a vector in an n-space. And this n-dimension is comprised by the amount of weights. See its very very complicated to understand. What infact is happening is the regular association of weight to blendshape doesnt exist. But its made to look like it does because generally its a 1 to 1 association i.e you have the same amount of weights as target mesh’s.

You have a base i.e neutral, your targets and the weights - for instance 2 targets = 2 weights = ([1,0],[0,1]) also they dont have to be at 1.

So back to our two targets A and B and two weights - this gives us a n-dimension of 2. eg. [0,0] and because we have two targets our association is: ([1,0],[0,1]) now when we combine A and B’s weight like so, to give us a vector of: [1,1] we probably get a mess. And this is where the magic of n-space combinations work. We can associate a target to multiple weights. (or i suppose a vector sum of weights in a way)

If we associate a new target to [1,1] we now have a combination shape.

So to reiterate:

[ol]

[li]We devise an n-space based on the number of weights (e.g the number of sliders) e.g 2n-space. Like a point 2.[/li][li]We associate a target (i.e blendshape) to a vector in this space eg [0.5,0].[/li][li]Combination shapes, in the standard sence dont exist. You just associating a target/fix to the combination vector of the weights.[/li][/ol]This makes the system amazingly powerful, i mean any slider can be combined with any other, the results in theory wont break. You just have to not think in the standard way of blendshape analogy. This vector thats built from the weights could drive anything - infact a bone or muscle setup.

Whats complicated though is acheive the final delta, something i need to think about. (hopefully not another 3 months) Ive been scribbling of post-its all day!

Edit:

If i can work out the math, i’ll try and post my findings (hopefully wont go over your heads)

cheers,