I took another look at some research on n-space combination sculpture today and the light-bulb ( i think) finally went off in my head as to how it works. Essentially you have four parts:

- A n-space comprised of weights
- A set of targets (i.e shapes)
- An orgin/neutral shape
- A vector (the sum of the weights)

The old ideas of standard blendshapes basically go out the window, but the power you gain is pretty amazing – and in theory can be used for any facial type setup including bones and muscle rigs.

In simple terms, you associate a target(shape) to a weight,this for all instances is standard blendshape stuff – but with n-space combinations you can associate a target to more than one weight.

For example lets say we have two targets: A and B, and there respective weights: w1[1,0] and w2[0,1] remember weights exist in an n-space so if there was 3 it would be as follow w1[1,0,0] , w2[0,1,0] and w3 [0,0,1]. These do nothing atm, until we associate a target(s) to them so e.g target a is associated to w1 at [0.5,0] ( a target doesnt have to be at 1 of the weight)

Still follow? Well simply put we define a space from weights so point1 would be just one weight, a point2 would be 2 weights and a point3 would be three weights.. and so on. If we have a space of the nth number its an n-space so if we have 30 weights, i.e sliders in our rig we have…. yes….. an n-space of 30 dimensions!

Now the clever part comes in that the system basically cant break. The cool part comes in that you can associate a target shape to 1 or more weights(sliders)! so say we set weight w1 at a value of 1 so [1,0] and w2 the same [0,1] we now have a combined value of: [1,1] and this shape combination may not work. So we associate a new shape to this weight vector.

All that changing the value of the weights does is that it moves a vector through the space of what its comprise of eg. 3 weights [.3,0,0] [0,.2,0] [0,0,.7] we have a vector in this space: [0.3,0.2,0.7].

What i dont fully understand is achieving the final, delta. But im working on it – the funny thing is Jason Osipas setup is very reminesent of this n-space idea, working in planes etc. And could easily i think be adapted to work with it.

more to come..

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