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Absolute poses in weight space.

May 23, 2012

Charles

From my earlier posts if we break the idea of a pose being directly attached to weight 1:1,  we can place it anywhere in a n-dimensional space made up of multiple weights. E.g.

pose A = weight A @ 1.0
pose B = weight B @ 1.0
pose C = weight A @ 1.0 * weight B @ 1.0

The @ denotes the position along the weight governing its interpolation e.g. if the position was at 0.5 the interpolation would go from 0.0 – 1.0 (0.5) – 0.0. Likewise if the position was at 0.0 the interpolation would go from 1.0 – 0.0 and vice verse if it was at 1.0.

Zero value positions

If we include  dimensions with zero values we can have absolute interpolation. We can show this with a 2d space:

Pose A = weight A @ 1.0 * weight B @ 0.0
Pose B = weight A @ 0.0 * weight B @ 1.0

If weight A is at 1.0 and weight B at 0.0 the pose A will be at 1.0, once we start to introduce weight B,  pose A gets reduced until 0.0 when weight B is at 1.0.

Mixing additive and absolute poses

This can be done simply by deciding on the dimensionality of the poses. If we have three weights: A, B and C we could have poses for weights A and B additive and absolute for C:

Pose A = weight A @ 1.0 * weight C @ 0.0
Pose B = weight B @ 1.0 * weight C @ 0.0
Pose C  = weight C @ 1.0

Plus a corrective could still be applied:

Pose D = weight A @ 1.0 * weight B @ 1.0

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