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Posts tagged ‘Axis’

Is orthogonality found in nature?

October 12, 2009

Charles

I wonder whether orthogonality is found in nature? We can dictate a direction with an axis and its spin about that axis with a second axis – the third axis is really a product for keeping the second orthogonal to the first.  I wonder whether this is needed in nature or whether it copes quite well with skew? Skew itself seems quite common in nature and the very fact that skin, muscles, etc skew is important for flexibility, movement and kinesis.

I wonder if allowing a transform to skew, without affect its scale has benefits to rigging. Tensegrity and its biological form certainly allow for skew against multiple planes, and the fact that they work under tension allows them to always find a resolution.

More on matrices: basics

May 30, 2009

Charles

Most object transforms in 3d software are matrices’ heres a rough breakdown of what they are.

A matrix in 3d is an axis defined by three vectors: X,Y and Z and fourth being it’s positional offset from an origin. The length of each axis from the origin defines the scale of that axis; 1.0 being 100%. The ‘identity’ matrix is an objects base transform e.g.

matrix3 [1,0,0] [0,1,0] [0,0,1] [0,0,0] – for the X, Y, Z axis’ and the positional offset from the origin.

So for instance if we wanted to scale an object by 200% along its X axis our matrix transform would look like this – matrix3 [2,0,0] [0,1,0] [0,0,1] [0,0,0]

Notice also that each axis is perpendicular to each other axis (90 degrees) – this is important is if it wasnt we would get skewing. Now each axis’ can point in any direction as long as the other two are perpendicular to it.