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Transformation for 3-D Shearing
2-dimensional xy-shearing transformation, as explained in equation, can also be simply extended to 3-dimensional case. All coordinates are translated as a function of displacements of another two coordinates, which is,
Shxyz= x'=x+a.y+b.z
y'=y+c.x+d.z
z'=z+e.x+f.y
Here a,b,c,d,e and f are the shearing factors in the respective directions. Equation (46) in terms of homogeneous HC system, is:
That is, P'h = Ph.Shxyz
Here remember that the off-diagonal terms in the upper left 3x3 sub-matrix of the generalized 4x4 transformation matrix in equation produce shear in 3-dimensions.
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