Transformation for 3-d shearing, Computer Graphics

2-dimensional xy-shearing transformation, as explained in equation (19), 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--------(46)

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:

7_equation 47.png

That is, P'h = Ph.Shxyz          --------------(47)

Here remember that the off-diagonal terms in the upper left 3x3 sub-matrix of the generalized 4x4 transformation matrix in equation (31) produce shear in 3-dimensions.

Posted Date: 3/22/2013 7:23:47 AM | Location : United States







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