Transformation for 3-D Scaling

As we already seen that the scaling process is mainly utilized to change the size of an object. The scale factors find out whether the scaling is a magnification as s>1 or a reduction, s<1. 2-dimensional scaling, is in equation (8), can be simply extended to scaling in 3-dimensional case by consisting the z-dimension.

For any point (x,y,z), we move in (x.s_x,y.s_y,z.s_z), here s_x, s_y, and s_z are the scaling factors in the x,y, and z-directions correspondingly.

Hence, scaling w.r.t. origin is given by:

Ss_x,s_y,s_z =    x'= x.s_x

         y'= y.s_y                                                  

z'= z.s_z

In matrix form:

In terms of Homogeneous coordinate system, above equation is written as:

As, P'=P. Ss_x,s_y,s_z