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}