Scaling

Definition

• Scaling changes the size of an object. It multiplies the dimensions of an object by scaling factors.
• Scaling factors different from 1 will change the object’s size.
• In matrix form, scaling is represented by diagonal matrix elements corresponding to scaling factors.

$$\text{Scale:}\left[\begin{array}{cccc}{s}_x& 0& 0& 0\\ 0& s_y& 0& 0\\ 0& 0& s_z& 0\\ 0& 0& 0& 1\end{array}\right]$$

Method:

$$\text{For scaling factors }{s}_x\text{ and }{s}_y,\text{ the scaling matrix is: }\left[\begin{array}{ccc}{s}_x& 0& 0\\ 0& s_y& 0\\ 0& 0& 1\end{array}\right]$$

Example:

$$\text{Scale a point }(2,3)\text{ by }{s}_x=2\text{ and }{s}_y=3:\left[\begin{array}{ccc}2& 0& 0\\ 0& 3& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}2\\ 3\\ 1\end{array}\right]=\left[\begin{array}{c}4\\ 9\\ 1\end{array}\right]$$