4.A] Explain two-dimensional pivot point scaling with neat sequences of an object. Explain with matrix representations and equations.
Answer:
To produce a two-dimensional scaling with respect to a selected fixed position (xf, yf), following sequence is followed.
1. Translate the object so that the fixed point coincides with the coordinate origin.
2. Scale the object with respect to the coordinate origin.
3. Use the inverse of the translation in step (1) to return the object to its original position.
Concatenating the matrices for these three operations produces the required scaling matrix:
This transformation is generated automatically in systems that provide a scale function that accepts coordinates for the fixed point.