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Derive 2D transformation matrix for fixed point scaling.
written 6.9 years ago by gravatar for prof.vaibhavbadbe prof.vaibhavbadbe • 1.7k modified 4.6 years ago by gravatar for sanketshingote sanketshingote • 100
computer graphics
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written 6.8 years ago by gravatar for prof.vaibhavbadbe prof.vaibhavbadbe • 1.7k

Solution:-

To determine the general form of the scaling matrix with respect to a fixed point P (h, k) we have to perform three steps:

  1. Translate point P(h, k) at the origin by performing translation (T1).

  2. Scale the point or object by performing scaling (S).

  3. Translate the origin back by performing reverse translation (T2).

Therefore, the general form of the scaling matrix is a composition of T1 S T2 matrices. It can be given as

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