Transformations - Transformations and Projections in Computer Graphics - page 51

2. The transformation can be reversed by translating the coordinate system in the
reverse directions (i.e., by − m and − n units) by using an (unknown) transformation

matrix M .
Since the two methods produce the same result, we conclude that M = S = T − 1 .
Transformingthecoordinateaxesisthereforedonebyamatrixthat'stheinverseof
transforming a point. This is true for any a ne transformations, not just translation.

The magic transformation from the minute to the vast has
not been so cunningly effected but that the rich adornment
still counteracts the impression of space and loftiness.
—Nathaniel Hawthorne, TheMarbleFaun (1860)