Inversion is another operation that can be performed on
`Transforms`

. This makes it possible to reverse the effect of a
`Transform`

, which may represent multiple transformations.

Point p; Transform t; t.shift(1, 2, 3); t.scale(2, 3, 4); t.rotate(45, 45, 30); t.show("t:"); -| t: 1.22 0.707 1.41 0 0.238 2.59 -1.5 0 -3.15 1.45 2 0 -7.74 10.2 4.41 1 p *= t; p.show("p:"); -| p: (-7.74, 10.2, 4.41) Transform u; u = t.inverse(); u.show("u:"); -| u: 0.306 0.0265 -0.197 2.85e-09 0.177 0.287 0.0906 -1.12e-09 0.354 -0.167 0.125 0 -1 -2 -3 1 p *= u; p.show("p:"); -| p: (0, 0, 0) u *= t; u.show("u:"); -| u: 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1

If `inverse()`

is called with no argument, or with the argument
`false`

, it returns a
`Transform`

representing its inverse, and remains unchanged. If it
is called with the argument `true`

, it is set to its inverse.

Complete reversal of the transformations applied to a `Point`

, as
in the previous example, probably won't make much sense. However,
partial reversal is a valuable technique. For example, it is used in
`rotate()`

for rotation about a line defined by two `Points`

.
The following example merely demonstrates the basic principle; an
example that does something useful would be too complicated.

Transform t; t.shift(3, 4, 5); t.rotate(45); t.scale(2, 2, 2); Point p; p *= t; p.show("p:"); -| p: (6, 12.7279, 1.41421) t.inverse(true); p.rotate(90, 90); p *= t; p.show("p:"); -| p: (3.36396, -5.62132, -2.37868)