>
|
|
Define a pair of 2-dimensional manifolds.
>
|
|
Example 1.
Define a simple transformation Phi1: M -> N with a unique global inverse.
>
|
|
| (1) |
>
|
|
| (2) |
Use ComposeTransformations to checks the result of InverseTransformation.
>
|
|
| (3) |
>
|
|
| (4) |
Example 2.
Define a transformation Phi2: M -> N with multiple local inverses.
>
|
|
| (5) |
>
|
|
| (6) |
To get explicit solutions:
>
|
|
| (7) |
>
|
|
| (8) |
To get all possible inverses:
>
|
|
| (9) |
Since Phi2([- 1, - 1]) = [1, 1], we can ask for that particular inverse which maps [1, 1] to [- 1, - 1]. We can use either [1, 1] or [u = 1, v = 1] as arguments in the command InverseTransformation to indicate the coordinates of the point.
>
|
|
| (10) |
>
|
|
| (11) |
M >
|
|