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Apply forward spatial transformation

```
[X,Y] =
tformfwd(T,U,V)
```

`[X1,X2,...,X_ndims_out] = tformfwd(T,U1,U2,...,U_ndims_in)`

`X = tformfwd(T,U)`

`[X1,X2,...,X_ndims_out] = tformfwd(T,U)`

`X = tformfwd(T,U1,U2,...,U_ndims_in)`

`[`

applies the 2D-to-2D forward spatial transformation defined in
`X`

,`Y`

] =
tformfwd(`T`

,`U`

,`V`

)`T`

to coordinate arrays `U`

and
`V`

, mapping the point `[U(k) V(k)]`

to the
point `[X(k) Y(k)]`

.

Both `T.ndims_in`

and `T.ndims_out`

must equal
2. `U`

and `V`

are typically column vectors,
but they can have any dimensionality. `X`

and
`Y`

are the same size as `U`

and
`V`

.

`[`

applies the `X1,X2,...,X_ndims_out`

] = tformfwd(`T`

,`U1,U2,...,U_ndims_in`

)`ndims_in`

-to-`ndims_out`

spatial
transformation defined in `T`

to the coordinate arrays
`U1,U2,...,U_ndims_in`

. The transformation maps the point
`[U1(k) U2(k) ...U_ndims_in(k)]`

to the point ```
[X1(k)
X2(k) ... X_ndims_out(k)]
```

.

The number of input coordinate arrays, `ndims_in`

, must equal
`T.ndims_in`

. The number of output coordinate arrays,
`ndims_out`

, must equal `T.ndims_out`

. The
arrays `U1,U2,...,U_ndims_in`

can have any dimensionality, but
must be the same size. The output arrays `X1,X2,...,X_ndims_out`

must be this size also.

applies the spatial transformation defined in `X`

= tformfwd(`T`

,`U`

)`T`

to coordinate
array `U`

.

When

`U`

is a 2-D matrix with dimensions*m*-by-`ndims_in`

,`X`

is a 2-D matrix with dimensions*m*-by-`ndims_out`

.`tformfwd`

applies the`ndims_in`

-to-`ndims_out`

transformation to to each row of`U`

.`tformfwd`

maps the point`U`

(*k*, : ) to the point`X`

(*k*, : ).When

`U`

is an (*N*+1)-dimensional array,`tformfwd`

maps the point`U`

(*k*_{1},*k*_{2}, … ,*k*_{N}, : ) to the point`X`

(*k*_{1},*k*_{2}, … ,*k*_{N}, : ).`size(U,N+1)`

must equal`ndims_in`

.`X`

is an (*N*+1)-dimensional array, with`size(X,I)`

equal to`size(U,I)`

for`I`

= 1, … ,*N*, and`size(X,N+1)`

equal to`ndims_out`

.

The syntax `X = tformfwd(U,T)`

is an older
form of this syntax that remains supported for backward compatibility.

`[`

maps one (`X1,X2,...,X_ndims_out`

] = tformfwd(`T`

,`U`

)*N*+1)-dimensional array to `ndims_out`

equally sized *N*-dimensional arrays.

maps `X`

= tformfwd(`T`

,`U1,U2,...,U_ndims_in`

)`ndims_in`

*N*-dimensional arrays to one (*N*+1)-dimensional
array.

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