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#### 15.5.413 orientation

```orientation, data, widths [, orientation, values, wavenumbers, grid, aspect, order, /vocal, /getj]```

Determines local orientation in 2D or 3D data employing a method based on local Fourier Transforms.

data

The 2D or 3D array in which orientations are to be determined.

widths

must be a 2 or 3-element vector containing the FWHM of the Gaussian smoothing kernels applied in the dimensions (0 means no smoothing).

grid

is a 2 or 3-element vector containing the desired dimensions of the results. If it is not specified, then the results will have the same dimensions as `data`.

aspect

specifies the dimensions of a pixel, if they do not have an aspect ratio of 1.

order

contains the approximation order of the calculations, a number between 1 and 4 (default, most accurate).

orientation

The found orientation is returned in this argument (if specified), unless `/getj` is specified. The orientation is expressed in the 2d case as an angle in radians measured counterclockwise from the positive x-axis, and in the 3D case as a 2-element vector containing the x and y coordinates of the orientation vector relative to a unit z coordinate.

values

The found eigenvalues (measures for the data gradients in the principal directions) are returned in this argument (if specified), unless `/getj` is specified. The eigenvalues are returned in descending order.

wavenumber

By default, the determined local wavenumber in the direction of the found orientation is returned in this argument (if specified), unless `/getj` is specified. If `/perpendicular` is specified, then – for two-dimensional data only – the local wavenumber in the direction perpendicular to the found orientation is returned instead. The wavenumber is measured in units of one data element. A data set with values equal to sin(x) returns a wavenumber of 1 for the perpendicular wavenumber, and 0 for the parallel wavenumber. If a random data set is smoothed over FWHM `w` in one direction, then the parallel local wavenumber is on average equal to about 1.65/`w`.

`/getj`

If specified, then the unique elements of the inertia tensor are returned in `values` (the diagonal elements) and `orientation` (the off-diagonal elements), and the local power in `wavenumber`. This keyword is supplied for debugging purposes and may be withdrawn in the future.

`/vocal`

Induces periodical display of the progress status.

The returned orientations are ambiguous over 180 degrees.

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