This function operates a centering of the QTS around the geometric mean of its quaternions. This is effectively achieved by left-multiplying each quaternion by the inverse of their geometric mean.

## Arguments

- x
An object of class

`qts`

.- standardize
A boolean specifying whether to standardize the QTS in addition to centering it. Defaults to

`FALSE`

.- keep_summary_stats
A boolean specifying whether the mean and standard deviation used for standardizing the data should be stored in the output object. Defaults to

`FALSE`

in which case only the centered`qts`

is returned.

## Value

If `keep_summary_stats = FALSE`

, an object of class `qts`

in which
quaternions have been centered (and possibly standardized) around their
geometric mean. If `keep_summary_stats = TRUE`

, a list with three
components:

`qts`

: an object of class`qts`

in which quaternions have been centered (and possibly standardized) around their geometric mean;`mean`

: a numeric vector with the quaternion Fréchet mean;`sd`

: a numeric value with the quaternion Fréchet standard deviation.

## Examples

```
centring(vespa64$igp[[1]])
#> # A tibble: 101 × 5
#> time w x y z
#> <int> <dec:.5!> <dec:.5!> <dec:.5!> <dec:.5!>
#> 1 0 0.99364 0.09383 0.06049 0.01484
#> 2 1 0.99425 0.08868 0.05824 0.01455
#> 3 2 0.99489 0.08343 0.05518 0.01401
#> 4 3 0.99553 0.07811 0.05153 0.01307
#> 5 4 0.99606 0.07365 0.04805 0.01184
#> 6 5 0.99650 0.06989 0.04468 0.01037
#> 7 6 0.99686 0.06694 0.04146 0.00869
#> 8 7 0.99714 0.06478 0.03830 0.00674
#> 9 8 0.99738 0.06307 0.03503 0.00451
#> 10 9 0.99761 0.06156 0.03147 0.00204
#> # ℹ 91 more rows
```