# Transform spline coordinates between cartesian and polar

#### Stefano Coretta

#### 2025-09-07

It is possible to transform the coordinates of your spline data from cartesian to polar and vice versa, with `transform_coord()`. Let’s attach the package `rticulate` and load the data set `tongue`.

    library(rticulate)
    data(tongue)
    tongue
    #> # A tibble: 3,612 × 28
    #>    speaker seconds rec_date            prompt  label TT_displacement TT_velocity
    #>    <fct>     <dbl> <fct>               <fct>   <fct>           <dbl>       <dbl>
    #>  1 it01       1.31 29/11/2016 15:10:57 Dico p… max_…            67.1       36.6
    #>  2 it01       1.20 29/11/2016 15:11:03 Dico p… max_…            77.9       -7.73
    #>  3 it01       1.08 29/11/2016 15:11:25 Dico p… max_…            65.9       21.1
    #>  4 it01       1.12 29/11/2016 15:11:35 Dico p… max_…            64.4        8.76
    #>  5 it01       1.42 29/11/2016 15:11:57 Dico p… max_…            76.9       -4.72
    #>  6 it01       1.35 29/11/2016 15:12:53 Dico p… max_…            78.1       -5.68
    #>  7 it01       1.07 29/11/2016 15:13:44 Dico p… max_…            69.9      -40.0
    #>  8 it01       1.17 29/11/2016 15:13:49 Dico p… max_…            78.0       -7.31
    #>  9 it01       1.28 29/11/2016 15:14:11 Dico p… max_…            67.1       34.5
    #> 10 it01       1.10 29/11/2016 15:14:22 Dico p… max_…            75.9      -23.5
    #> # ℹ 3,602 more rows
    #> # ℹ 21 more variables: TT_abs_velocity <dbl>, TD_displacement <dbl>,
    #> #   TD_velocity <dbl>, TD_abs_velocity <dbl>, TR_displacement <dbl>,
    #> #   TR_velocity <dbl>, TR_abs_velocity <dbl>, fan_line <int>, X <dbl>, Y <dbl>,
    #> #   word <fct>, item <dbl>, ipa <fct>, c1 <fct>, c1_phonation <fct>,
    #> #   vowel <fct>, anteropost <fct>, height <fct>, c2 <fct>, c2_phonation <fct>,
    #> #   c2_place <fct>

Now let’s convert the cartesian coordinates to polar. `transform_coord()` converts to polar coordinates by default. Your data set must contain columns named `X` and `Y` with, respectively, the x and y coordinates (if the columns are named differently, you will have to rename them). The function extracts `xy` data from two fan lines (the defaults are `10`, and `25`), and it uses these data to find the origin. By default, a column named `fan_line` is used for the fan lines number, but it can be supplied by the user with the argument `fan_line_col` as a string.

If you have imported data using `read_aaa()`, the defaults will work, so you can just use `transform_coord(your-data)`.

    polar <- tongue %>%
        filter(speaker == "it01", X < 40) %>%
        transform_coord()
    #> The origin is x = 14.3901267816422, y = -65.2315420525847.

The function returns a data set with two new columns: `radius` and `theta`. It also prints the calculated origin.

If you get an error relating to `lm.fit`, try to change the `fan_lines` to values different from the default.

We can now plot the contours using polar coordinates in a cartesian system. Notice that the tip of the tongue is on the left (rather than the right, as in the original data).

    polar %>%
        ggplot(aes(angle, radius, colour = c2_place)) +
        geom_point() +
        scale_colour_discrete(name = "Place of C2") +
        theme(legend.position = "top")

Plotting in polar coordinates gives a sense of the actual shape of the tongue, but it is a bit trickier and it does not look very nice… (the tip is again on the left). (Thanks to Michele Gubian who has suggested a fix to the code).

    polar %>%
        ggplot(aes(angle, radius, colour = c2_place, group = rec_date)) +
        geom_path() +
        scale_colour_discrete(name = "Place of C2") +
        coord_radial(theta = "x",
                 start = -0.5 * pi, end = 0.5 * pi,
                 direction = -1, expand = FALSE) +
        scale_x_continuous(breaks = pi/4 * (0:4),
                         labels = expression(0, pi/4, pi/2, 3/4*pi, pi),
                         limits = c(0, pi)) +
        ylim(0, 100) +
        theme(legend.position = "top", axis.title = element_blank(),
            panel.border = element_blank())