---
title: "Transform spline coordinates between cartesian and polar"
author: "Stefano Coretta"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Transform spline coordinates between cartesian and polar}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  out.width = "500px", fig.align = "center", dpi = 300
)
library(dplyr)
library(ggplot2)
theme_set(theme_bw())
library(rticulate)
```

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`.

```{r load-data}
library(rticulate)
data(tongue)
tongue
```

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)`.

```{r}
polar <- tongue %>%
    filter(speaker == "it01", X < 40) %>%
    transform_coord()
```

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).

```{r}
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).

```{r}
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())
```