# Radius Aesthetics

## Radius scales and guides

### Size does matter

A vector has a radius (i.e., length) and an angle (direction). When you depict a vector field, the radius often has a specific meaning: it reflects a certain magnitude. For instance, a vector can represent the magnitude and direction of a velocity. It could help your audience to read your plot if they knew which magnitudes the length of the arrows in your plot represent. This is why `ggfields` provides a legend key for the `radius` aesthetic specified with `ggplot2::aes()`.

In order to provide a frame of reference, you need to specify `max_radius` in your call to `geom_fields()` (default is 0.5 cm). This `max_radius` should have a absolute or relative length unit (`grid::unit()`). Arrows in your vector field will be scaled between zero and this `max_radius`. This same `max_radius` is also used to scale arrows in your legend keys.

Note that the axes are not trained on the size of the vectors (only on the vector origins). You need to expand your x and y scales manually if vectors are cut off. Also if the `max_radius` is larger than the key width, you may run into visual problems. For large `max_radius` values you have to increase the key width manually, as shown in the example below.

    library(ggplot2)
    library(ggfields)
    library(stars)
    #> Warning: package 'stars' was built under R version 4.3.3
    #> Warning: package 'sf' was built under R version 4.3.3
    theme_set(theme_light())
    data("seawatervelocity")

    p <-
      ggplot() +
      geom_fields(
        aes(radius = as.numeric(v),
            angle  = as.numeric(angle)),
        seawatervelocity[,3:11,6:11],
        max_radius = grid::unit(1.5, "cm")) +
      labs(radius  = "v [m/s]") +
      ## We have to increase the 'keywidth' as otherwise `max_radius` won't fit:
      guides(radius = guide_legend(keywidth = grid::unit(1.5, "cm")))
    p

### Stay positive

It is important that the radius you wish to plot has only non-negative values. This is because it is impossible to distinguish between a vector with a negative magnitude and a vector with the same positive magnitude with an angle rotate 180 degrees (i.e, a vector with `radius = 1` and and `angle = 0` will look the same as a vector with `radius = -1` and `angle = pi`). Therefore, from the plot, you cannot tell which vectors have a positive and which have a negative value. This is why `geom_fields()` will throw an error if you try to plot negative radii.

This is also why you need to be careful with transformations. Although, it is technically possible to log-transform your radii, you might run into problems due to potentially resulting negative values. You should also wonder whether transformed values accurately convey information about the magnitude of your vectors. If you are considering to apply transformations, try using binned or discrete scales instead.

### One key to rule them all

The `radius` key in the guide legend can be combined into one key with many other aesthetics, such as `colour`, `linewidth`, `linetype`, etc. All you have to do is make sure that all aesthetics use are assigned to the same variable and use `ggplot2::guide_legend()`. The example below illustrates how `colour` and `linewidth` can be combined with `radius` in one legend.

    p +
      aes(col = as.numeric(v), linewidth = as.numeric(v)) +
      ## Let's give the aesthetics all the same name
      labs(col = "v [m/s]", linewidth = "v [m/s]") +
      ## Make sure that the colour aesthetic uses the same guide as radius ("legend")
      scale_colour_viridis_c(guide = "legend") +
      ## Make sure all keys have the same width
      guides(colour    = guide_legend(keywidth = grid::unit(1.5, "cm")),
             linewidth = guide_legend(keywidth = grid::unit(1.5, "cm")))

## Vector components

What if you only have the x and y component of a vector instead of its angle and radius? Can you provide those components as aesthetics to `geom_fields()`? Unfortunately, the answer is no. At least not directly, as `radius` is required early on in the data wrangling machinery of `ggplot2::ggplot()`. However, the x and y components of a vector can easily be converted into its angle and radius, as shown in the example below.

    ggplot() +
      geom_fields(aes(radius = as.numeric(pythagoras(vo, uo)),
                      angle  = atan2(as.numeric(vo), as.numeric(uo))),
                  seawatervelocity)