### Name: path_curves
### Title: Draw the path that the geodesics took.
### Aliases: path_curves

### ** Examples

path1d <- save_history(flea[, 1:6], grand_tour(1), 10)
path2d <- save_history(flea[, 1:6], grand_tour(2), 10)

if (require("ggplot2")) {
  plot(path_curves(path1d))
  plot(path_curves(interpolate(path1d)))

  plot(path_curves(path2d))
  plot(path_curves(interpolate(path2d)))

  # Instead of relying on the built in plot method, you might want to
  # generate your own.  Here are few examples of alternative displays:

  df <- path_curves(path2d)
  ggplot(data = df, aes(x = step, y = value, group = obs:var, colour = var)) +
    geom_line() +
    facet_wrap(~obs)

  library(tidyr)
  ggplot(
    data = pivot_wider(df,
      id_cols = c(obs, step),
      names_from = var, names_prefix = "Var",
      values_from = value
    ),
    aes(x = Var1, y = Var2)
  ) +
    geom_point() +
    facet_wrap(~step) +
    coord_equal()
}