Coordinate systems and axes

Claus O. Wilke

2026-01-17

The Grammar-of-Graphics pipeline: Coordinate systems

Most data visualizations use Cartesian coordinates

 

Changing units does not change the plot

 

 

If scale units are unrelated, aspect ratio is arbitrary

 

If scale units are unrelated, aspect ratio is arbitrary

 

Non-linear scales and coordinate systems

Logarithmic scales (log scales)

Visualize these five values: 1,   3.16,   10,   31.6,   100


 

 

 

Example: Population number of Texas counties

A linear scale emphasizes large counties

 

Example: Population number of Texas counties

A log scale shows symmetry around the median

 

Nonlinear coordinate systems: Polar coordinates

 

 

Cartesian vs polar example

 

 

Scales and coordinate systems in ggplot2

Getting the data

The boxoffice dataset:

boxoffice <- tibble(
  rank = 1:5,
  title = c("Star Wars", "Jumanji", "Pitch Perfect 3", "Greatest Showman", "Ferdinand"),
  amount = c(71.57, 36.17, 19.93, 8.81, 7.32) # million USD
)

The tx_counties dataset:

tx_counties <- read_csv("https://wilkelab.org/SDS366/datasets/US_census.csv") |> 
  filter(state == "Texas") |>
  mutate(popratio = pop2010/median(pop2010)) |>
  arrange(desc(popratio)) |>
  mutate(index = 1:n())

Getting the data

The temperatures and temps_wide datasets (long and wide format of the same data):

# long format
temperatures <- read_csv("https://wilkelab.org/SDS366/datasets/tempnormals.csv") |>
  mutate(
    location = factor(
      location, levels = c("Death Valley", "Houston", "San Diego", "Chicago")
    )
  ) |>
  select(location, station_id, day_of_year, month, temperature)

# wide format
temps_wide <- temperatures |>
  pivot_wider(
    id_cols = c("month", "day_of_year"),
    names_from = "location", values_from = "temperature"
  )

Scale functions customize the x and y axes

Recall the box-office example from a prior lecture:

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col()

Scale functions customize the x and y axes

Add scale functions (no change in figure so far):

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous() +
  scale_y_discrete()

Scale functions customize the x and y axes

The parameter name sets the axis title:

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross (million USD)"
  ) +
  scale_y_discrete(
    name = NULL  # no axis title
  )

Note: We could do the same with xlab() and ylab()

Scale functions customize the x and y axes

The parameter limits sets the scale limits:

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross (million USD)",
    limits = c(0, 80)
  ) +
  scale_y_discrete(
    name = NULL
  )

Note: We could do the same with xlim() and ylim() but I advise against it, as these functions can have unexpected side-effects

Scale functions customize the x and y axes

The parameter breaks sets the axis tick positions:

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross (million USD)",
    limits = c(0, 80),
    breaks = c(0, 25, 50, 75)
  ) +
  scale_y_discrete(
    name = NULL
  )

Scale functions customize the x and y axes

The parameter labels sets the axis tick labels:

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross",
    limits = c(0, 80),
    breaks = c(0, 25, 50, 75),
    labels = c("0", "$25M", "$50M", "$75M")
  ) +
  scale_y_discrete(
    name = NULL
  )

Scale functions customize the x and y axes

The parameter expand sets the axis expansion:

ggplot(boxoffice) +
  aes(amount, fct_reorder(title, amount)) +
  geom_col() +
  scale_x_continuous(
    name = "weekend gross",
    limits = c(0, 80),
    breaks = c(0, 25, 50, 75),
    labels = c("0", "$25M", "$50M", "$75M"),
    expand = expansion(mult = c(0, 0.06))
  ) +
  scale_y_discrete(
    name = NULL
  )

Scale functions define transformations

Linear y scale:

ggplot(tx_counties) +
  aes(x = index, y = popratio) +
  geom_point() +
  scale_y_continuous()

 

Log y scale:

ggplot(tx_counties) +
  aes(x = index, y = popratio) +
  geom_point() +
  scale_y_log10()

 

Parameters work the same for all scale functions

Linear y scale:

ggplot(tx_counties) +
  aes(x = index, y = popratio) +
  geom_point() +
  scale_y_continuous(
    name = "population number / median",
    breaks = c(0, 100, 200),
    labels = c("0", "100", "200")
  )

 

Log y scale:

ggplot(tx_counties) +
  aes(x = index, y = popratio) +
  geom_point() +
  scale_y_log10(
    name = "population number / median",
    breaks = c(0.01, 1, 100),
    labels = c("0.01", "1", "100")
  )

 

Coords define the coordinate system

ggplot(temperatures, aes(day_of_year, temperature, color = location)) +
  geom_line() +
  coord_cartesian()  # cartesian coords are the default

 

Coords define the coordinate system

ggplot(temperatures, aes(day_of_year, temperature, color = location)) +
  geom_line() +
  coord_polar()   # polar coords

 

Coords define the coordinate system

ggplot(temperatures, aes(day_of_year, temperature, color = location)) +
  geom_line() +
  coord_polar() +
  scale_y_continuous(limits = c(0, 105))  # fix up temperature limits

 

Use coord_fixed() for fixed aspect ratio

ggplot(temps_wide, aes(`San Diego`, Houston)) +
  geom_path()

 

(Bad, x and y axis show the same values scaled differently)

Use coord_fixed() for fixed aspect ratio

ggplot(temps_wide, aes(`San Diego`, Houston)) +
  geom_path() +
  coord_fixed()

 

(Better, x and y axis are now scaled the same)

Use coord_fixed() for fixed aspect ratio

ggplot(temps_wide, aes(`San Diego`, Houston)) +
  geom_path() +
  coord_fixed() +
  scale_x_continuous(breaks = c(50, 60, 70), limits = c(50, 75))

 

(Even better, similar axis ticks along both axes)

Further reading