ggthemes (version 6.0.0)

bank_slopes: Bank Slopes to 45 degrees

Description

Calculate the optimal aspect ratio of a line graph by banking the slopes to 45 degrees as suggested by W.S. Cleveland. This maximizes the ability to visually differentiate differences in slope. This function will calculate the optimal aspect ratio for a line plot using any of the methods described in Herr and Argwala (2006). In their review of the methods they suggest using median absolute slope banking ('ms'), which produces aspect ratios which are generally the median of the various methods provided here.

Usage

bank_slopes(
  x,
  y,
  cull = FALSE,
  weight = NULL,
  method = c("ms", "as", "ao", "was"),
  ...
)

Value

numeric The aspect ratio (x , y).

Arguments

x

x values

y

y values

cull

logical. Remove all slopes of 0 or Inf.

weight

No longer used, but kept for backwards compatibility.

method

One of 'ms' (Median Absolute Slope), 'as' (Average Absolute Slope), 'ao' (Average Absolute Orientation), or 'was' (Weighted Average Absolute Slope).

...

No longer used, but kept for backwards compatibility.

Methods

As written, all of these methods calculate the aspect ratio (x /y), but bank_slopes will return (y / x) to be compatible with link[ggplot2]{coord_fixed()}.

Median Absolute Slopes Banking

Let the aspect ratio be \(\alpha = \frac{w}{h}\) then the median absolute slop banking is the \(\alpha\) such that, $$ median \left| \frac{s_i}{\alpha} \right| = 1 $$

Let \(R_z = z_{max} - z_{min}\) for \(z = x, y\), and \(M = median \| s_i \|\). Then, $$ \alpha = M \frac{R_x}{R_y} $$

Average Absolute Slope Banking

Let the aspect ratio be \(\alpha = \frac{w}{h}\). then the mean absolute slope banking is the \(\alpha\) such that, $$ mean \left| \frac{s_i}{\alpha} \right| = 1 $$

Average Absolute Orientation Banking

Rather than averaging the slopes themselves, this method averages the orientation (angle) of each segment, since perceived slope differences are more closely related to angle than to the raw ratio \(dy/dx\). Let \(s'_i = s_i R_x / R_y\) be the range-normalized slopes. Then \(\alpha\) is chosen such that, $$ mean \left| \arctan \left( \frac{s'_i}{\alpha} \right) \right| = \frac{\pi}{4} $$ This has no closed-form solution and is found numerically with uniroot.

Weighted Average Absolute Slope Banking

Identical to Average Absolute Slope Banking, except each segment's contribution is weighted by its horizontal run, \(dx_i\), so that segments spanning more horizontal (screen) space are weighted more heavily than segments that happen to be sampled more densely in \(x\). Using \(s'_i\) as above, $$ \alpha = \frac{\sum_i dx_i \left| s'_i \right|}{\sum_i dx_i} $$

Heer and Agrawala (2006) also discuss multi-scale (global and local) orientation resolution, which extend these single-scale methods by aggregating slopes computed at multiple scales rather than only between adjacent points. These are not implemented here. In general, the median, average, or average-orientation absolute slope methods will produce reasonable results without requiring this additional complexity.

References

Cleveland, W. S., M. E. McGill, and R. McGill. The Shape Parameter of a Two-Variable Graph. Journal of the American Statistical Association, 83:289-300, 1988

Heer, Jeffrey and Maneesh Agrawala, 2006. 'Multi-Scale Banking to 45' IEEE Transactions On Visualization And Computer Graphics.

Cleveland, W. S. 1993. 'A Model for Studying Display Methods of Statistical Graphs.' Journal of Computational and Statistical Graphics.

Cleveland, W. S. 1994. The Elements of Graphing Data, Revised Edition.

See Also

banking(), bank_plot to bank a ggplot using its own data.

Examples

library("ggplot2")

# Use the classic sunspot data from Cleveland's original paper
x <- seq_along(sunspot.year)
y <- as.numeric(sunspot.year)
# Without banking
m <- ggplot(data.frame(x = x, y = y), aes(x = x, y = y)) +
  geom_line()
m

## Using the default method, Median Absolute Slope
ratio <- bank_slopes(x, y)
m + coord_fixed(ratio = ratio)

## Average Absolute Slope
m + coord_fixed(ratio = bank_slopes(x, y, method = "as"))

## Average Absolute Orientation
m + coord_fixed(ratio = bank_slopes(x, y, method = "ao"))

## Weighted Average Absolute Slope: each segment is weighted by its run in
## x, so this only differs from "as" when x is not evenly spaced
m + coord_fixed(ratio = bank_slopes(x, y, method = "was"))

## Culling removes slopes of 0 or Inf before banking, which matters when
## the data contains runs of repeated x or y values
bank_slopes(x, y, cull = TRUE)