Axis/Scale Boundaries

When charting unknown data, we would like to set the axis scale such that the details in the data are clear and the end points on the scale are aesthetically pleasing.

D3 and Protovis use the "nice" algorithm for linear scales (and a modification for logarithmic scales). The pull request implementing the algorithm in JavaScript is on github, but, mathematically, for an array of data containing a \(min\) and \(max\) value:

Let $$step = 10^{round(log_{10}(max - min)) - 1}$$

then,

$$scale_{min} = \lfloor\frac{min}{step}\rfloor \times step$$
$$scale_{max} = \lceil\frac{max}{step}\rceil \times step$$

If the data has a range of 0.002454 to 0.1455, the scale will extend from 0.002 to 0.015. Visually, the bounding boxes (tan and green) will look like: