Algorithm for Optimal Scaling on a Chart Axis
- March 15th, 2011
- By Steffen L. Norgren
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UPDATE: Seems the fellow (Han Solo? hehe) over at Harmonic Code developed some nice examples of this algorithm in action.
I’ve been working on an Android charting application for an assignment and ran into a bit of an issue when it came to presenting the chart in a nicely scaled format. I spent a some time trying to create this algorithm on my own and came awfully close, but in the end I found a pseudo-code example in a book called “Graphics Gems, Volume 1” by Andrew S. Glassner. An excellent description of the problem is given in the chapter on “Nice Numbers for Graph Labels“:
When creating a graph by computer, it is desirable to label the x and y axes with “nice” numbers: simple decimal numbers. For example, if the data range is 105 to 543, we’d probably want to plot the range from 100 to 600 and put tick marks every 100 units. Or if the data range is 2.04 to 2.16, we’d probably plot a range from 2.00 to 2.20 with a tick spacing of 0.05. Humans are good at choosing such “nice” numbers, but simplistic algorithms are not. The naïve label-selection algorithm takes the data range and divides it into n equal intervals, but this usually results in ugly tick labels. We here describe a simple method for generating nice graph labels.
The primary observation is that the “nicest” numbers in decimal are 1, 2, and 5, and all power-of-ten multiples of these numbers. We will use only such numbers for the tick spacing, and place tick marks at multiples of the tick spacing…

