I wish to discuss 3 points:
1. From the "Scales and Intervals Specification"
(http://specs.openoffice.org/chart/Chart_Scales_and_Intervals.odt):
1.
Interval frequency
*Frequency for major intervals*
The frequency of major intervals of a linear scaled axis is defined as
step width (expressed similar the axis corresponding data) (e.g. 2.0,
7.65 or 1000.0). The number of major intervals over the axis results
from it.
The major interval for logarithmic scales behaves like this: 1 is one
order of magnitude. 2 is 2 orders of magnitude etc. That means log(x2)
- log (x1) = major interval, where x1 is one major tick and x2 is the
next one.
For example typically you want to have major tickmarks at 1, 10 ,100,
1000 and so on. You have to set it to 1, because of: log(100) - log
(10) = 1.
/Question: Is it useful that values below 1 are allowed?/
Values below 1 are sometimes useful, too. For very small variations, one
may choose 0.5 (and also sometimes a different base for the logarithm:
e.g. for some binary data log base 2 is more appropriate, see also point
2 below). A very good example is chemistry: when working with pH (e.g. a
titration curve), we may want smaller divisions, like 7.5 .. 8.0 .. 8.5,
or IF plotting the pI of a mixture of proteins, then even smaller values
may be needed (the pI may differ by as little as 0.1, so even 0.5 may be
large; see http://en.wikipedia.org/wiki/Isoelectric_point for an
explanation of the isoelectric point and also this example for a better
understanding: http://www.pierroton.inra.fr/genetics/2D/variation.html).
Another useful logarithmic scale is based on dB: e.g. the audiogram, see
http://www.sfu.ca/sonic-studio/handbook/Audiogram.html for an example
(dB = 20 * log (p2/p1), where p is sound pressure ). Here, the hearing
loss is coded as positive dB, BUT the scale is inverse (it is increasing
from top to bottom and thus decreasing in the opposite direction, aka
top is 0 dB and bottom is 80 dB; the frequency changes in steps of 2,
i.e. step of 1 for log base 2, but step less than 1 if the log is base 10).
2. Would it be possible to add different bases for the logarithm. While
base 10 is more often used (easier visualisation), sometimes base 2 (or
ln with base e) are more advisable.
3. Have option to display original values for logarithmic scale OR the
logarithm values: this latter approach is often used when referring to
changes of a parameter over its baseline (e.g. by a factor of 10 = 1 in
log scale). It also becomes impractical to display the actual value when
having a very wide scale, e.g. 1- >10^8 (it is easier to display 0..8).
For further examples see also the figures inside the following articles:
http://www.nature.com/hdy/journal/v93/n6/pdf/6800559a.pdf and
http://www.jneurosci.org/cgi/reprint/25/43/10049 (both are free).
This article (http://doi.ieeecomputersociety.org/10.1109/TVCG.2006.126)
may be also interesting (for other reasons), but I do not have access to it.
I hope this is useful,
Leonard
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