# Re: manual ticks of an axis

• From: John Denker <jsd av8n com>
• To: gnumeric-list gnome org
• Subject: Re: manual ticks of an axis
• Date: Tue, 25 Nov 2014 07:36:37 -0700

On 11/25/2014 05:15 AM, Jean Brefort wrote:

There is already an enhancement request:
https://bugzilla.gnome.org/show_bug.cgi?id=600482.

I'm unsure about random ticks. I'd like a significant use case for them
before trying to implement them.

Could we please call them /manual/ ticks or /arbitrary/
ticks rather than "random" ticks?

Also note that it is the ticks and labels that are important;
the "axis" itself becomes a nuisance and a source of confusion
as soon as you try to do anything nontrivial, such as a
spacetime diagram or ternary phase diagram;  for details see
https://www.av8n.com/physics/axes.htm

=============

The discussion of use cases starts with the observation that a
gnumeric XY plot offers two "types" of axes: linear and logarithmic.
These must be considered two special cases in a vast universe of
possibilities.  It would be nice to handle the general case.

Case 1:  Arrhenius law:  rate proportional to exp(1/T).
To represent this as a straight line, it is necessary
to plot log(rate) versus 1/T.
It would be nice to have ticks labeled in terms of T, not 1/T:

position        label
1/4            T=4
1/2            T=2
2/3            T=1.5
1             T=1

Case 2:  Ohm's law.  Current as a function of inverse resistance
at constant voltage.  Similar to case 1, without the exponential.

Case 3:  The resistance of a carbon-comp resistor at very
low temperatures is exponential in the square root of 1/T.
Such things are used as thermometers.  For plotting the
calibration curve, it's really nice to have a straight
line plot, plotted as a function of 1/√T, with ticks
labeled in units of T.

Case 4:  If you want to get serious, consider tilted ticks
and iso-contours as in any ternary plot:
http://en.wikipedia.org/wiki/Ternary_plot

Case 5:  Tilted ticks and iso-contours due to rotation in the
XY plane, e.g. magnetic north versus geographical north.

Case 6:  Tilted ticks and iso-contours due to rotation in the
XT plane in spacetime, using /hyperbolic/ trigonometry.
https://www.av8n.com/physics/axes.htm#sec-spacetime

Case 7:  If you want to get really serious, consider the
task of labeling all *four* sets of iso-contours in
a chart such as this psychrometric chart:
https://www.av8n.com/physics/axes.htm#fig-PsychrometricChart-SeaLevel-SI

Case 8:  Similarly, the *four* sets of iso-contours in
a thermodynamic "indicator diagram" such as
https://www.av8n.com/physics/thermo/path-cycle.html#fig-path-pv

===========================

I could go on, but I reckon you get the idea.  There are
a lot of serious real-world applications for tick-marks
and iso-contours that are not simply linear in X or
logarithmic in X.