Re: manual ticks of an axis

[John Denker <jsd av8n com>]

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.