 #1
DrGreg
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I have a scalar quantity ##V## (let's call it a voltage for concreteness) that is a function of angle ##\theta##. There are two obvious ways to plot it, as a Cartesian plot (see A above) or as a polar plot (see B). I can also express the polar plot in terms of Cartesian coordinates ##V_x = V \, \cos \theta## and ##V_y = V \, \sin \theta## (see C). A particular mathematical process that I have to document involves calculating ##V_x## and ##V_y## as an intermediate step to providing a final output of ##V## and ##\theta##.
(The plots above are illustrative and do not show the function that I have to document in my realworld problem.)
In my document, there is a part where I can describe all this in detail using equations and plots, but there are other parts of the document where I have to summarise the steps of the process in words only. I want to find words to describe A, B, C in just a few words per plot, but still clearly and unambiguously. I have no hesitation in describing B as a "polar plot", but A and C are more problematic. Both could be described as "Cartesian plots" but that isn't enough to distinguish them. Indeed my coauthor has unintentionally described both A and C identically, including the phrase "in Cartesian coordinates". I don't really like to describe ##(V,\theta)## as Cartesian coordinates even in the context of Plot A.
As I see it, A and B show the same coordinates but different plots, whereas B and C show the same plot with different coordinates.
Part of my difficulty is that I'm not sure whether the words "polar" and "Cartesian" (or "rectangular" if you prefer) are properties of the coordinates, or of the plots, or the combination of both.
For clarification, ##\theta## does represent a geometrical angle in the real world, but ##V## does not represent a distance.
My suggested terminology is
A = directional voltage response as a Cartesian plot
B = directional voltage response as a polar plot
C = ??
##(V,\theta)## = polar coordinates (or polar voltage coordinates??)
##(V_x,V_y)## = ??
Any thoughts?
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