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Controlling bubble size in bubble plots


I use the bubble plot a lot in reports, where consistent bubble sizing is needed across multiple plots. It is extremely useful. Just one issue: What is the policy that determines how the bubbles are sized?
This question has two parts:
A) relating to scale/range
relating to function/linearity
A) is not a big problem:
A workaround for controlling bubble size scale/range is to insert a dummy maximum size bubble and dummy minimum size bubble into the data, and also to clip the real data between these two levels. This forces the plotter to look at a pre-determined range, and allows for some some consistency between different charts in a series of bubble plots. It works well enough for me, but...
is a bigger problem:
Neither the diameter nor the area of the bubbles seems to be proportional (or even affine) to the data values. What is the relationship? If I remember correctly from some experiments a while back, the diameter seemed to be a slightly concave function.
Even if there is no direct method of controlling bubble size (am I just missing something?) it would be a tremendous help to just know the policy, as that would allow the user to control bubble size by carrying out the appropriate preprocessing of the data (e.g. linearlization, offset-from-dummy etc.)...
This question has two parts:
A) relating to scale/range

A) is not a big problem:
A workaround for controlling bubble size scale/range is to insert a dummy maximum size bubble and dummy minimum size bubble into the data, and also to clip the real data between these two levels. This forces the plotter to look at a pre-determined range, and allows for some some consistency between different charts in a series of bubble plots. It works well enough for me, but...

Neither the diameter nor the area of the bubbles seems to be proportional (or even affine) to the data values. What is the relationship? If I remember correctly from some experiments a while back, the diameter seemed to be a slightly concave function.
Even if there is no direct method of controlling bubble size (am I just missing something?) it would be a tremendous help to just know the policy, as that would allow the user to control bubble size by carrying out the appropriate preprocessing of the data (e.g. linearlization, offset-from-dummy etc.)...
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