# Proportional Symbol Calculations

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### #1 Bjorn Posted 18 June 2008 - 05:51 PM

Bjorn

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I need a verification on symbol scaling. Since I'm making my own Thematic Mapping Engine, I need to understand the math behind proportional symbol calculations.

I'm having both 2D (circle/square) and 3D objects (sphere/cube) that should be proportional to a statistical value. I'm using area to scale 2D symbols and volume for 3D objects. I also want to scale irregular 3D objects like humans and mobile phones...

Originally, I thought I would need different equations for different geometric shapes, and my book in cartography gave me the same impression.

But after seeing this article, I asked a math genius if it could be done in an easier way.

So now I only have two equations; one for area calculation and one for volume calculation (max size of a symbol/object is known - it's just a scale factor):

Area: scale = maxScale * sqrt(value/maxValue)
Using square root: http://en.wikipedia....iki/Square_root

Volume: scale = maxScale * pow(value/maxValue, 1/3)
Using cube root: http://en.wikipedia.org/wiki/Cube_root

Still, I'm not sure if life is so easy... anyone who can verify if this is the case?

Bjorn

Ps! I should probably know this after 20 years in school, but math was not my favorite subject...

### #2 mika Posted 20 June 2008 - 02:27 AM

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Bjorn,

Both statements are true Though I'd use slightly different words to describe it...

So to calculate the symbol's size in relation to the maxSymbolSize you do:

anySymbolSize = power(value/maxValue; 1/2) for areas
anySymbolSize = power(value/maxValue; 1/3) for volumes

As you see in both cases you're dealing with a percentage of the biggest symbol and therefore the biggest size of the symbol is always 1. And here you incorporate the maxSymbolSize to scale symbols again for the presentation, so:

anySymbolSize = maxSymbolSize * power(value/maxValue; 1/2) for areas
anySymbolSize = maxSymbolSize * power(value/maxValue; 1/3) for volumes

Hope this makes it a bit easier to understand

### #3 Bjorn Posted 23 June 2008 - 06:38 AM

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Thanks mika!

I've just published a proportional symbol tutorial:

Proportional symbols in three dimensions

Bjorn

### #4 john789 Posted 31 October 2008 - 11:04 PM

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Since I'm making my own Thematic Mapping Engine, I need to understand the math behind proportional symbol calculations. Originally, I thought I would need different equations for different geometric shapes, and my book in cartography gave me the same impression.

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