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I asked this question on Graphic Design SE about the name for a technique I use to fix the centering of problematic icons. For example:

enter image description here

Based on width and height of the icon, the play button is technically centered within its container, however optically, it doesn't look quite right. It feels like the icon has more empty space to the right side, and therefore appears to not be perfectly balanced. So to center it, I would push it over to the right a bit, so that it's centered based on volume.

My question here is, How can I determine the "Volumetric Center" of a shape mathematically? This seems really hard because icons can have such complex shapes. The answer might be that it isn't even possible to describe an icon's volumetric center mathematically without programming logic. If that's the case just let me know!

Edit, just found this: Helpful article on this topic.

In vector icons, I can access the vertices of the shape based on a coordinate plane, so any answers that describe how to calculate the volumetric center based on a set of coordinates would be interesting.

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J.Todd
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    First world problems... :-$)$ – Lucian Sep 10 '15 at 01:15
  • I’ll bet two nickels: first nickel says that the most efficient way to do it (and the way that gives the most esthetic result) is with a scissors and pieces of white and dark-gray paper; second nickel says that the result will be different with the colors reversed. – Lubin Sep 10 '15 at 01:54
  • Mathematically, I suppose you want the center of the triangle at the center of the square. But the center of the triangle here is $1/3$ the way from the lefthand (vertical) edge of the triangle. – Lubin Sep 10 '15 at 02:01
  • @Lubin I'd like to get the center by volume of icons other than just the triangle. Is that possible? – J.Todd Sep 10 '15 at 02:20
  • I really do think that this is not science or mathematics, but esthetics. – Lubin Sep 10 '15 at 12:30
  • @Lubin you don't think math should be used to perfect esthetic balance? – J.Todd Sep 10 '15 at 12:48
  • Mathematics should be used for any moral purpose you like including esthetic effect. My claim is that direct esthetic judgment will be more reliable. – Lubin Sep 12 '15 at 00:40
  • On the question of finding a center, that definitely depends on your definition of “center”. The article you made reference to used a definition that I would never have thought of using; rather, I would expect to use the centroid, which amounts to the balance point, found by standard techniques from freshman Calculus. – Lubin Sep 12 '15 at 00:44
  • @Lubin I just said it was interesting / related to my question, not for use as the definition of "center" – J.Todd Sep 12 '15 at 03:24

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