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jamnitzer

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My question is if someone has heard of this or done something similar, and/or if anyone knows where to find more information.

Using the shoelace method of measuring area and/or after calculating the center of mass, I want to find a way to find either a horizontal line that will divide the top and bottom of a shape or a vertical line that will divide left and right such that the area of the shape on either side will be equal.

So the half-way line in terms of area, but only from one direction. I'm hoping there's already a name for this somewhere and I just haven't been able to find it. If this is more of a calculus question let me know. Really any information will be appreciated.

Some simple examples:

These are two shapes defined with their coordinates (x,y), repeating the first at the end.

{(4,0),(6,0),(6,2),(8,4),(4,4),(4,6),(2,4),(0,4),(4,0)} Area = 20

{(1,0),(1,1),(7,1),(4,0),(8,0),(8,1),(6,4),(4,2),(2,4),(6,6),(8,8),(0,8),(0,4),(1,0)} Area = 40.5

For the first shape, the vertical line evenly dividing left and right the area is x= 4.

The horizontal line dividing top and bottom is y= 4/sqrt(2).

In the second shape, the vertical line is x= -(sqrt(109)-20)/3

The horizontal line is y= (sqrt(2)sqrt(5.5)+6)/2