maths question

[stormbind]

I forgot my A Level maths!!!

How do I find the centre of gravity in a 2D shape? The shapes have four edges, intersecting at arbitrary angles.

If these were physical (or even in an image editor) then I could seperate them into combinations of triangles and rectangles, but I don't see how that can work in this case.

The shapes in question are generated on the fly in a computer program. The coordinate of each corner is known.

Thanks genies!

 

[Truronian]

Average x co-ordinate and average y co-ordinate, assuming the shape is of uniform mass

 

[stormbind]

Thanks. Can you define uniform mass for me?

 

[Shaihulud]

Logically, find the line of symmetry and bisect the shape, do it again. The line of intersectin should be the COG. Alternatively, if you do not have symmetry. The COG is the center of mass, area in a 2d case will define mass. quater the shape that you have with each quater having the same area.

 

[Truronian]

Probably not very well...

It basically just needs a constant "2-D density". If you cut out a segment of the shape, the area of that segment over its mass must always equal the same value (irrespective of where the segment came from on the original shape)

For example, a sheet of paper would have uniform mass, whereas a used towel would not (wetter areas would be heavier).

I hope that makes sense...

 

[stormbind]

Thanks again. They are uniform masses