How to generate a random shape convex polygon with the same area?

Hi, I want to generate a number of random shape convex polygons. They must have the same value of area. It dosen't matter how much vertex it has.

I know how to generate a bunch of random shape convex polygons, but if I additionally want them to have the same value of area, it is difficult for me.

Thanks,

[Image Analyst]

The same as what? What other area should the polygon's area match? Why not just create one, then scale it to force it to have the area you want?

[toby]

Thanks for your reply. I mean all random convex polygon need to have the same area. I think the scale method might be a good one. Could you please be more specific?

Answer 1

[Image Analyst]

Make a random polygon and use polyarea() to find it's area. Then calculate the centroid and then change the distance from the centroid to the vertices by the proper amount so that the area is what is desired. I think if the radius changes by a factor F then the area will change by F^2. Try that and see how it goes.

[toby]

thank you very much! But I still have some question about the convex polygon generation. Is there some available functions in matlab to generate convex polygon?

[Image Analyst]

You can use the rand() function to generate random coordinates.