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

Question

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,

Answer 1

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.