Adaptively Subdividing the Grid

Explaining adaptive subdivision

In order to use adaptive subdivision to make our cells more uniform in size, we need to know what size they should be. Squares look pretty good in an orthogonal grid, but polar grids can’t give us real squares because there are no parallel lines in a polar grid. But although we can’t have squares, we can approximate them. We’ll just say we want the length of the inner wall to be approximately the same as the height of the cell (the distance between the inner and outer walls).

With that rule in mind, let's take a look at the figure below, which shows one column of our polar grid, and take steps to make it a bit more uniform.