I thought I was done with the topic but I just discovered that I messed up with the code. And I didn’t notice the problem because I didn’t test the program well.

Here is how it happened. The algorithm for roundness computes the perimeter first. More precisely, it computes the “adjusted” perimeter. The reason is that the perimeter computed as the number of steps in the curve depends on the orientation of the curve with respect to the grid. This “first degree approximation” produces the same roundness for a square and a 5×1 rectangle. To compute the better adjusted perimeter we use the “second degree approximation” that takes into account both the perimeter and the curvature (number of turns). Some error is still there but the results were supposed to be much better. And they were until I tried a diagonally oriented square. The roundness was way off!

Fortunately no-one was hurt and the error was quickly located and fixed. The results are slightly different though. Pixcavator can’t distinguish circles and squares unless they are quite large. Circles of diameter 100 and squares 100×100 both have roundness close to 80. However, circles of radius 200 have roundness 89. That of course makes sense. As before elongated objects are easily detectable. For example, the roundness of a 200×200 rectangle is 79 while that of 200×270 is 77. I’ll need more testing. The article in the wiki is being rewritten.