Looks like GeoGeometry.overlap function is not perfect

[sashadu]

The overlap method consider two polygons to overlap if any one of them contains the center of the other or if any one of them contains any vertex of the other. Unfortunately it is not always the case - see the example:

As you can see, their centers do not lie inside each other, and their vertexes also do not lie inside each other.

In my opinion, an algorithm would better assume that two polygons overlap if:
(polygonA crosses PolygonB) or (polygonA contains PolygonB) or (polygonB contains PolygonA),
where "crosses" means that any of the sides of the polygon A crosses any of the sides of the polygon B (linesCross method); and "contains" means that polygonA contains all points of polygonB.
Best regards,

[Jilles van Gurp]

Interesting, it's been a while since I did anything on this code base. The problem with the example above (for the algorithm) is that in this case all of the points lie outside each other's polygon. So it fails to find an overlap.

A fix could be to check for line intersection for each segment as well. If any of the lines intersect, the polygons overlap. It should be possible to reuse the linesCross method for this. This will make things a bit slower of course but not massively. There may be some more efficient algorithms out there for this.

Feel free to provide a PR. If not, I might look at this at some point but very low priority for me. In any case, thanks for reporting this.

[sashadu]

Yes. These are existing test polygons:

Polygons p, p2 and p4 centers are very close and lie inside each other, so it is simple.
Consider this example:

(p3 overlaps with p5).

Or even this:

(p3 does not overlap with p6).

Here is my version of shouldOverlap test which fails (p5overlapP3 is yellow polygon on the image above, p6aroundP3 is magenta) :

`
public void shouldOverlap() {
double[][] polygon = new double[][] {
{50, 15},
{53, 15},
{53, 11},
{50, 11}
};

	double[][] p2overlapping = new double[][] {
			{51, 16},
			{52, 16},
			{52, 10},
			{51, 10}
	};
	double[][] p3outside = new double[][] {
			{60, 15},
			{63, 15},
			{63, 11},
			{60, 11}
	};
	double[][] p4inside = new double[][] {
			{51, 14},
			{52, 14},
			{52, 12},
			{51, 12}
	};
	// polygon which overlaps with p3 but does not have center or any vertexes inside the p3
	double[][] p5overlapP3 = new double[][] {
			{60.3, 10},
			{60.3, 22},
			{61, 22},
			{61, 10}
	};
	// polygon which lays around the p3 without overlapping
	// polygon 6 is concave with its center lying outside of p6 but inside the p3
	double[][] p6aroundP3 = new double[][] {
		{	63.39152174400882 , 16.3916015625 },
		{	63.38167869302983 , 17.2705078125 },
		{	64.30182213914463 , 17.02880859375 },
		{	64.24459476798195 , 8.349609375 },
		{	58.790978406215565, 8.349609375 },
		{	58.83649009392136 , 16.040039062499996  },
		{	59.40036514079251 , 16.171875 },
		{	59.377988012638895, 9.3603515625 },
		{	63.763065186029074, 9.3603515625 },
		{	63.918058296491104, 16.34765625 }
	};

	Assert.assertTrue(GeoGeometry.overlap(polygon,polygon));

	Assert.assertTrue(GeoGeometry.overlap(polygon, p2overlapping));
	Assert.assertTrue(GeoGeometry.overlap(p2overlapping,polygon));

	Assert.assertFalse(GeoGeometry.overlap(p3outside,polygon));
	
	Assert.assertTrue(GeoGeometry.overlap(polygon,p4inside));
	Assert.assertTrue(GeoGeometry.overlap(p4inside,polygon));

	// with overlap logic which check only center and vertexes this test fails
	// edge intersections should be checked as well
	Assert.assertTrue(GeoGeometry.overlap(p3outside,p5overlapP3));
	Assert.assertTrue(GeoGeometry.overlap(p5overlapP3, p3outside));

	// this test also fails because of the center logic.
	// polygon 6 is concave with its center lying outside of p6 but inside the p3
	// they do not overlap
	Assert.assertFalse(GeoGeometry.overlap(p3outside,p6aroundP3));
	Assert.assertFalse(GeoGeometry.overlap(p6aroundP3, p3outside));
}

`

[Jilles van Gurp]

Thanks for clarifying, I'll spend some time on improving this when I have a free moment.

[Jilles van Gurp]

I finally looked into this. The algorithm does not support concave polygons currently. p6 is concave. I added a clarification on this. Wikipedia hints at an algorithm that we might use but that would be a bit more work. https://en.wikipedia.org/wiki/Point_in_polygon