Wrapping does not work near corners

[dan-modsi-io]

So, first, love this series of videos. Learning so much. Thanks!

Now, bug report.

When north-south wrapping is turned on the Hex.GetNeighbours() function returns "incorrect" values when the origin Hex is in a corner. Specifically when the origin is 0,0. I have not had time to test the other corners, but given the nature of the issue I imagine they all have the same issue. In fact, my best guess is any coordinate along the north or south borders will suffer from this.

So, on a Rows = 30 by Columns = 40 map, if your origin Hex is 0,0 and you enable East-West and North-South wrapping, then the tiles surrounding 0,0 in function order are

1,0    39,0    0,1    25,29    26,29    39,1

however, the results of Hex.GetNeighbours() are

1,0    39,0    0,1    0,29    1,29    39,1

So we can clearly see the issue is with the two R minus 1 coordinates. If you turn wrapping off you can clearly see why the GetNeighbours values are chosen. The values make sense mathematically with the skewed (rhomboid?) shape. But visually they are incorrect. And from a user's perspective nobody cares about the correctness of the math as their units are jumping all over the board for no apparent reason.

I'll continue to work on this, but I'm not sure if my math skills are up to snuff.

Keep up the fantastic work!

[dan-modsi-io]

Ok, a little more detail...

So it appears, to me, that this is happening because with North-South wrapping turned on the rhombus is being wrapped around the Y axis of the screen... while the Q axis of the rhombus actually lies at 60 degrees to the screen's vertical axis.

Thus to solve the issue... I think we need to use a little trigonometry.
I AM NOT A MATH EXPERT. I have no real idea what I am doing when it comes to trig.
Please correct me if I am wrong.

So what I've done, mathematically, is cut the 2 ends (right-triangles) off, leaving the middle rectangle. Then calculate the base of the triangle. If the hypotenuse is 30 (row count), and the angle opposite the base is 60 degrees... then the base can be calculated by base = hyp. * cos(60 degrees); or 30 * cos(60 degrees), which I believe equals 15.
Then subtracting the base from the length (column count) of the rhombus (40 - 15) we get 25... which appears to be the correct Q value for Q + 0, R - 1 !

Have I totally screwed up? Does this look even remotely right?

This is as far as I've gotten. Haven't even attempted to incorporate it into the code for Hex.GetNeighbours() yet.

[dan-modsi-io]

Ok. This is what appears to work... but more testing is required before I can be confident.

public IQPathTile[] GetNeighbours() {
	List<IQPathTile> neighbours = new List<IQPathTile>();

	neighbours.Add(HexMap.GetHexAt(Q + +1, R +  0));
	neighbours.Add(HexMap.GetHexAt(Q + -1, R +  0));

	int trigQ = (int)Mathf.Ceil ((float)HexMap.RowCount * Mathf.Cos(60.0f * Mathf.PI / 180.0f));
	if (R == HexMap.RowCount - 1) {
		neighbours.Add(HexMap.GetHexAt(trigQ, R + +1));
	} else {
		neighbours.Add(HexMap.GetHexAt(Q +  0, R + +1));
	}
	
	if (R == 0) {
		neighbours.Add(HexMap.GetHexAt(HexMap.ColumnCount - trigQ, R + -1));
	} else {
		neighbours.Add(HexMap.GetHexAt(Q +  0, R + -1));
	}

	if (R == 0) {
		neighbours.Add(HexMap.GetHexAt(HexMap.ColumnCount - trigQ + 1, R + -1));
	} else {
		neighbours.Add(HexMap.GetHexAt(Q + +1, R + -1));
	}

	if (R == HexMap.RowCount - 1) {
		neighbours.Add(HexMap.GetHexAt(trigQ - 1, R + +1));
	} else {
		neighbours.Add(HexMap.GetHexAt(Q + -1, R + +1));
	}

	neighbours = neighbours
		.Where(n => null != n)
		.ToList();

	return neighbours.ToArray();
}

and if it does happen to work, it probably only works for pointy-top hexes and not for flat-top hexes.