/// <summary>
/// Obtains the center point (x,y) of an hexagon given its LocationUv (u,v)
/// </summary>
/// <param name="location"></param>
/// <param name="hexagonDefinition"></param>
/// <returns></returns>
public static PointXY GetCenterPointXYOfHexagonLocationUV(HexagonLocationUV location,
HexagonDefinition hexagonDefinition)
{
var x = hexagonDefinition.NarrowWidth * location.U;
var y = hexagonDefinition.Height * (location.U * 0.5 + location.V);
return(new PointXY(x, y));
}
/// <summary>
/// </summary>
/// <param name="source"></param>
/// <param name="destination"></param>
/// <param name="hexagonDefinition"></param>
/// <returns></returns>
public static int GetDistanceBetweenHexagonLocationUVs(HexagonLocationUV source, HexagonLocationUV destination,
HexagonDefinition hexagonDefinition)
{
var du = destination.U - source.U;
var dv = destination.V - source.V;
return(du * dv > 0 ? Math.Abs(du + dv) : Math.Max(Math.Abs(du), Math.Abs(dv)));
}
/// <summary>
/// Determines if a specified point (x,y) is inside a given hexagon Location (u,v)
/// </summary>
/// <param name="point"></param>
/// <param name="location"></param>
/// <param name="hexagonDefinition"></param>
/// <returns>True if inside the hexagon, false otherwise</returns>
public static bool IsPointXYInsideHexagonLocationUV(PointXY point, HexagonLocationUV location,
HexagonDefinition hexagonDefinition)
{
var center = GetCenterPointXYOfHexagonLocationUV(location, hexagonDefinition);
var d = hexagonDefinition.Diameter;
var dx = Math.Abs(point.X - center.X) / d;
var dy = Math.Abs(point.Y - center.Y) / d;
var a = 0.25 * Math.Sqrt(3.0);
return(dy <= a && a * dx + 0.25 * dy <= 0.5 * a);
}
public static IEnumerable <TileInfo> GetTilesContainingHexagon(Hexagon hexagon, int minZoomLevel, int maxZoomLevel,
HexagonDefinition hexagonDefinition, int tileSize)
{
var tiles = new HashSet <TileInfo>();
var points = GetPointsXYOfHexagon(hexagon.LocationUV, hexagonDefinition);
var topLeft = new PointXY(points[0].X, points[1].Y);
var topRight = new PointXY(points[3].X, points[1].Y);
var bottomLeft = new PointXY(points[0].X, points[4].Y);
var bottomRight = new PointXY(points[3].X, points[4].Y);
for (var zoomLevel = minZoomLevel; zoomLevel <= maxZoomLevel; zoomLevel++)
{
tiles.Add(GetTileOfPoint(topLeft, zoomLevel, tileSize, hexagonDefinition));
tiles.Add(GetTileOfPoint(topRight, zoomLevel, tileSize, hexagonDefinition));
tiles.Add(GetTileOfPoint(bottomLeft, zoomLevel, tileSize, hexagonDefinition));
tiles.Add(GetTileOfPoint(bottomRight, zoomLevel, tileSize, hexagonDefinition));
}
return(tiles);
}
public static IEnumerable <HexagonLocationUV> GetHexagonsInsideBoundingBox(PointXY topLeftCorner, PointXY bottomRightCorner,
HexagonDefinition hexagonDefinition)
{
var topLeftUV = GetHexagonLocationUVForPointXY(topLeftCorner, hexagonDefinition);
var bottomLeftUV =
GetHexagonLocationUVForPointXY(new PointXY(topLeftCorner.X, bottomRightCorner.Y), hexagonDefinition);
var bottomRightUV = GetHexagonLocationUVForPointXY(bottomRightCorner, hexagonDefinition);
var rowsEven = bottomLeftUV.V - topLeftUV.V + 1;
var topLeftUVCenter = GetCenterPointXYOfHexagonLocationUV(topLeftUV, hexagonDefinition);
var minX2 = topLeftUVCenter.X + hexagonDefinition.NarrowWidth;
var topLeftUV2 = GetHexagonLocationUVForPointXY(new PointXY(minX2, topLeftCorner.Y), hexagonDefinition);
var bottomLeftUV2 =
GetHexagonLocationUVForPointXY(new PointXY(minX2, bottomRightCorner.Y), hexagonDefinition);
var rowsOdd = bottomLeftUV2.V - topLeftUV2.V + 1;
var columns = bottomRightUV.U - topLeftUV.U + 1;
for (var i = 0; i < columns; i++)
{
var rows = i % 2 == 0 ? rowsEven : rowsOdd;
for (var j = 0; j < rows; j++)
{
var offset = topLeftUV.V == topLeftUV2.V
? Convert.ToInt32(Math.Floor((double)i / 2))
: Convert.ToInt32(Math.Ceiling((double)i / 2));
var u = topLeftUV.U + i;
var v = topLeftUV.V + j - offset;
yield return(new HexagonLocationUV(u, v));
}
}
}
public static IList <PointXY> GetPointsXYOfHexagon(HexagonLocationUV location, HexagonDefinition hexagonDefinition)
{
var center = GetCenterPointXYOfHexagonLocationUV(location, hexagonDefinition);
return(new List <PointXY>
{
new PointXY(center.X - hexagonDefinition.Diameter / 2.0, center.Y),
new PointXY(center.X - hexagonDefinition.EdgeSize / 2.0, center.Y - hexagonDefinition.Height / 2.0),
new PointXY(center.X + hexagonDefinition.EdgeSize / 2.0, center.Y - hexagonDefinition.Height / 2.0),
new PointXY(center.X + hexagonDefinition.Diameter / 2.0, center.Y),
new PointXY(center.X + hexagonDefinition.EdgeSize / 2.0, center.Y + hexagonDefinition.Height / 2.0),
new PointXY(center.X - hexagonDefinition.EdgeSize / 2.0, center.Y + hexagonDefinition.Height / 2.0),
new PointXY(center.X - hexagonDefinition.Diameter / 2.0, center.Y)
});
}
/// <summary>
/// Obtains the Hexagon Location (u,v) for a given point (x,y)
/// </summary>
/// <remarks>
/// This algorithm follows a two step approach. The first one is very first and although doesn't have false positives
/// might have false negatives.
/// Thus, on a second iteration (if the first didn't return true) it checks the vicinity hexagons and uses a more
/// deterministic polygon intersection mechanism.
/// </remarks>
/// <param name="point">A given X,Y point</param>
/// <param name="hexagonDefinition"></param>
/// aaa
/// <returns>An hexagon U,V Location</returns>
public static HexagonLocationUV GetHexagonLocationUVForPointXY(PointXY point, HexagonDefinition hexagonDefinition)
{
var u = Convert.ToInt32(Math.Round(point.X / hexagonDefinition.NarrowWidth));
var v = Convert.ToInt32(Math.Round(point.Y / hexagonDefinition.Height - u * 0.5));
if (IsPointXYInsideHexagonLocationUV(point, new HexagonLocationUV(u, v), hexagonDefinition))
{
return(new HexagonLocationUV(u, v));
}
var surroundingHexagons = new List <HexagonLocationUV>
{
new HexagonLocationUV(u, v - 1),
new HexagonLocationUV(u, v + 1),
new HexagonLocationUV(u - 1, v),
new HexagonLocationUV(u + 1, v),
new HexagonLocationUV(u - 1, v + 1),
new HexagonLocationUV(u + 1, v - 1)
};
foreach (var hex in surroundingHexagons)
{
if (IsPointXYInsideHexagonLocationUV(point, hex, hexagonDefinition))
{
return(hex);
}
}
return(null);
}
private static TileInfo GetTileOfPoint(PointXY pointXY, int zoomLevel, int tileSize, HexagonDefinition hexagonDefinition)
{
var pixelFactor = Math.Pow(2, zoomLevel - hexagonDefinition.ReferenceZoom);
var tileX = Convert.ToInt32(Math.Floor(pointXY.X * pixelFactor / tileSize));
var tileY = Convert.ToInt32(Math.Floor(pointXY.Y * pixelFactor / tileSize));
return(new TileInfo(zoomLevel, tileX, tileY));
}
