/// <summary>
/// Returns the position of the nearest vertex.
/// </summary>
/// <returns>
/// Position of the nearest vertex.
/// </returns>
///
/// <param name="grid">
/// The rectangular grid instance.
/// </param>
/// <param name="point">
/// Point in world space.
/// </param>
/// <param name="system">
/// Coordinate system to use.
/// </param>
///
/// <remarks>
/// Returns the position of the nearest vertex from a given point in
/// either grid- or world space.
/// </remarks>
public static Vector3 NearestVertex(this HexGrid grid, Vector3 point, CoordinateSystem system)
{
// Vertices in the hex-grid are dual to faces in the triangular
// tessellation of the grid. Convert the point to cubic coordinates
var cubicPoint = grid.WorldToCubic(point);
cubicPoint.x = Mathf.Floor(cubicPoint.x) + .5f;
cubicPoint.y = Mathf.Floor(cubicPoint.y) + .5f;
cubicPoint.z = Mathf.Floor(cubicPoint.z) + .5f;
cubicPoint.w = Mathf.Round(cubicPoint.w);
switch (system)
{
case CoordinateSystem.Cubic:
return(cubicPoint);
case CoordinateSystem.HerringboneUp:
return(grid.CubicToHerringU(cubicPoint));
case CoordinateSystem.HerringboneDown:
return(grid.CubicToHerringD(cubicPoint));
case CoordinateSystem.RhombicUp:
return(grid.CubicToRhombic(cubicPoint));
case CoordinateSystem.RhombicDown:
return(grid.CubicToRhombicD(cubicPoint));
case CoordinateSystem.World:
return(grid.CubicToWorld(cubicPoint));
}
throw new System.ComponentModel.InvalidEnumArgumentException();
}
/// <summary>
/// Returns the position of the nearest face.
/// </summary>
/// <returns>
/// Position of the nearest face.
/// </returns>
/// <param name="grid">
/// The rectangular grid instance.
/// </param>
/// <param name="point">
/// Point in world space.
/// </param>
/// <param name="system">
/// Coordinate system to use.
/// </param>
/// <remarks>
/// <para>
/// Returns the coordinates of a face on the grid closest to a
/// given point. Since the face is enclosed by four vertices, the
/// returned value is the point in between all four of the
/// vertices. You also need to specify on which plane the face
/// lies.
/// </para>
/// </remarks>
public static Vector3 NearestFace(
this HexGrid grid, Vector3 point, CoordinateSystem system
)
{
// Faces in the hex-grid are dual to vertices in the triangular
// tessellation of the grid. Convert the point to cubic coordinates
var cubic = grid.WorldToCubic(point);
// We need the original cubic coordinates and the rounded ones, so
// use a separate variable
var rounded = new Vector4(
Mathf.Round(cubic.x),
Mathf.Round(cubic.y),
Mathf.Round(cubic.z),
Mathf.Round(cubic.w)
);
// Rounding all three coordinates does not guarantee that their sum
// is zero. Therefore we will find the coordinate with the largest
// change and compute its value from the other two instead of its
// rounded value.
var deltaX = Mathf.Abs(rounded.x - cubic.x);
var deltaY = Mathf.Abs(rounded.y - cubic.y);
var deltaZ = Mathf.Abs(rounded.z - cubic.z);
if (deltaX > deltaY && deltaX > deltaZ)
{
rounded.x = -rounded.y - rounded.z;
}
else if (deltaY > deltaZ)
{
rounded.y = -rounded.x - rounded.z;
}
else
{
rounded.z = -rounded.x - rounded.y;
}
switch (system)
{
case CoordinateSystem.Cubic:
return(rounded);
case CoordinateSystem.HerringboneUp:
return(grid.CubicToHerringU(rounded));
case CoordinateSystem.HerringboneDown:
return(grid.CubicToHerringD(rounded));
case CoordinateSystem.RhombicUp:
return(grid.CubicToRhombic(rounded));
case CoordinateSystem.RhombicDown:
return(grid.CubicToRhombicD(rounded));
case CoordinateSystem.World:
return(grid.CubicToWorld(rounded));
}
throw new System.ComponentModel.InvalidEnumArgumentException();
}