/// <summary>
/// Creates reference points for triangulation.
///
/// The first is guaranteed to be the origin, and the second will be the opposite corner and
/// have "max" for each of its coordinate values, where max = (2^bits) - 1.
/// After that, the patterns will be:
/// { max, 0, max, 0, max, 0, ... }
/// { max, max, 0, 0, max, max, 0, 0, ... }
/// { max, max, max, 0, 0, 0, max, max, max, 0, 0, 0, ... }
/// { max, max, max, max, 0, 0, 0, 0, max, max, max, max, 0, 0, 0, 0, ... }
/// </summary>
/// <returns>The reference points.</returns>
/// <param name="dimensions">Number of Dimensions for each point.</param>
/// <param name="bits">Bits per coordinate.</param>
/// <param name="numTriangulationPoints">Number of triangulation points to create.</param>
private static UnsignedPoint[] CreateReferencePoints(int dimensions, int bits, int numTriangulationPoints)
{
var tPoints = new UnsignedPoint[numTriangulationPoints];
var max = (uint)((1 << bits) - 1);
// The origin
tPoints[0] = new UnsignedPoint(new uint[dimensions]);
// The corner opposite the origin.
tPoints[1] = new UnsignedPoint(
Enumerable.Range(0, dimensions).Select(i => max).ToArray()
);
foreach (var i in Enumerable.Range(2, numTriangulationPoints - 2))
{
var coordinates = new uint[dimensions];
for (var iDim = 0; iDim < dimensions; iDim++)
{
if ((iDim / (i - 1)) % 2 == 0)
{
coordinates[i] = max;
}
}
tPoints[i] = new UnsignedPoint(coordinates);
}
return(tPoints);
}
public Triangulator(UnsignedPoint point, int bits, int numTriangulationPoints = 10)
{
Key = LookupKey(point.Dimensions, bits, numTriangulationPoints);
var refPoints = GetReferencePoints(point.Dimensions, bits, numTriangulationPoints);
ReferenceSquareDistances = new long[numTriangulationPoints];
ReferenceDistances = new double[numTriangulationPoints];
for (var iTri = 0; iTri < numTriangulationPoints; iTri++)
{
ReferenceSquareDistances[iTri] = point.Measure(refPoints[iTri]);
ReferenceDistances[iTri] = Math.Sqrt(ReferenceSquareDistances[iTri]);
}
}
/// <summary>
/// If the point is already a HilbertPoint, return it unchanged, otherwise create a new one
/// that contains the same coordinates yet has a Hilbert index.
/// </summary>
/// <returns>A HilbertPoint.</returns>
/// <param name="uPoint">U point.</param>
/// <param name="bitsPerDimension">Bits per dimension.</param>
/// <param name="useSameKey">If true and a new point is created, it will share the same key as the original.</param>
public static HilbertPoint CastOrConvert(UnsignedPoint uPoint, int bitsPerDimension, bool useSameKey = false)
{
HilbertPoint hPoint = uPoint as HilbertPoint;
if (hPoint == null || hPoint.BitsPerDimension != bitsPerDimension)
{
if (useSameKey)
{
hPoint = new HilbertPoint(uPoint.Coordinates, bitsPerDimension, uPoint.MaxCoordinate, uPoint.SquareMagnitude, uPoint.UniqueId);
}
else
{
hPoint = new HilbertPoint(uPoint.Coordinates, bitsPerDimension, uPoint.MaxCoordinate, uPoint.SquareMagnitude);
}
}
return(hPoint);
}
/// <summary>
/// Can Triangulation bypass the need to compute the ful distance?
///
/// THis method is only used for testing.
/// </summary>
/// <param name="other">Other.</param>
/// <param name="squareDistance">Square distance.</param>
public bool Triangulatable(UnsignedPoint other, long squareDistance)
{
var hPoint = other as HilbertPoint;
if (hPoint == null)
{
return(false);
}
if (Triangulation.ArePointsFartherForSure(hPoint.Triangulation, squareDistance))
{
return(true);
}
if (Triangulation.ArePointsNearerForSure(hPoint.Triangulation, squareDistance))
{
return(true);
}
return(false);
}
public override int SquareDistanceCompare(UnsignedPoint other, long squareDistance)
{
var hPoint = other as HilbertPoint;
if (hPoint == null)
{
return(base.SquareDistanceCompare(other, squareDistance));
}
if (Triangulation.ArePointsFartherForSure(hPoint.Triangulation, squareDistance))
{
return(1);
}
if (Triangulation.ArePointsNearerForSure(hPoint.Triangulation, squareDistance))
{
return(-1);
}
return(Measure(other).CompareTo(squareDistance));
}