public static void DrawBaseCurveKml(Point2D lowerLeft,
Point2D upperRight, CurveType curve)
{
double ux = (3 * upperRight.X + lowerLeft.X) / 4;
double lx = (3 * lowerLeft.X + upperRight.X) / 4;
double uy = (3 * upperRight.Y + lowerLeft.Y) / 4;
double ly = (3 * lowerLeft.Y + upperRight.Y) / 4;
if (curve == CurveType.UpLeft)
{
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
}
else if (curve == CurveType.UpRight)
{
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
}
else if (curve == CurveType.DownLeft)
{
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
}
else if (curve == CurveType.DownRight)
{
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
}
else if (curve == CurveType.LeftTop)
{
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
}
else if (curve == CurveType.LeftBottom)
{
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
}
else if (curve == CurveType.RightTop)
{
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
}
else if (curve == CurveType.RightBottom)
{
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(ly.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(lx.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
Console.Write(ux.ToString("###.##############\\,"));
Console.Write(uy.ToString("##.##############\\,"));
Console.Write("0 ");
}
}
/// <summary>
/// Gets the quadrant in which the point p is in. This method first
/// subdivide the space into 4 quadrants. The quadrants have the
/// following index: upper left 0, lower left 1, lower right 2,
/// upper right 3.
/// </summary>
/// <param name="p">The point</param>
/// <param name="lowerLeft">The lower left point of the space.</param>
/// <param name="upperRight">The upper right point of the space.</param>
/// <returns>An integer representing the quadrant index.</returns>
/// <exception cref="ArgumentException">If point is not in the bounds of
/// lower left and upper right.</exception>
public static int GetQuadIndex(Point2D p, Point2D lowerLeft,
Point2D upperRight)
{
//Check if p is in bound.
if (p.X < lowerLeft.X || p.X > upperRight.X ||
p.Y < lowerLeft.Y || p.Y > upperRight.Y)
throw new ArgumentException("Point is out of bound.");
//Find the boundaries of the quadrants.
double xBisector = (lowerLeft.X + upperRight.X) / 2;
double yBisector = (lowerLeft.Y + upperRight.Y) / 2;
if (p.X <= xBisector)
{
if (p.Y <= yBisector) return 1;
else return 0;
}
else
{
if (p.Y <= yBisector) return 2;
else return 3;
}
}
/// <summary>
/// Transforms a 2D point to an Hilbert value.
/// </summary>
/// <param name="p">The point to be transformed.</param>
/// <param name="lowerLeft">The lower-left corner of the bound.</param>
/// <param name="upperRight">The upper-right corner of the bound.</param>
/// <param name="order">Hilbert curve order (or level).</param>
/// <param name="curve">The direction of the curve.</param>
/// <returns></returns>
/// <exception cref="ArgumentException">If p is not within bound
/// or curve order is less than 1.</exception>
public static int Transform(Point2D p, Point2D lowerLeft,
Point2D upperRight, int order, CurveType curve)
{
//TODO: Specify the precision of coordinates.
if (order < 1) throw new ArgumentException("Order must be 1 or greater.");
double xBisector = (lowerLeft.X + upperRight.X) / 2;
double yBisector = (lowerLeft.Y + upperRight.Y) / 2;
//Get the quadrant the point is in.
int quadIndex = GetQuadIndex(p, lowerLeft, upperRight);
//Translate quadrant into curve quadrant order.
int curveQuadIndex = GetCurveQuadIndex(quadIndex, curve);
//Base case when the order is 1
if (order == 1) return curveQuadIndex;
//Other cases when order is greater than 1.
Point2D nextLowerLeft = new Point2D();
Point2D nextUpperRight = new Point2D();
if (quadIndex == 0)
{
nextLowerLeft.X = lowerLeft.X;
nextLowerLeft.Y = yBisector;
nextUpperRight.X = xBisector;
nextUpperRight.Y = upperRight.Y;
}
else if (quadIndex == 1)
{
nextLowerLeft.X = lowerLeft.X;
nextLowerLeft.Y = lowerLeft.Y;
nextUpperRight.X = xBisector;
nextUpperRight.Y = yBisector;
}
else if (quadIndex == 2)
{
nextLowerLeft.X = xBisector;
nextLowerLeft.Y = lowerLeft.Y;
nextUpperRight.X = upperRight.X;
nextUpperRight.Y = yBisector;
}
else if (quadIndex == 3)
{
nextLowerLeft.X = xBisector;
nextLowerLeft.Y = yBisector;
nextUpperRight.X = upperRight.X;
nextUpperRight.Y = upperRight.Y;
}
return (int)Math.Pow(4, order - 1) * curveQuadIndex +
Transform(p, nextLowerLeft, nextUpperRight, order - 1,
ctMatrix[(int)curve, curveQuadIndex]);
}
public static void DrawCurveKml(Point2D lowerLeft,
Point2D upperRight, int order, CurveType curve)
{
//TODO: Specify the precision of coordinates.
if (order < 1) throw new ArgumentException("Order must be 1 or greater.");
if (order == 1)
{
DrawBaseCurveKml(lowerLeft, upperRight, curve);
return;
}
double xBisector = (lowerLeft.X + upperRight.X) / 2;
double yBisector = (lowerLeft.Y + upperRight.Y) / 2;
if (curve == CurveType.UpLeft)
{
DrawCurveKml(new Point2D(lowerLeft.X, yBisector),
new Point2D(xBisector, upperRight.Y), order - 1,
ctMatrix[(int)curve, 0]);
DrawCurveKml(new Point2D(lowerLeft.X, lowerLeft.Y),
new Point2D(xBisector, yBisector), order - 1,
ctMatrix[(int)curve, 1]);
DrawCurveKml(new Point2D(xBisector, lowerLeft.Y),
new Point2D(upperRight.X, yBisector), order - 1,
ctMatrix[(int)curve, 2]);
DrawCurveKml(new Point2D(xBisector, yBisector),
new Point2D(upperRight.X, upperRight.Y), order - 1,
ctMatrix[(int)curve, 3]);
}
else if (curve == CurveType.UpRight)
{
DrawCurveKml(new Point2D(xBisector, yBisector),
new Point2D(upperRight.X, upperRight.Y), order - 1,
ctMatrix[(int)curve, 0]);
DrawCurveKml(new Point2D(xBisector, lowerLeft.Y),
new Point2D(upperRight.X, yBisector), order - 1,
ctMatrix[(int)curve, 1]);
DrawCurveKml(new Point2D(lowerLeft.X, lowerLeft.Y),
new Point2D(xBisector, yBisector), order - 1,
ctMatrix[(int)curve, 2]);
DrawCurveKml(new Point2D(lowerLeft.X, yBisector),
new Point2D(xBisector, upperRight.Y), order - 1,
ctMatrix[(int)curve, 3]);
}
else if (curve == CurveType.DownLeft)
{
DrawCurveKml(new Point2D(lowerLeft.X, lowerLeft.Y),
new Point2D(xBisector, yBisector), order - 1,
ctMatrix[(int)curve, 0]);
DrawCurveKml(new Point2D(lowerLeft.X, yBisector),
new Point2D(xBisector, yBisector), order - 1,
ctMatrix[(int)curve, 1]);
DrawCurveKml(new Point2D(xBisector, yBisector),
new Point2D(upperRight.X, upperRight.Y), order - 1,
ctMatrix[(int)curve, 2]);
DrawCurveKml(new Point2D(xBisector, lowerLeft.Y),
new Point2D(upperRight.X, yBisector), order - 1,
ctMatrix[(int)curve, 3]);
}
else if (curve == CurveType.DownRight)
{
DrawCurveKml(new Point2D(xBisector, lowerLeft.Y),
new Point2D(upperRight.X, yBisector), order - 1,
ctMatrix[(int)curve, 0]);
DrawCurveKml(new Point2D(xBisector, yBisector),
new Point2D(upperRight.X, upperRight.Y), order - 1,
ctMatrix[(int)curve, 1]);
DrawCurveKml(new Point2D(lowerLeft.X, yBisector),
new Point2D(xBisector, upperRight.Y), order - 1,
ctMatrix[(int)curve, 2]);
DrawCurveKml(new Point2D(lowerLeft.X, lowerLeft.Y),
new Point2D(xBisector, yBisector), order - 1,
ctMatrix[(int)curve, 3]);
}
else if (curve == CurveType.LeftTop)
{
DrawCurveKml(new Point2D(lowerLeft.X, yBisector),
new Point2D(xBisector, upperRight.Y), order - 1,
ctMatrix[(int)curve, 0]);
DrawCurveKml(new Point2D(xBisector, yBisector),
new Point2D(upperRight.X, upperRight.Y), order - 1,
ctMatrix[(int)curve, 1]);
DrawCurveKml(new Point2D(xBisector, lowerLeft.Y),
new Point2D(upperRight.X, yBisector), order - 1,
ctMatrix[(int)curve, 2]);
DrawCurveKml(new Point2D(lowerLeft.X, lowerLeft.Y),
new Point2D(xBisector, yBisector), order - 1,
ctMatrix[(int)curve, 3]);
}
else if (curve == CurveType.LeftBottom)
{
DrawCurveKml(new Point2D(lowerLeft.X, lowerLeft.Y),
new Point2D(xBisector, yBisector), order - 1,
ctMatrix[(int)curve, 0]);
DrawCurveKml(new Point2D(xBisector, lowerLeft.Y),
new Point2D(upperRight.X, yBisector), order - 1,
ctMatrix[(int)curve, 1]);
DrawCurveKml(new Point2D(xBisector, yBisector),
new Point2D(upperRight.X, upperRight.Y), order - 1,
ctMatrix[(int)curve, 2]);
DrawCurveKml(new Point2D(lowerLeft.X, yBisector),
new Point2D(xBisector, upperRight.Y), order - 1,
ctMatrix[(int)curve, 3]);
}
else if (curve == CurveType.RightTop)
{
DrawCurveKml(new Point2D(xBisector, yBisector),
new Point2D(upperRight.X, upperRight.Y), order - 1,
ctMatrix[(int)curve, 0]);
DrawCurveKml(new Point2D(lowerLeft.X, yBisector),
new Point2D(xBisector, upperRight.Y), order - 1,
ctMatrix[(int)curve, 1]);
DrawCurveKml(new Point2D(lowerLeft.X, lowerLeft.Y),
new Point2D(xBisector, yBisector), order - 1,
ctMatrix[(int)curve, 2]);
DrawCurveKml(new Point2D(xBisector, lowerLeft.Y),
new Point2D(upperRight.X, yBisector), order - 1,
ctMatrix[(int)curve, 3]);
}
else if (curve == CurveType.RightBottom)
{
DrawCurveKml(new Point2D(xBisector, lowerLeft.Y),
new Point2D(upperRight.X, yBisector), order - 1,
ctMatrix[(int)curve, 0]);
DrawCurveKml(new Point2D(lowerLeft.X, lowerLeft.Y),
new Point2D(xBisector, yBisector), order - 1,
ctMatrix[(int)curve, 1]);
DrawCurveKml(new Point2D(lowerLeft.X, yBisector),
new Point2D(xBisector, upperRight.Y), order - 1,
ctMatrix[(int)curve, 2]);
DrawCurveKml(new Point2D(xBisector, yBisector),
new Point2D(upperRight.X, upperRight.Y), order - 1,
ctMatrix[(int)curve, 3]);
}
}