/// <summary>
/// Projection of a 2D-function <paramref name="f"/> onto a DG-Field
/// </summary>
public static void ProjectField(this DGField u, _2D f)
{
if (u.Basis.GridDat.SpatialDimension != 2)
{
throw new ArgumentException("mismatch in spatial dimension");
}
u.ProjectField(f.Vectorize());
}
/// <summary>
/// L2Error w.r.t. a 2D-function <paramref name="f"/> of a DG-Field
/// </summary>
public static double L2Error(this DGField u, _2D f)
{
if (u.Basis.GridDat.SpatialDimension != 2)
{
throw new ArgumentException("mismatch in spatial dimension");
}
return(u.L2Error(f.Vectorize()));
}
public static bool IsPointOnLine(_2D.Point point, _2D.Point lineStart, _2D.Point lineEnd)
{
double crossProd = (point.Y - lineStart.Y) * (lineEnd.X - point.X) - (point.X - lineStart.X) * (lineEnd.Y - lineStart.Y);
if (Math.Abs(crossProd) > 0)
return false;
double dotProd = (point.X - lineStart.X) * (lineEnd.X - lineStart.X) + (point.Y - lineStart.Y) * (lineEnd.Y - lineStart.Y);
if (dotProd < 0)
return false;
double lineLenSqr = _2D.Math2D.DistanceSquared(lineStart, lineEnd);
if (dotProd > lineLenSqr)
return false;
return true;
}
/// <summary>
/// Vectorized 1D function (<see cref="ScalarFunction"/>) from a scalar implementation, with fixed time
/// </summary>
/// <param name="f">calling sequence: f(<paramref name="time"/>,x)</param>
/// <param name="time">fixed time</param>
/// <returns></returns>
public static ScalarFunction Vectorize(this _2D f, double time)
{
return(delegate(MultidimensionalArray inp, MultidimensionalArray res) {
int D = inp.GetLength(1);
if (D != 1)
{
throw new ArgumentException("wrong spatial dimension.");
}
for (int i = 0; i < inp.GetLength(0); i++)
{
double x = inp[i, 0];
res[i] = f(time, x);
}
});
}
public static _2D.Point LineWithVectorIntersection(_2D.Point line1Start, _2D.Point line1End, _2D.Point line2Start, _2D.Point line2End)
{
_2D.Point p;
double a1 = line1End.X - line1Start.X, a2 = line2End.Y - line2Start.Y;
double b1 = line1Start.X - line1End.X, b2 = line2Start.X - line2End.X;
double c1, c2;
double det = a1 * b2 - a2 * b1;
if (det == 0)
return null;
c1 = a1 * line1Start.X + b1 * line1Start.Y;
c2 = a2 * line2Start.X + b2 * line2Start.Y;
p = new _2D.Point((b2 * c1 - b1 * c2) / det, (a1 * c2 - a2 * c1) / det);
if (p.X >= Math.Min(line1Start.X, line1End.X) && p.X <= Math.Max(line1Start.X, line1End.X) &&
p.Y >= Math.Min(line1Start.Y, line1End.Y) && p.Y <= Math.Max(line1Start.Y, line1End.Y))
return p;
return null;
}
public static _2D.Point ClosestPointOnLineFromPoint(_2D.Point point, _2D.Point lineStart, _2D.Point lineEnd)
{
double a1 = lineEnd.Y - lineStart.Y, b1 = lineStart.X - lineEnd.X;
double c1 = (lineEnd.Y - lineStart.Y) * lineStart.X + (lineStart.X - lineEnd.X) * lineStart.Y;
double c2 = (-1 * b1) * point.X + a1 * point.Y;
double det = a1 * a1 + b1 * b1;
double cx, cy;
if (det != 0)
{
cx = (a1 * c1 - b1 * c2) / det;
cy = (a1 * c2 + b1 * c1) / det;
}
else
{
cx = point.X;
cy = point.Y;
}
return new _2D.Point(cx, cy);
}
public static double Determinate(_2D.Vector v1, _2D.Vector v2)
{
return v1.X * v2.Y - v1.Y * v2.X;
}
/// <summary>
/// Scalar function conversion.
/// </summary>
public static Func <double[], double, double> Convert_tx2Xt(this _2D f)
{
return((double[] X, double t) => f(t, X[0]));
}
/// <summary>
/// Scalar function conversion.
/// </summary>
public static Func <double[], double> Convert_xy2X(this _2D f)
{
return((double[] X) => f(X[0], X[1]));
}
public PowerupGenerator(_2D.Point center, double arenaHeight)
{
}
public MultiBallPowerup(Texture2D sprite, CollidableObjects.TriangleType triangleType, _2D.Point center, double width, double height)
: base(sprite, triangleType, center, width, height)
{
_powerupColor = Microsoft.Xna.Framework.Color.Red;
}