/// <summary>
/// Given four points -- p1, p2, p3, p4 -- determine the z value for a fifth point with (x, y) coordinates (xStar, yStar)
/// Points should be arrayed as:
/// 2 - 4
/// | |
/// 1 - 3
/// </summary>
public static double BilinearInterpolation(ThreeDPoint p1, ThreeDPoint p2, ThreeDPoint p3, ThreeDPoint p4, double xStar, double yStar, out double wt1, out double wt2, out double wt3, out double wt4)
{
if (!(p1.X == p2.X && p1.Y == p3.Y && p2.Y == p4.Y && p3.X == p4.X))
{
throw new ArgumentException("Points are not lined up correctly");
}
double x1 = p1.X;
double x2 = p3.X;
double y1 = p1.Y;
double y2 = p2.Y;
double k = 1.0 / ((x2 - x1) * (y2 - y1));
wt1 = k * (x2 - xStar) * (y2 - yStar);
wt2 = k * (x2 - xStar) * (yStar - y1);
wt3 = k * (xStar - x1) * (y2 - yStar);
wt4 = k * (xStar - x1) * (yStar - y1);
double zStar = wt1 * p1.Z + wt2 * p2.Z + wt3 * p3.Z + wt4 * p4.Z;
return(zStar);
}
public bool Equals(ThreeDPoint point)
{
return(point.X == X && point.Y == Y && point.Z == Z);
}