public static bool IsInsideTriangle(Coords2D _xyA, Coords2D _xyB, Coords2D _xyC, Coords2D _xy, bool _check_triangle = false)
{
if (_check_triangle)
{
if (!Coords2D.InGeneralPosition(_xyA, _xyB, _xyC))
{
return(false);
}
}
if (_xyA == null || _xyB == null || _xyC == null)
{
return(false);
}
double diff_xA = _xy.X - _xyA.X;
double diff_xB = _xy.X - _xyB.X;
double diff_xC = _xy.X - _xyC.X;
bool inside_x = (Math.Sign(diff_xA) != Math.Sign(diff_xB)) || (Math.Sign(diff_xA) != Math.Sign(diff_xC));
double diff_yA = _xy.Y - _xyA.Y;
double diff_yB = _xy.Y - _xyB.Y;
double diff_yC = _xy.Y - _xyC.Y;
bool inside_y = (Math.Sign(diff_yA) != Math.Sign(diff_yB)) || (Math.Sign(diff_yA) != Math.Sign(diff_yC));
return(inside_x && inside_y);
}
public static void GetBarycentricCoords(Coords2D _xyA, Coords2D _xyB, Coords2D _xyC, Coords2D _xy,
out double a, out double b, out double c)
{
a = double.NaN;
b = double.NaN;
c = double.NaN;
if (!Coords2D.IsInsideTriangle(_xyA, _xyB, _xyC, _xy, true))
{
return;
}
// solving the eq system:
// _xy.X = a * _xyA.X + b * _xyB.X + (1 - a - b) * _xyC.X
// _xy.Y = a * _xyA.Y + b * _xyB.Y + (1 - a - b) * _xyC.Y
double denominator = (_xyB.Y - _xyC.Y) * (_xyA.X - _xyC.X) + (_xyC.X - _xyB.X) * (_xyA.Y - _xyC.Y);
if (Math.Abs(denominator) < Calculation.MIN_DOUBLE_VAL)
{
return;
}
a = ((_xyB.Y - _xyC.Y) * (_xy.X - _xyC.X) + (_xyC.X - _xyB.X) * (_xy.Y - _xyC.Y)) / denominator;
b = ((_xy.Y - _xyC.Y) * (_xyA.X - _xyC.X) + (_xyC.X - _xy.X) * (_xyA.Y - _xyC.Y)) / denominator;
c = 1 - a - b;
}
private static Dictionary <Coords2D, double> Lists2Func2D(List <double> _xs, List <double> _ys, List <double> _zs)
{
if (_xs == null || _ys == null || _zs == null)
{
return(null);
}
int n = _xs.Count;
if (n < 1 || n != _ys.Count || n != _zs.Count)
{
return(new Dictionary <Coords2D, double>());
}
Dictionary <Coords2D, double> Fxy = new Dictionary <Coords2D, double>();
for (int i = 0; i < n; i++)
{
Coords2D xy = new Coords2D(_xs[i], _ys[i]);
if (Fxy.ContainsKey(xy))
{
continue;
}
Fxy.Add(xy, _zs[i]);
}
return(Fxy);
}
public static bool InGeneralPosition(Coords2D _xy1, Coords2D _xy2)
{
if (_xy1 == null || _xy2 == null)
{
return(false);
}
double diffX = _xy1.X - _xy2.X;
double diffY = _xy1.Y - _xy2.Y;
return(Math.Abs(diffX) >= Calculation.MIN_DOUBLE_VAL || Math.Abs(diffY) >= Calculation.MIN_DOUBLE_VAL);
}
public static bool InGeneralPosition(Coords2D _xy1, Coords2D _xy2, Coords2D _xy3)
{
return(Coords2D.InGeneralPosition(_xy1, _xy2) &&
Coords2D.InGeneralPosition(_xy2, _xy3) &&
Coords2D.InGeneralPosition(_xy3, _xy1));
}
public static double Interpolate2D(Coords2D _xy, List <Coords2D> _XYs, List <double> _Zs)
{
Dictionary <Coords2D, double> Fxy = Lists2Func2D(_XYs, _Zs);
return(Interpolate2D(_xy, Fxy));
}
private static double Interpolate2D(Coords2D _xy, Dictionary <Coords2D, double> _Fxy)
{
if (_Fxy == null || _Fxy.Count < 3)
{
return(double.NaN);
}
// find closest xy values
SortedList <double, Coords2D> distances = new SortedList <double, Coords2D>();
foreach (Coords2D xy_current in _Fxy.Keys)
{
double dist = Math.Abs(_xy.X - xy_current.X) + Math.Abs(_xy.Y - xy_current.Y);
distances.Add(dist, xy_current);
}
// construct the smallest well-defined triangle containing _xy
Coords2D xyA = distances.ElementAt(0).Value;
Coords2D xyB = distances.ElementAt(1).Value;
int i = 1;
if (!Coords2D.InGeneralPosition(xyA, xyB))
{
for (; i < distances.Count; i++)
{
xyB = distances.ElementAt(i).Value;
if (Coords2D.InGeneralPosition(xyA, xyB))
{
break;
}
}
}
if (!Coords2D.InGeneralPosition(xyA, xyB))
{
return(double.NaN);
}
Coords2D xyC = null;
for (int j = 1; j < distances.Count && j != i; j++)
{
xyC = distances.ElementAt(j).Value;
if (Coords2D.InGeneralPosition(xyA, xyB, xyC) && Coords2D.IsInsideTriangle(xyA, xyB, xyC, _xy, false))
{
break;
}
}
if (!Coords2D.InGeneralPosition(xyA, xyB, xyC) || !Coords2D.IsInsideTriangle(xyA, xyB, xyC, _xy, false))
{
return(double.NaN);
}
// perform actual interpolation
double a, b, c;
Coords2D.GetBarycentricCoords(xyA, xyB, xyC, _xy, out a, out b, out c);
if (double.IsNaN(a) || double.IsNaN(b) || double.IsNaN(c))
{
return(double.NaN);
}
return(a * _Fxy[xyA] + b * _Fxy[xyB] + c * _Fxy[xyC]);
}