static Matrix GetIntegratedBasisMatrix(Triangle triangle, List <Point> points)
{
double triangleSquare = MinimalAngleAlgorithm.getTriangleSquare(triangle, points);
double[ , ] res = new double[3, 3]
{
{ 2, 1, 1 },
{ 1, 2, 1 },
{ 1, 1, 2 },
};
return((2 * triangleSquare) / 24.0 * (new Matrix(res)));
}
static Matrix FormatGrammMatrix(Triangle triangle, List <Point> points, Matrix A)
{
double triangleSquare = 2 * MinimalAngleAlgorithm.getTriangleSquare(triangle, points);
Matrix res = new Matrix(3, 3);
Point p1 = points[triangle.A];
Point p2 = points[triangle.B];
Point p3 = points[triangle.C];
double bi = p2.Y - p3.Y;
double ci = p3.X - p2.X;
double bj = p3.Y - p1.Y;
double cj = p1.X - p3.X;
double bm = p1.Y - p2.Y;
double cm = p2.X - p1.X;
res[0, 0] = 1 / (2.0 * triangleSquare) * (A[0, 0] * bi * bi + A[1, 1] * ci * ci);
res[0, 1] = res[1, 0] = 1 / (2.0 * triangleSquare) * (A[0, 0] * bi * bj + A[1, 1] * ci * cj);
res[0, 2] = res[2, 0] = 1 / (2.0 * triangleSquare) * (A[0, 0] * bi * bm + A[1, 1] * ci * cm);
res[1, 1] = 1 / (2.0 * triangleSquare) * (A[0, 0] * bj * bj + A[1, 1] * cj * cj);
res[1, 2] = res[2, 1] = 1 / (2.0 * triangleSquare) * (A[0, 0] * bj * bm + A[1, 1] * cj * cm);
res[2, 2] = 1 / (2.0 * triangleSquare) * (A[0, 0] * bm * bm + A[1, 1] * cm * cm);
return(res);
}
