private PolygonIntegrals GetPolygonIntegrals(int polyNumber, int a, int b, int c)
{
ProjectionIntegrals pi = GetProjectionIntegrals(polyNumber, a, b);
Vector3 n = _polygons[polyNumber].Normal;
float w = -_polygons[polyNumber].Distance;
float k1 = 1.0f / n.Get(c);
float k2 = k1 * k1;
float k3 = k2 * k1;
float k4 = k3 * k1;
PolygonIntegrals integrals = new PolygonIntegrals();
integrals.Fa = k1 * pi.Pa;
integrals.Fb = k1 * pi.Pb;
integrals.Fc = -k2 * (n.Get(a) * pi.Pa + n.Get(b) * pi.Pb + w * pi.P1);
integrals.Faa = k1 * pi.Paa;
integrals.Fbb = k1 * pi.Pbb;
integrals.Fcc = k3 * (idMath.Square(n.Get(a)) * pi.Paa + 2 * n.Get(a) * n.Get(b) * pi.Pab + idMath.Square(n.Get(b)) * pi.Pbb
+ w * (2 * (n.Get(a) * pi.Pa + n.Get(b) * pi.Pb) + w * pi.P1));
integrals.Faaa = k1 * pi.Paaa;
integrals.Fbbb = k1 * pi.Pbbb;
integrals.Fccc = -k4 * (idMath.Cube(n.Get(a)) * pi.Paaa + 3 * idMath.Square(n.Get(a)) * n.Get(b) * pi.Paab
+ 3 * n.Get(a) * idMath.Square(n.Get(b)) * pi.Pabb + idMath.Cube(n.Get(b)) * pi.Pbbb
+ 3 * w * (idMath.Square(n.Get(a)) * pi.Paa + 2 * n.Get(a) * n.Get(b) * pi.Pab + idMath.Square(n.Get(b)) * pi.Pbb)
+ w * w * (3 * (n.Get(a) * pi.Pa + n.Get(b) * pi.Pb) + w * pi.P1));
integrals.Faab = k1 * pi.Paab;
integrals.Fbbc = -k2 * (n.Get(a) * pi.Pabb + n.Get(b) * pi.Pbbb + w * pi.Pbb);
integrals.Fcca = k3 * (idMath.Square(n.Get(a)) * pi.Paaa + 2 * n.Get(a) * n.Get(b) * pi.Paab + idMath.Square(n.Get(b)) * pi.Pabb
+ w * (2 * (n.Get(a) * pi.Paa + n.Get(b) * pi.Pab) + w * pi.Pa));
return(integrals);
}
private ProjectionIntegrals GetProjectionIntegrals(int polyNumber, int a, int b)
{
ProjectionIntegrals integrals = new ProjectionIntegrals();
TraceModelPolygon polygon = _polygons[polyNumber];
int count = polygon.Edges.Length;
for(int i = 0; i < count; i++)
{
int edgeNumber = polygon.Edges[i];
Vector3 v1 = _vertices[_edges[(int) idMath.Abs(edgeNumber)].V[(edgeNumber < 0) ? 1 : 0]];
Vector3 v2 = _vertices[_edges[(int) idMath.Abs(edgeNumber)].V[(edgeNumber > 0) ? 1 : 0]];
float a0 = v1.Get(a);
float b0 = v1.Get(b);
float a1 = v2.Get(a);
float b1 = v2.Get(b);
float da = a1 - a0;
float db = b1 - b0;
float a0_2 = a0 * a0;
float a0_3 = a0_2 * a0;
float a0_4 = a0_3 * a0;
float b0_2 = b0 * b0;
float b0_3 = b0_2 * b0;
float b0_4 = b0_3 * b0;
float a1_2 = a1 * a1;
float a1_3 = a1_2 * a1;
float b1_2 = b1 * b1;
float b1_3 = b1_2 * b1;
float C1 = a1 + a0;
float Ca = a1 * C1 + a0_2;
float Caa = a1 * Ca + a0_3;
float Caaa = a1 * Caa + a0_4;
float Cb = b1 * (b1 + b0) + b0_2;
float Cbb = b1 * Cb + b0_3;
float Cbbb = b1 * Cbb + b0_4;
float Cab = 3 * a1_2 + 2 * a1 * a0 + a0_2;
float Kab = a1_2 + 2 * a1 * a0 + 3 * a0_2;
float Caab = a0 * Cab + 4 * a1_3;
float Kaab = a1 * Kab + 4 * a0_3;
float Cabb = 4 * b1_3 + 3 * b1_2 * b0 + 2 * b1 * b0_2 + b0_3;
float Kabb = b1_3 + 2 * b1_2 * b0 + 3 * b1 * b0_2 + 4 * b0_3;
integrals.P1 += db * C1;
integrals.Pa += db * Ca;
integrals.Paa += db * Caa;
integrals.Paaa += db * Caaa;
integrals.Pb += da * Cb;
integrals.Pbb += da * Cbb;
integrals.Pbbb += da * Cbbb;
integrals.Pab += db * (b1 * Cab + b0 * Kab);
integrals.Paab += db * (b1 * Caab + b0 * Kaab);
integrals.Pabb += da * (a1 * Cabb + a0 * Kabb);
}
integrals.P1 *= (1.0f / 2.0f);
integrals.Pa *= (1.0f / 6.0f);
integrals.Paa *= (1.0f / 12.0f);
integrals.Paaa *= (1.0f / 20.0f);
integrals.Pb *= (1.0f / -6.0f);
integrals.Pbb *= (1.0f / -12.0f);
integrals.Pbbb *= (1.0f / -20.0f);
integrals.Pab *= (1.0f / 24.0f);
integrals.Paab *= (1.0f / 60.0f);
integrals.Pabb *= (1.0f / -60.0f);
return integrals;
}
private ProjectionIntegrals GetProjectionIntegrals(int polyNumber, int a, int b)
{
ProjectionIntegrals integrals = new ProjectionIntegrals();
TraceModelPolygon polygon = _polygons[polyNumber];
int count = polygon.Edges.Length;
for (int i = 0; i < count; i++)
{
int edgeNumber = polygon.Edges[i];
Vector3 v1 = _vertices[_edges[(int)idMath.Abs(edgeNumber)].V[(edgeNumber < 0) ? 1 : 0]];
Vector3 v2 = _vertices[_edges[(int)idMath.Abs(edgeNumber)].V[(edgeNumber > 0) ? 1 : 0]];
float a0 = v1.Get(a);
float b0 = v1.Get(b);
float a1 = v2.Get(a);
float b1 = v2.Get(b);
float da = a1 - a0;
float db = b1 - b0;
float a0_2 = a0 * a0;
float a0_3 = a0_2 * a0;
float a0_4 = a0_3 * a0;
float b0_2 = b0 * b0;
float b0_3 = b0_2 * b0;
float b0_4 = b0_3 * b0;
float a1_2 = a1 * a1;
float a1_3 = a1_2 * a1;
float b1_2 = b1 * b1;
float b1_3 = b1_2 * b1;
float C1 = a1 + a0;
float Ca = a1 * C1 + a0_2;
float Caa = a1 * Ca + a0_3;
float Caaa = a1 * Caa + a0_4;
float Cb = b1 * (b1 + b0) + b0_2;
float Cbb = b1 * Cb + b0_3;
float Cbbb = b1 * Cbb + b0_4;
float Cab = 3 * a1_2 + 2 * a1 * a0 + a0_2;
float Kab = a1_2 + 2 * a1 * a0 + 3 * a0_2;
float Caab = a0 * Cab + 4 * a1_3;
float Kaab = a1 * Kab + 4 * a0_3;
float Cabb = 4 * b1_3 + 3 * b1_2 * b0 + 2 * b1 * b0_2 + b0_3;
float Kabb = b1_3 + 2 * b1_2 * b0 + 3 * b1 * b0_2 + 4 * b0_3;
integrals.P1 += db * C1;
integrals.Pa += db * Ca;
integrals.Paa += db * Caa;
integrals.Paaa += db * Caaa;
integrals.Pb += da * Cb;
integrals.Pbb += da * Cbb;
integrals.Pbbb += da * Cbbb;
integrals.Pab += db * (b1 * Cab + b0 * Kab);
integrals.Paab += db * (b1 * Caab + b0 * Kaab);
integrals.Pabb += da * (a1 * Cabb + a0 * Kabb);
}
integrals.P1 *= (1.0f / 2.0f);
integrals.Pa *= (1.0f / 6.0f);
integrals.Paa *= (1.0f / 12.0f);
integrals.Paaa *= (1.0f / 20.0f);
integrals.Pb *= (1.0f / -6.0f);
integrals.Pbb *= (1.0f / -12.0f);
integrals.Pbbb *= (1.0f / -20.0f);
integrals.Pab *= (1.0f / 24.0f);
integrals.Paab *= (1.0f / 60.0f);
integrals.Pabb *= (1.0f / -60.0f);
return(integrals);
}
