double GLGPU3DDataset::Flux(int face) const
{
// TODO: pre-compute the flux
switch (face) {
case 0: return -dx() * dy() * Bz();
case 1: return -dy() * dz() * Bx();
case 2: return -dz() * dx() * By();
case 3: return dx() * dy() * Bz();
case 4: return dy() * dz() * Bx();
case 5: return dz() * dx() * By();
default: assert(false);
}
return 0.0;
}
float GLGPUDataset::QP(const float X0[], const float X1[]) const
{
const float *L = Lengths(),
*O = Origins();
float d[3] = {X1[0] - X0[0], X1[1] - X0[1], X1[2] - X0[2]};
int p[3] = {0}; // 0: not crossed; 1: positive; -1: negative
for (int i=0; i<3; i++) {
d[i] = X1[i] - X0[i];
if (d[i]>L[i]/2) {d[i] -= L[i]; p[i] = 1;}
else if (d[i]<-L[i]/2) {d[i] += L[i]; p[i] = -1;}
}
const float X[3] = {X0[0] - O[0], X0[1] - O[1], X0[2] - O[2]};
if (By()>0 && p[0]!=0) { // By>0
return p[0] * L[0] * (Bz()*X[1] - By()*X[2]);
} else if (p[1]!=0) {
return p[1] * L[1] * (Bx()*X[2] - Bz()*X[0]);
} else return 0.0;
}
double GLGPU3DDataset::GaugeTransformation(const double X0[], const double X1[]) const
{
double gx, gy, gz;
double dx = X1[0] - X0[0],
dy = X1[1] - X0[1],
dz = X1[2] - X0[2];
double x = X0[0] + 0.5*dx,
y = X0[1] + 0.5*dy,
z = X0[2] + 0.5*dz;
if (By()>0) { // Y-Z gauge
gx = dx * Kex();
gy =-dy * x * Bz(); // -dy*x^hat*Bz
gz = dz * x * By(); // dz*x^hat*By
} else { // X-Z gauge
gx = dx * y * Bz() + dx * Kex(); // dx*y^hat*Bz + dx*K
gy = 0;
gz =-dz * y * Bx(); // -dz*y^hat*Bx
}
return gx + gy + gz;
}
// float Ax(const float X[3], int slot=0) const {if (By()>0) return 0; else return -X[1]*Bz();}
float Ay(const float X[3], int slot=0) const {if (By()>0) return X[0]*Bz(); else return 0;}
float Ax(const float X[3], int slot=0) const {if (By()>0) return -Kex(slot); else return -X[1]*Bz()-Kex(slot);}