void radial_limits( const Real eps, const Real L, Real Rlimits[2] ) {
// Solve third order polynomial:
double results[MAXDEGREE] = {0};
double results_im[MAXDEGREE] = {0};
double coeffs[MDP1];
int degree = 3;
// See limits_r.nb
// We first solve limits for u=1/Rmax
// c[0]u^3+...
coeffs[0] = (pow(L,4) * Rs)
/ pow(eps,2);
coeffs[1] = -1 * pow(L,4)
/ pow(eps,2);
coeffs[2] = pow(L,2) * Rs
/ pow(eps,2);
coeffs[3] = ( pow(L,2)- pow(L,2)/pow(eps,2) );
// Solve:
rpoly_ak1(coeffs, °ree, results, results_im);
// Check results:
for( int i = 0; i < 3; ++i ) { if( results_im[i] != 0) {
Rlimits[0]=ERROR; Rlimits[1]=ERROR; return;} }
if( results[0] <= 0 ) { Rlimits[0]=ERROR; Rlimits[1]=ERROR; cout << "bad data" << endl; return;}
if( results[0] > results[1]){ Rlimits[0]=ERROR; Rlimits[1]=ERROR; cout << "errordata" << endl; return; }
Rlimits[0] = 1.0/results[1];
Rlimits[1] = 1.0/results[0];
assert( Rlimits[1] >= Rlimits[0] );
return;
}
void omni3d2pixel( double &x, double &y, const Eigen::Vector3d &xx, int length_poly, double *ss, int width, int height )
{
// convert 3D coordinates vector into 2D pixel coordinates
double denom = sqrt( xx[0]*xx[0] + xx[1]*xx[1] );
double m = xx[2] / denom;
double rho = 0;
double *op = (double*) malloc( sizeof(double)*length_poly );
for ( int i = 0; i < length_poly; i++ ) op[i] = ss[ length_poly - 1 - i ];
op[length_poly - 2] = op[length_poly - 2] - m;
int degree = length_poly - 1;
double zeror[MAXDEGREE];
double zeroi[MAXDEGREE];
rpoly_ak1( op, °ree, zeror, zeroi );
free(op);
for ( int i = 0; i < degree; i++ ) {
if ( zeroi[i] == 0 && zeror[i] > 0 && zeror[i] < height ) {
rho = zeror[i];
break;
}
}
x = xx[0] / denom * rho ;
y = xx[1] / denom * rho ;
}
void u_limits( const Real eps, const Real L, Real ulimits[2] ) {
// Solve third order polynomial:
double results[MAXDEGREE] = {0};
double results_im[MAXDEGREE] = {0};
double coeffs[MDP1];
int degree = 3;
// See FourVelocity.nb
// We first solve limits for u
// c[0]u^3+...
const Real mp= 1; // Mass of the particle
const Real c = 1; // Speed of light
coeffs[0] = -1.*(pow(L,4) * Rs)
/ (pow(eps,2)*pow(mp,2));
coeffs[1] = pow(L,4)
/ (pow(eps,2)*pow(mp,2));
coeffs[2] = -1.*pow(c,2) * pow(L,2) * Rs
/ pow(eps,2);
coeffs[3] = ( pow(c,2) * pow(L,2) )
/ pow(eps,2)
-
pow(L,2)
/ ( pow(c,2) * pow(mp,2) );
// Solve:
rpoly_ak1(coeffs, °ree, results, results_im);
// Check results:
for( int i = 0; i < 3; ++i ) {
if( results_im[i] != 0) { ulimits[0]=ERROR; ulimits[1]=ERROR; return;}
}
if( results[0] <= 0 ) { ulimits[0]=ERROR; ulimits[1]=ERROR; cout << "bad data" << endl; return;}
if( results[0] > results[1]){ ulimits[0]=ERROR; ulimits[1]=ERROR; cout << "errordata" << endl; return; }
ulimits[0] = results[0];
ulimits[1] = results[1];
assert( ulimits[1] >= ulimits[0] );
return;
}
