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// coords.hh -- coordinate systems and conversions
// $Id$
//
// ***** coordinate systems *****
// ***** conversions between different local coordinate systems *****
// ***** bit masks for coordinates ****
// global_coords - conversions between global and local coordinates
//
//
// prerequisites:
// "jt/util++.hh"
// fp.hh
//
//******************************************************************************
//
// ***** coordinate systems *****
//
//
// We use the following terminology for coordinates:
// {a,b,c} == any one of (a,b,c) == a | b | c
// ((a,b,c)) == any two of (a,b,c) == (a,b) | (a,c) | (b,c)
// (r,(a,b,c)) == r and any two of (a,b,c) == (r,a,b) | (r,a,c) | (r,b,c)
//
//
// We use the following coordinates and coordinate systems:
// global_(x,y,z) global Cartesian x,y,z coordinates
// (these are the coordinates Cactus gives us)
// (x,y,z) local Cartesian x,y,z coordinates relative to a
// local origin point (stored in this object);
// This origin should be chosen to be somewhere
// at least vaguely in the "middle" of our
// apparent horizon
// (r,theta,phi) polar spherical coordinates about the local
// origin point
// (r,(mu,nu,phi)) patch coordinates about the local origin point
// mu arctan(y/z) = rotation about local x axis
// nu arctan(x/z) = rotation about local y axis
// phi arctan(y/x) = rotation about local z axis
// = usual polar spherical phi
// (rho,sigma) generic patch angular coordinates, these will
// be whichever two of (mu,nu,phi) are nonsingular
// throughout the patch
// tau the third member of (mu,nu,phi) (the one which
// is neither rho nor sigma)
// (perp,par) (rho,sigma) coordinates (perpendicular,parallel)
// to a patch boundary; these are defined by class
// patch_edge and used by a lot of the boundary code
//
//
// We also use prefixes on coordinates, eg.
// irho integer grid coordinate
// rho floating point angular coordinate, measured in radians
// drho floating point angular coordinate, measured in degrees
// I/O uses the degree coordinates in preference to radian ones.
//
//
// We also define plotting coordinates (px,py) (in both fp and degrees-fp
// variants), based on the conventional "looking down the z axis" picture
// of a patch system. Unfortunately there's no good place to stick a -z
// patch in this scheme, so we arbitrarily put it just beyond the +x patch:
//
// py axis
// |
// +-------+
// | |
// | +y |
// | |
// +-------+-------+-------+-------+
// | | | | |
// --| -x | +z | +x | -z |-- px axis
// | | | | |
// +-------+-------+-------+-------+
// | |
// | -y |
// | |
// +-------+
// |
//
// The main (in fact only) use of these coordinates is in their degrees
// forms (dpx,dpy), for I/O and constructor arguments.
//
//*****************************************************************************
//
// ***** conversions between different local coordinate systems *****
//
// Bugs:
// These functions aren't optimally efficient: they do lots
// of could-be-optimized away arithmetic and trig calls. But
// In practice this doesn't matter, since we don't call these
// functions inside inner loops (instead, we cache their values
// at grid points).
//
namespace local_coords
{
// ((mu,nu,phi)) --> the 3rd
fp phi_of_mu_nu(fp mu, fp nu );
fp nu_of_mu_phi(fp mu, fp phi);
fp mu_of_nu_phi(fp nu, fp phi);
// (r,(mu,nu,phi)) <--> (x,y,z)
void xyz_of_r_mu_nu (fp r, fp mu, fp nu , fp& x, fp& y, fp& z);
void xyz_of_r_mu_phi(fp r, fp mu, fp phi, fp& x, fp& y, fp& z);
void xyz_of_r_nu_phi(fp r, fp nu, fp phi, fp& x, fp& y, fp& z);
void r_mu_nu_of_xyz(fp x, fp y, fp z, fp& r, fp& mu, fp& nu );
void r_mu_phi_of_xyz(fp x, fp y, fp z, fp& r, fp& mu, fp& phi);
void r_nu_phi_of_xyz(fp x, fp y, fp z, fp& r, fp& nu, fp& phi);
// usual polar spherical (r,theta,phi) <--> (x,y,z)
void xyz_of_r_theta_phi(fp r, fp theta, fp phi, fp& x, fp& y, fp& z);
void r_theta_phi_of_xyz(fp x, fp y, fp z, fp& r, fp& theta, fp& phi);
// ((mu,nu,phi)) <--> usual polar spherical (theta,phi)
// ... note phi is the same coordinate in both systems
void theta_phi_of_mu_nu (fp mu, fp nu , fp& ps_theta, fp& ps_phi);
void theta_phi_of_mu_phi(fp mu, fp phi, fp& ps_theta, fp& ps_phi);
void theta_phi_of_nu_phi(fp nu, fp phi, fp& ps_theta, fp& ps_phi);
void mu_nu_of_theta_phi(fp ps_theta, fp ps_phi, fp& mu, fp& nu );
void mu_phi_of_theta_phi(fp ps_theta, fp ps_phi, fp& mu, fp& phi);
void nu_phi_of_theta_phi(fp ps_theta, fp ps_phi, fp& nu, fp& phi);
}; // close namespace local_coords::
//*****************************************************************************
//
// ***** bit masks for coordinates ****
//
//
// We need to manipulate coordinates to do calculations like "which
// coordinate do these two patches have in common". We do these by
// Boolean operations on integers using the following bit masks:
//
namespace local_coords
{
typedef int coords_set;
static const int set_mu = 0x1;
static const int set_nu = 0x2;
static const int set_phi = 0x4;
static const int set_empty = 0x0;
static const int set_all = set_mu | set_nu | set_phi;
// human-readable coordinate names for debugging etc
const char *name_of_coords_set(coords_set S);
// set complement of coordinates
inline
coords_set coords_set_not(coords_set S)
{ return set_all & ~S; }
}; // close namespace local_coords::
//******************************************************************************
//
// This class stores the origin point of our local coordinates, and
// provides conversions between local and global coordinates.
//
class global_coords
{
public:
// global (x,y,z) --> local (x,y,z)
fp local_x_of_global_x(fp global_x) const
{ return global_x - origin_x_; }
fp local_y_of_global_y(fp global_y) const
{ return global_y - origin_y_; }
fp local_z_of_global_z(fp global_z) const
{ return global_z - origin_z_; }
// local (x,y,z) --> global (x,y,z)
fp global_x_of_local_x(fp local_x) const
{ return origin_x_ + local_x; }
fp global_y_of_local_y(fp local_y) const
{ return origin_y_ + local_y; }
fp global_z_of_local_z(fp local_z) const
{ return origin_z_ + local_z; }
// get global (x,y,z) coordinates of local origin point
fp origin_x() const { return origin_x_; }
fp origin_y() const { return origin_y_; }
fp origin_z() const { return origin_z_; }
// constructor: specify global (x,y,z) coordinates of local origin point
global_coords(fp origin_x_in, fp origin_y_in, fp origin_z_in)
: origin_x_(origin_x_in),
origin_y_(origin_y_in),
origin_z_(origin_z_in)
{ }
// destructor: compiler-generated no-op is ok
private:
// we forbid copying and passing by value
// by declaring the copy constructor and assignment operator
// private, but never defining them
global_coords(const global_coords& rhs);
global_coords& operator=(const global_coords& rhs);
private:
// global (x,y,z) coordinates of local origin point
fp origin_x_, origin_y_, origin_z_;
};
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