add functions to compute direction cosines of wrt local coords origin

git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinAnalysis/AHFinderDirect/trunk@561 f88db872-0e4f-0410-b76b-b9085cfa78c5

3 files changed, 92 insertions, 1 deletions

diff --git a/src/patch/coords.cc b/src/patch/coords.cc
index f209abf..473e375 100644
--- a/src/patch/coords.cc
+++ b/src/patch/coords.cc
@@ -13,6 +13,7 @@
 //
 // usual polar spherical (r,theta,phi) <--> (x,y,z)
 // ((mu,nu,phi)) <--> usual polar spherical (theta,phi)
+// ((mu,nu,phi)) --> direction cosines (alpha,beta,gamma)
 //
 // local_coords::mu_nu_phi::name_of_coords_set
 //
@@ -422,6 +423,49 @@ assert( fuzzy_EQ_ang(phi, ps_phi) );
 	  }
 
 //******************************************************************************
+
+//
+// these functions convert ((mu,nu,phi)) to the direction cosines
+// (alpha,beta,gamma)
+//
+
+namespace local_coords
+	  {
+void alpha_beta_gamma_of_mu_nu (fp mu, fp nu , fp& alpha, fp& beta, fp& gamma)
+{
+fp x, y, z;
+xyz_of_r_mu_nu(1.0,mu,nu, x,y,z);
+alpha = x;
+beta  = y;
+gamma = z;
+}
+	  }
+
+namespace local_coords
+	  {
+void alpha_beta_gamma_of_mu_phi(fp mu, fp phi, fp& alpha, fp& beta, fp& gamma)
+{
+fp x, y, z;
+xyz_of_r_mu_phi(1.0,mu,phi, x,y,z);
+alpha = x;
+beta  = y;
+gamma = z;
+}
+	  }
+
+namespace local_coords
+	  {
+void alpha_beta_gamma_of_nu_phi(fp nu, fp phi, fp& alpha, fp& beta, fp& gamma)
+{
+fp x, y, z;
+xyz_of_r_nu_phi(1.0,nu,phi, x,y,z);
+alpha = x;
+beta  = y;
+gamma = z;
+}
+	  }
+
+//******************************************************************************
 //******************************************************************************
 //******************************************************************************
 
diff --git a/src/patch/coords.hh b/src/patch/coords.hh
index 3f81bba..f101b1f 100644
--- a/src/patch/coords.hh
+++ b/src/patch/coords.hh
@@ -53,6 +53,13 @@
 //
 
 //
+// We also use direction cosines (alpha,beta,gamma):
+// alpha = x/r = cos(angle between vector from origin to (x,y,z), and x axis)
+// beta  = y/r = cos(angle between vector from origin to (x,y,z), and y axis)
+// gamma = z/r = cos(angle between vector from origin to (x,y,z), and z axis)
+//
+
+//
 // We also use prefixes on coordinates, eg.
 //	irho		integer grid coordinate
 //	 rho		floating point angular coordinate, measured in radians
@@ -122,7 +129,6 @@ fp modulo_reduce_dang(fp dang, fp min_dang, fp max_dang);
 
 namespace local_coords
 	  {
-
 // (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);
@@ -171,6 +177,10 @@ 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);
 
+// ((mu,nu,phi)) --> direction cosines (alpha,beta,gamma)
+void alpha_beta_gamma_of_mu_nu (fp mu, fp nu , fp& alpha, fp& beta, fp& gamma);
+void alpha_beta_gamma_of_mu_phi(fp mu, fp phi, fp& alpha, fp& beta, fp& gamma);
+void alpha_beta_gamma_of_nu_phi(fp nu, fp phi, fp& alpha, fp& beta, fp& gamma);
 	  };	// close namespace local_coords::
 
 //*****************************************************************************
diff --git a/src/patch/patch.hh b/src/patch/patch.hh
index 5bae6cb..9364d4b 100644
--- a/src/patch/patch.hh
+++ b/src/patch/patch.hh
@@ -211,6 +211,13 @@ public:
 	virtual fp   rho_of_xyz(fp x, fp y, fp z) const = 0;
 	virtual fp sigma_of_xyz(fp x, fp y, fp z) const = 0;
 
+	// convert (rho,sigma) --> direction cosines (alpha,beta,gamma)
+	//                         with respect to the local coordinate system
+	virtual void alpha_beta_gamma_of_rho_sigma
+		(fp rho, fp sigma,
+		 fp& alpha, fp& beta, fp& gamma)
+		const = 0;
+
 	// partial (rho,sigma) / partial (x,y,z)
 	virtual fp partial_rho_wrt_x(fp x, fp y, fp z) const = 0;
 	virtual fp partial_rho_wrt_y(fp x, fp y, fp z) const = 0;
@@ -573,6 +580,16 @@ public:
 	fp sigma_of_xyz(fp x, fp y, fp z) const
 		{ return local_coords::nu_of_xz(x,z); }
 
+	// convert (rho,sigma) --> direction cosines (alpha,beta,gamma)
+	//                         with respect to the local coordinate system
+	void alpha_beta_gamma_of_rho_sigma(fp rho, fp sigma,
+					   fp& alpha, fp& beta, fp& gamma)
+		const
+		{
+		local_coords::alpha_beta_gamma_of_mu_nu(rho,sigma,
+							alpha,beta,gamma);
+		}
+
 	// partial (rho,sigma) / partial (x,y,z)
 	fp partial_rho_wrt_x(fp x, fp y, fp z) const { return 0.0; }
 	fp partial_rho_wrt_y(fp x, fp y, fp z) const
@@ -685,6 +702,16 @@ public:
 	fp sigma_of_xyz(fp x, fp y, fp z) const
 		{ return local_coords::phi_of_xy(x, y); }
 
+	// convert (rho,sigma) --> direction cosines (alpha,beta,gamma)
+	//                         with respect to the local coordinate system
+	void alpha_beta_gamma_of_rho_sigma(fp rho, fp sigma,
+					   fp& alpha, fp& beta, fp& gamma)
+		const
+		{
+		local_coords::alpha_beta_gamma_of_nu_phi(rho,sigma,
+							 alpha,beta,gamma);
+		}
+
 	// partial (rho,sigma) / partial (x,y,z)
 	fp partial_rho_wrt_x(fp x, fp y, fp z) const
 		{ return local_coords::partial_nu_wrt_x(x,z); }
@@ -799,6 +826,16 @@ public:
 	fp sigma_of_xyz(fp x, fp y, fp z) const
 		{ return local_coords::phi_of_xy(x, y); }
 
+	// convert (rho,sigma) --> direction cosines (alpha,beta,gamma)
+	//                         with respect to the local coordinate system
+	void alpha_beta_gamma_of_rho_sigma(fp rho, fp sigma,
+					   fp& alpha, fp& beta, fp& gamma)
+		const
+		{
+		local_coords::alpha_beta_gamma_of_mu_phi(rho,sigma,
+							 alpha,beta,gamma);
+		}
+
 	// partial (rho,sigma) / partial (x,y,z)
 	fp partial_rho_wrt_x(fp x, fp y, fp z) const { return 0.0; }
 	fp partial_rho_wrt_y(fp x, fp y, fp z) const