functions in rays.i -

             best_rays(rays)  
 
     returns 5-element (x,y,z,theta,phi) representation of RAYS.  
     The first dimension of RAYS may be length 3, 5, or 6 to represent  
     the ray(s) in TDG/DIRT coordinates (x,y,theta), "best" coordinates  
     (x,y,z,theta,phi), or internal coordinates (cos,sin,y,z,x,r),  
     respectively.  The first dimension of the result always has length 5.  
     The "best" coordinate system is the easiest to visualize:  
     (x,y,z) represents any point on the ray, while (theta,phi)  
     represents the ray direction in standard spherical coordinates  
     relative to the +z-axis.  Namely, theta is the angle from the  
     +z-direction to the ray direction (between 0 and pi), and phi is  
     the counterclockwise angle from the +x-axis to the projection of  
     the ray direction into the xy-plane, assuming xyz is a right-handed  
     coordinate system.  
     As a specification of a ray, this system is doubly redundant because  
     the point (x,y,z) could be any point on the ray, and the underlying  
     mesh through which the ray propagates is cylindrically symmetric about  
     the z-axis.  
     However, the slimits parameter -- used to specify the points along  
     a ray where the transport integration starts and stops -- is  
     measured from the point (x,y,z) specified as a part of the  
     (x,y,z,theta,phi) ray coordinate.  Thus, any change in the point  
     (x,y,z) on a ray must be accompanied by a corresponding change in  
     the slimits for that ray.  

             dirt_rays(rays)  
 
     returns 3-element (x,y,theta) representation of RAYS.  
     The first dimension of RAYS may be length 3, 5, or 6 to represent  
     the ray(s) in TDG/DIRT coordinates (x,y,theta), "best" coordinates  
     (x,y,z,theta,phi), or internal coordinates (cos,sin,y,z,x,r),  
     respectively.  The first dimension of the result always has length 3.  
     The TDG/DIRT coordinate system is based on the coordinates (x,y)  
     in a plane normal to the ray.  Unfortunately, the old TDG and DIRT  
     codes used an angle theta which has the opposite sense from the  
     "best" and internal coordinates.  Therefore, conversion from  
     TDG/DIRT coordinates to internal coordinates will reverse the  
     sign of theta.  Conversion from TDG/DIRT coordinates to "best"  
     coordinates always results in positive theta, but the angle phi  
     will be pi for positive input theta.  
     The slimits parameter -- used to specify the points along  
     a ray where the transport integration starts and stops -- is  
     measured from the point of closest approach of the ray described  
     by (x,y,theta) to the origin x=y=z=0.  Therefore, slimits is  
     independent of the TDG/DIRT ray coordinate representation.  

             best= form_rays( [x, y, z, theta, phi] )  
          or dirt= form_rays( [x, y, theta] )  
          or internal= form_rays( [cos, sin, y, z, x, r] )  
 
     forms 5-by-nrays, 3-by-nrays, or 6-by-nrays ray representation  
     given individual lists of array coordinates.  The [...]  
     operator builds an nrays-by-5, nrays-by-3, or nrays-by-6  
     array, which form_rays transposes.  The "nrays" may represent  
     zero or more actual dimensions.  

             get_s0(rays)  
 
     returns the s-coordinate of the point of closest approach of  
     the RAYS to the origin x=y=z=0.  The length of the first dimension  
     of RAYS may be either 3, 5, or 6; this first dimension will not  
     be present in the result.  
     The s-coordinate represents distance along the ray, increasing in  
     the direction the ray moves.  The 5 and 6 component ray coordinates  
     include a reference point (x,y,z) on the ray; s=0 at that point.  
     For the 3 component ray coordinate, get_s0 always returns 0.  

             internal_rays(rays)  
 
     returns 6-element (cos,sin,y,z,x,r) representation of RAYS.  
     The first dimension of RAYS may be length 3, 5, or 6 to represent  
     the ray(s) in TDG/DIRT coordinates (x,y,theta), "best" coordinates  
     (x,y,z,theta,phi), or internal coordinates (cos,sin,y,z,x,r),  
     respectively.  The first dimension of the result always has length 6.  
     The internal coordinates are what Drat uses internally to  
     describe the ray.  The coordinate system is rotated about the  
     z-axis until the ray lies in a plane of constant y (there are at  
     least two ways to do this).  The point (x,y,z) can be any point on  
     the ray, and r=sqrt(x^2+y^2) is the corresponding cylindrical radius.  
     The clockwise angle theta from the +z-axis to the ray direction  
     (which always lies in the zx-plane) determines cos=cos(theta) and  
     sin=sin(theta).  
     As a specification of a ray, this system is triply redundant because  
     the point (x,y,z) could be any point on the ray, both the sine and  
     cosine of theta appear, and r=sqrt(x^2+y^2).  
     However, the slimits parameter -- used to specify the points along  
     a ray where the transport integration starts and stops -- is  
     measured from the point (x,y,z) specified as a part of the  
     (cos,sin,y,z,x,r) ray coordinate.  Thus, any change in the point  
     (x,y,z) on a ray must be accompanied by a corresponding change in  
     the slimits for that ray.  

             picture_rays(xpict, ypict, ray)  
          or picture_rays(xpict, ypict, ray, theta_up, phi_up)  
 
     returns 2-D array of rays, one at the center of each zone (which  
     represents a pixel here) of the mesh (XPICT, YPICT).  The rays are  
     all parallel to the given RAY (a 3, 5, or 6 element vector).  The  
     (XPICT, YPICT) coordinates are in the plane perpendicular to the rays,  
     with the origin XPICT=YPICT=0 at the given RAY.  
     If (THETA_UP, PHI_UP) are given, the +YPICT-axis will lie along the  
     projection of the (THETA_UP, PHI_UP) direction into the (XPICT, YPICT)  
     plane.  The default (THETA_UP, PHI_UP) is (pi/2, pi/2) -- the +y-axis  
     -- unless (THETA, PHI) is the y-axis, in which case it is (pi/2, 0)  
     -- the +x-axis.  This matches the DIRT/TDG ray coordinate convention  
     in the sense that if RAY is [0,0,theta], then  
     (zncen(XPICT),zncen(YPICT)) are the DIRT/TDG (x,y) coordinates for  
     the rays.  
     If XPICT and YPICT are imax-by-jmax, the returned array will have  
     dimensions 5-by-(imax-1)-by-(jmax-1).  That is, "best" coordinates  
     are returned.  The (x,y,z) of all of the returned rays will lie in  
     the plane perpendicular to the ray passing through the given central  
     RAY.  

             plray, ray  
 
     where RAY is a vector of length 5 representing [x, y, z, theta, phi]  
     -- a point (x,y,z) on the ray, and the ray direction (theta,phi)  
     relative to the z-axis.  The ray hyperbola is plotted with the  
     z-axis horizontal.  The portion of the ray plotted is determined  
     by the plray_lims command, which must be issued prior to the first  
     plray.  
     The 3 and 6 component ray formats are also accepted.  

             plray_lims, zmin, zmax, rmax  
 
     sets the (z,r) coordinate limits for the plray command.  Subsequent  
     rays will be clipped to the region from z=ZMIN to z=ZMAX, and from  
     r=0 to r=RMAX.