functions in pl3d.i -

             aim3, xa,ya,za  
 
     move the current 3D plot to put the point (XA,YA,ZA) in object  
     coordinates at the point (0,0,0) -- the aim point -- in the  
     viewer's coordinates.  If any of XA, YA, or ZA is nil, it defaults  
     to zero.  

             cage3  
          or cage3, onoff  
 
     Toggle the cage display.  If ONOFF is non-nil and non-zero,  
     turn on the cage.  If ONOFF is zero, turn off the cage.  
     The cage draws a rectangular box "behind" the 3D object and  
     attempts to put ticks and labels around the edge of the box.  

             clear3  
 
     Clear the current 3D display list.  

             draw3  
 
     Draw the current 3D display list.  
     (Ordinarily triggered automatically when the drawing changes.)  

             get3_centroid(xyz, nxyz)  
          or get3_centroid(xyz)  
 
     return 3D centroids for polygons with vertices XYZ.  If NXYZ is  
     specified, XYZ should be 3-by-sum(nxyz), with NXYZ being the  
     list of numbers of vertices for each polygon (as for the plfp  
     function).  If NXYZ is not specified, XYZ should be a quadrilateral  
     mesh, 3-by-ni-by-nj (as for the plf function).  In the first case,  
     the return value is 3-by-numberof(NXYZ); in the second case, the  
     return value is 3-by-(ni-1)-by-(nj-1).  
     The centroids are constructed as the mean value of all vertices  
     of each polygon.  

             get3_light(xyz, nxyz)  
          or get3_light(xyz)  
 
     return 3D lighting for polygons with vertices XYZ.  If NXYZ is  
     specified, XYZ should be 3-by-sum(nxyz), with NXYZ being the  
     list of numbers of vertices for each polygon (as for the plfp  
     function).  If NXYZ is not specified, XYZ should be a quadrilateral  
     mesh, 3-by-ni-by-nj (as for the plf function).  In the first case,  
     the return value is numberof(NXYZ); in the second case, the  
     return value is (ni-1)-by-(nj-1).  
     The parameters of the lighting calculation are set by the  
     light3 function.  

             get3_normal(xyz, nxyz)  
          or get3_normal(xyz)  
 
     return 3D normals for polygons with vertices XYZ.  If NXYZ is  
     specified, XYZ should be 3-by-sum(nxyz), with NXYZ being the  
     list of numbers of vertices for each polygon (as for the plfp  
     function).  If NXYZ is not specified, XYZ should be a quadrilateral  
     mesh, 3-by-ni-by-nj (as for the plf function).  In the first case,  
     the return value is 3-by-numberof(NXYZ); in the second case, the  
     return value is 3-by-(ni-1)-by-(nj-1).  
     The normals are constructed from the cross product of the lines  
     joining the midpoints of two edges which as nearly quarter the  
     polygon as possible (the medians for a quadrilateral).  No check  
     is made that these not be parallel; the returned "normal" is  
     [0,0,0] in that case.  Also, if the polygon vertices are not  
     coplanar, the "normal" has no precisely definable meaning.  

             get3_xy, xyz, x, y  
          or get3_xy, xyz, x, y, z, 1  
 
     Given 3-by-anything coordinates XYZ, return X and Y in viewer's  
     coordinate system (set by rot3, mov3, orient3, etc.).  If the  
     fifth argument is present and non-zero, also return Z (for use  
     in sort3d or get3_light, for example).  If the camera position  
     has been set to a finite distance with setz3, the returned  
     coordinates will be tangents of angles for a perspective  
     drawing (and Z will be scaled by 1/zc).  

             gnomon  
          or gnomon, onoff  
 
     Toggle the gnomon display.  If ONOFF is non-nil and non-zero,  
     turn on the gnomon.  If ONOFF is zero, turn off the gnomon.  
     The gnomon shows the X, Y, and Z axis directions in the  
     object coordinate system.  The directions are labeled.  
     The gnomon is always infinitely far behind the object  
     (away from the camera).  
     There is a mirror-through-the-screen-plane ambiguity in the  
     display which is resolved in two ways: (1) The (X,Y,Z)  
     coordinate system is right-handed, and (2) If the tip of an  
     axis projects into the screen, it's label is drawn in opposite  
     polarity to the other text on the screen.  

             light3, ambient=a_level,  
                     diffuse=d_level,  
                     specular=s_level,  
                     spower=n,  
                     sdir=xyz  
 
     Sets lighting properties for 3D shading effects.  
     A surface will be shaded according to its to its orientation  
     relative to the viewing direction.  
     The ambient level A_LEVEL is a light level (arbitrary units)  
     that is added to every surface independent of its orientation.  
     The diffuse level D_LEVEL is a light level which is proportional  
     to cos(theta), where theta is the angle between the surface  
     normal and the viewing direction, so that surfaces directly  
     facing the viewer are bright, while surfaces viewed edge on are  
     unlit (and surfaces facing away, if drawn, are shaded as if they  
     faced the viewer).  
     The specular level S_LEVEL is a light level proportional to a high  
     power spower=N of 1+cos(alpha), where alpha is the angle between  
     the specular reflection angle and the viewing direction.  The light  
     source for the calculation of alpha lies in the direction XYZ (a  
     3 element vector) in the viewer's coordinate system at infinite  
     distance.  You can have ns light sources by making S_LEVEL, N, and  
     XYZ (or any combination) be vectors of length ns (3-by-ns in the  
     case of XYZ).  (See source code for specular_hook function  
     definition if powers of 1+cos(alpha) aren't good enough for you.)  
     With no arguments, return to the default lighting.  
   EXAMPLES:  
     light3, diffuse=.1, specular=1., sdir=[0,0,-1]  
       (dramatic "tail lighting" effect)  
     light3, diffuse=.5, specular=1., sdir=[1,.5,1]  
       (classic "over your right shoulder" lighting)  
     light3, ambient=.1,diffuse=.1,specular=1.,  
             sdir=[[0,0,-1],[1,.5,1]],spower=[4,2]  
       (two light sources combining previous effects)  

             limit3, xmin,xmax, ymin,ymax  
          or limit3, xmin,xmax, ymin,ymax, zmin,zmax  
 
     Set the 3D axis limits for use with the cage.  
     Use keyword aspect=[ax,ay,az] to set the aspect ratios of the  
     cage to ax:ay:az -- that is, the ratios of the lengths of the  
     cage axes will become ax:ay:az.  

             mov3, xa,ya,za  
 
     move the current 3D plot by XA along viewer's x-axis,  
     YA along viewer's y-axis, and ZA along viewer's z-axis.  

             orient3, phi, theta  
          or orient3, phi  
          or orient3, , theta  
          or orient3  
 
     Set the "orientation" of the object to (PHI,THETA).  "Orientations"  
     are a subset of the possible rotation matrices in which the z-axis  
     of the object appears vertical on the screen (that is, the object  
     z-axis projects onto the viewer y-axis).  The THETA angle is the  
     angle from the viewer y-axis to the object z-axis, positive if  
     the object z-axis is tilted toward you (toward viewer +z).  PHI is  
     zero when the object x-axis coincides with the viewer x-axis.  If  
     neither PHI nor THETA is specified, PHI defaults to -pi/4 and  
     THETA defaults to pi/6.  If only one of PHI or THETA is specified,  
     the other remains unchanged, unless the current THETA is near pi/2,  
     in which case THETA returns to pi/6, or unless the current  
     orientation does not have a vertical z-axis, in which case the  
     unspecified value returns to its default.  
     Unlike rot3, orient3 is not a cumulative operation.  

             range3, zmin,zmax  
 
     Set the 3D axis z limits for use with the cage.  
     Use keyword aspect=[ax,ay,az] to set the aspect ratios of the  
     cage to ax:ay:az -- that is, the ratios of the lengths of the  
     cage axes will become ax:ay:az.  

             restore3, view  
 
     Restore a previously saved 3D viewing transformation and lighting.  
     If VIEW is nil, rotate object to viewer's coordinate system.  

             rot3, xa,ya,za  
 
     rotate the current 3D plot by XA about viewer's x-axis,  
     YA about viewer's y-axis, and ZA about viewer's z-axis.  

             view= save3()  
 
     Save the current 3D viewing transformation and lighting.  

             set3_object, drawing_function, _lst(arg1,arg2,...)  
 
     set up to trigger a call to draw3, adding a call to the  
     3D display list of the form:  
        DRAWING_FUNCTION, _lst(ARG1, ARG2, ...)  
     When draw3 calls DRAWING_FUNCTION, the external variable _draw3  
     will be non-zero, so DRAWING_FUNCTION can be written like this:  
     func drawing_function(arg1,arg2,...)  
     {  
       require, "pl3d.i";  
       if (_draw3) {  
         list= arg1;  
         arg1= _nxt(list);  
         arg2= _nxt(list);  
         ...  
         ......  
         ......  
         return;  
       }  
       ......  
       ......  
       set3_object, drawing_function, _lst(arg1,arg2,...);  
     }  

             setz3, zc  
 
     Set the camera position to z=ZC (x=y=0) in the viewer's coordinate  
     system.  If ZC is nil, set the camera to infinity (default).  

             sort3d(z, npolys, &list, &vlist)  
 
     given Z and NPOLYS, with numberof(Z)==sum(npolys), return  
     LIST and VLIST such that Z(VLIST) and NPOLYS(LIST) are  
     sorted from smallest average Z to largest average Z, where  
     the averages are taken over the clusters of length NPOLYS.  
     Within each cluster (polygon), the cyclic order of Z(VLIST)  
     remains unchanged, but the absolute order may change.  
     This sorting order produces correct or nearly correct order  
     for a plfp command to make a plot involving hidden or partially  
     hidden surfaces in three dimensions.  It works best when the  
     polys form a set of disjoint closed, convex surfaces, and when  
     the surface normal changes only very little between neighboring  
     polys.  (If the latter condition holds, then even if sort3d  
     mis-orders two neighboring polys, their colors will be very  
     nearly the same, and the mistake won't be noticeable.)  A truly  
     correct 3D sorting routine is impossible, since there may be no  
     rendering order which produces correct surface hiding (some polys  
     may need to be split into pieces in order to do that).  There  
     are more nearly correct algorithms than this, but they are much  
     slower.  

             spin3  
          or spin3, nframes  
          or spin3, nframes, axis  
 
     Spin the current 3D display list about AXIS over NFRAMES.  Keywords  
     tlimit= the total time allowed for the movie in seconds (default 60),  
     dtmin= the minimum allowed interframe time in seconds (default 0.0),  
     bracket_time= (as for movie function in movie.i)  
     The default AXIS is [-1,1,0] and the default NFRAMES is 30.  

             undo3  
          or undo3, n  
 
     Undo the effects of the last N (default 1) rot3, orient3, mov3, aim3,  
     setz3, or light3 commands.  

             window3  
          or window3, n  
 
     initialize style="nobox.gs" window for 3D graphics