functions in slice3.i -

             getc3(i, m3, chunk)  
          or getc3(i, m3, clist, l, u, fsl, fsu, cells)  
 
     return cell values of the Ith function attached to 3D mesh M3  
     for cells in the specified CHUNK.  The CHUNK may be a list of  
     cell indices, in which case getc3 returns a (dimsof(CHUNK))  
     list of vertex coordinates.  CHUNK may also be a mesh-specific data  
     structure used in the slice3 routine, in which case getc3 may  
     return a (ni)x(nj)x(nk) array of vertex values.  There is no  
     savings in the amount of data for such a CHUNK, but the gather  
     operation is cheaper than a general list of cell indices.  
     Use getc3 when writing colorng functions for slice3.  
     If CHUNK is a CLIST, the additional arguments L, U, FSL, and FSU  
     are vertex index lists which override the CLIST if the Ith attached  
     function is defined on mesh vertices.  L and U are index lists into  
     the 2x2x2x(dimsof(CLIST)) vertex value array, say vva, and FSL  
     and FSU are corresponding interpolation coefficients; the zone  
     centered value is computed as a weighted average of involving these  
     coefficients.  The CELLS argument is required by histogram to do  
     the averaging.  See the source code for details.  
     By default, this conversion (if necessary) is done by averaging  
     the eight vertex-centered values.  

             getv3(i, m3, chunk)  
 
     return vertex values of the Ith function attached to 3D mesh M3  
     for cells in the specified CHUNK.  The CHUNK may be a list of  
     cell indices, in which case getv3 returns a 2x2x2x(dimsof(CHUNK))  
     list of vertex coordinates.  CHUNK may also be a mesh-specific data  
     structure used in the slice3 routine, in which case getv3 may  
     return a (ni)x(nj)x(nk) array of vertex values.  For meshes which  
     are logically rectangular or consist of several rectangular  
     patches, this is up to 8 times less data, with a concomitant  
     performance advantage.  Use getv3 when writing slicing functions  
     for slice3.  

             mesh3(x,y,z)  
          or mesh3(x,y,z, f1,f2,...)  
          or mesh3(xyz, f1,f2,...)  
          or mesh3(nxnynz, dxdydz, x0y0z0, f1,f2,...)  
 
     make mesh3 argument for slice3, xyz3, getv3, etc., functions.  
     X, Y, and Z are each 3D coordinate arrays.  The optional F1, F2,  
     etc. are 3D arrays of function values (e.g. density, temperature)  
     which have one less value along each dimension than the coordinate  
     arrays.  The "index" of each zone in the returned mesh3 is  
     the index in these cell-centered Fi arrays, so every index from  
     one through the total number of cells indicates one real cell.  
     The Fi arrays can also have the same dimensions as X, Y, or Z  
     in order to represent point-centered quantities.  
     If X has four dimensions and the length of the first is 3, then  
     it is interpreted as XYZ (which is the quantity actually stored  
     in the returned cell list).  
     If X is a vector of 3 integers, it is interpreted as [nx,ny,nz]  
     of a uniform 3D mesh, and the second and third arguments are  
     [dx,dy,dz] and [x0,y0,z0] respectively.  (DXDYDZ represent the  
     size of the entire mesh, not the size of one cell, and NXNYNZ are  
     the number of cells, not the number of points.)  

             pl3surf, nverts, xyzverts  
          or pl3surf, nverts, xyzverts, values  
 
     Perform simple 3D rendering of an object created by slice3  
     (possibly followed by slice2).  NVERTS and XYZVERTS are polygon  
     lists as returned by slice3, so XYZVERTS is 3-by-sum(NVERTS),  
     where NVERTS is a list of the number of vertices in each polygon.  
     If present, the VALUES should have the same length as NVERTS;  
     they are used to color the polygon.  If VALUES is not specified,  
     the 3D lighting calculation set up using the light3 function  
     will be carried out.  Keywords cmin= and cmax= as for plf, pli,  
     or plfp are also accepted.  (If you do not supply VALUES, you  
     probably want to use the ambient= keyword to light3 instead of  
     cmin= here, but cmax= may still be useful.)  

             pl3tree, nverts, xyzverts  
          or pl3tree, nverts, xyzverts, values, plane  
 
     Add the polygon list specified by NVERTS (number of vertices in  
     each polygon) and XYZVERTS (3-by-sum(NVERTS) vertex coordinates)  
     to the currently displayed b-tree.  If VALUES is specified, it  
     must have the same dimension as NVERTS, and represents the color  
     of each polygon.  If VALUES is not specified, the polygons  
     are assumed to form an isosurface which will be shaded by the  
     current 3D lighting model; the isosurfaces are at the leaves of  
     the b-tree, sliced by all of the planes.  If PLANE is specified,  
     the XYZVERTS must all lie in that plane, and that plane becomes  
     a new slicing plane in the b-tree.    
     Each leaf of the b-tree consists of a set of sliced isosurfaces.  
     A node of the b-tree consists of some polygons in one of the  
     planes, a b-tree or leaf entirely on one side of that plane, and  
     a b-tree or leaf on the other side.  The first plane you add  
     becomes the root node, slicing any existing leaf in half.  When  
     you add an isosurface, it propagates down the tree, getting  
     sliced at each node, until its pieces reach the existing leaves,  
     to which they are added.  When you add a plane, it also propagates  
     down the tree, getting sliced at each node, until its pieces  
     reach the leaves, which it slices, becoming the nodes closest to  
     the leaves.  
     This structure is relatively easy to plot, since from any  
     viewpoint, a node can always be plotted in the order from one  
     side, then the plane, then the other side.  
     This routine assumes a "split palette"; the colors for the  
     VALUES will be scaled to fit from color 0 to color 99, while  
     the colors from the shading calculation will be scaled to fit  
     from color 100 to color 199.  (If VALUES is specified as a char  
     array, however, it will be used without scaling.)  
     You may specifiy a cmin= or cmax= keyword to affect the  
     scaling; cmin is ignored if VALUES is not specified (use the  
     ambient= keyword from light3 for that case).  

             plane3(normal, point)  
          or plane3([nx,ny,nz], [px,py,pz])  
 
     returns [nx,ny,nz,pp] for the specified plane.  

             slice2, plane, nverts, xyzverts  
          or slice2, plane, nverts, xyzverts, values  
 
     Slice a polygon list, retaining only those polygons or  
     parts of polygons on the positive side of PLANE, that is,  
     the side where xyz(+)*PLANE(+:1:3)-PLANE(4) > 0.0.  
     The NVERTS, XYZVERTS, and VALUES arrays serve as both  
     input and output, and have the meanings of the return  
     values from the slice3 function.  It is legal to omit the  
     VALUES argument (e.g.- if there is no fcolor function).  
     In order to plot two intersecting slices, one could  
     slice (for example) the horizontal plane twice (slice2x) -  
     first with the plane of the vertical slice, then with minus  
     that same plane.  Then, plot first the back part of the  
     slice, then the vertical slice, then the front part of the  
     horizontal slice.  Of course, the vertical plane could  
     be the one to be sliced, and "back" and "front" vary  
     depending on the view point, but the general idea always  
     works.  

             slice2_precision= precision  
 
     Controls how slice2 (or slice2x) handles points very close to  
     the slicing plane.  PRECISION should be a positive number or zero.  
     Zero PRECISION means to clip exactly to the plane, with points  
     exactly on the plane acting as if they were slightly on the side  
     the normal points toward.  Positive PRECISION means that edges  
     are clipped to parallel planes a distance PRECISION on either  
     side of the given plane.  (Polygons lying entirely between these  
     planes are completely discarded.)  
     Default value is 0.0.  

             slice2, plane, nverts, values, xyzverts  
 
     Slice a polygon list, retaining only those polygons or  
     parts of polygons on the positive side of PLANE, that is,  
     the side where xyz(+)*PLANE(+:1:3)-PLANE(4) > 0.0.  
     The NVERTS, VALUES, and XYZVERTS arrays serve as both  
     input and output, and have the meanings of the return  
     values from the slice3 function.  

             slice3, m3, fslice, nverts, xyzverts  
          or color_values= slice3(m3, fslice, nverts, xyzverts, fcolor)  
          or color_values= slice3(m3, fslice, nverts, xyzverts, fcolor, 1)  
 
     slice the 3D mesh M3 using the slicing function FSLICE, returning  
     the lists NVERTS and XYZVERTS.  NVERTS is the number of vertices  
     in each polygon of the slice, and XYZVERTS is the 3-by-sum(NVERTS)  
     list of polygon vertices.  If the FCOLOR argument is present, the  
     values of that coloring function on the polygons are returned as  
     the value of the slice3 function (numberof(color_values) ==  
     numberof(NVERTS) == number of polygons).  
     If the slice function FSLICE is a function, it should be of the  
     form:  
        func fslice(m3, chunk)  
     returning a list of function values on the specified chunk of the  
     mesh m3.  The format of chunk depends on the type of m3 mesh, so  
     you should use only the other mesh functions xyz3 and getv3 which  
     take m3 and chunk as arguments.  The return value of fslice should  
     have the same dimensions as the return value of getv3; the return  
     value of xyz3 has an additional first dimension of length 3.  
     If FSLICE is a list of 4 numbers, it is taken as a slicing plane  
     with the equation FSLICE(+:1:3)*xyz(+)-FSLICE(4), as returned by  
     plane3.  
     If FSLICE is a single integer, the slice will be an isosurface for  
     the FSLICEth variable associated with the mesh M3.  In this case,  
     the keyword value= must also be present, representing the value  
     of that variable on the isosurface.  
     If FCOLOR is nil, slice3 returns nil.  If you want to color the  
     polygons in a manner that depends only on their vertex coordinates  
     (e.g.- by a 3D shading calculation), use this mode.  
     If FCOLOR is a function, it should be of the form:  
        func fcolor(m3, cells, l, u, fsl, fsu, ihist)  
     returning a list of function values on the specified cells of the  
     mesh m3.  The cells argument will be the list of cell indices in  
     m3 at which values are to be returned.  l, u, fsl, fsu, and ihist  
     are interpolation coefficients which can be used to interpolate  
     from vertex centered values to the required cell centered values,  
     ignoring the cells argument.  See getc3 source code.  
     The return values should always have dimsof(cells).  
     If FCOLOR is a single integer, the slice will be an isosurface for  
     the FCOLORth variable associated with the mesh M3.  
     If the optional argument after FCOLOR is non-nil and non-zero,  
     then the FCOLOR function is called with only two arguments:  
        func fcolor(m3, cells)  

             split_bytscl(x, 0)  
          or split_bytscl(x, 1)  
 
     as bytscl function, but scale to the lower half of a split  
     palette (0-99, normally the color scale) if the second parameter  
     is zero or nil, or the upper half (100-199, normally the gray  
     scale) if the second parameter is non-zero.  

             split_palette  
          or split_palette, "palette_name.gp"  
 
     split the current palette or the specified palette into two  
     parts; colors 0 to 99 will be a compressed version of the  
     original, while colors 100 to 199 will be a gray scale.  

             to_corners(list, ni, nj)  
 
     convert a LIST of cell indices in an (NI-1)-by-(NJ-1)-by-(nk-1)  
     logically rectangular grid of cells into the list of  
     2-by-2-by-2-by-numberof(LIST) cell corner indices in the  
     corresponding NI-by-NJ-by-nk list of vertices.  

             xyz3(m3, chunk)  
 
     return vertex coordinates for CHUNK of 3D mesh M3.  The CHUNK  
     may be a list of cell indices, in which case xyz3 returns a  
     3x2x2x2x(dimsof(CHUNK)) list of vertex coordinates.  CHUNK may  
     also be a mesh-specific data structure used in the slice3  
     routine, in which case xyz3 may return a 3x(ni)x(nj)x(nk)  
     array of vertex coordinates.  For meshes which are logically  
     rectangular or consist of several rectangular patches, this  
     is up to 8 times less data, with a concomitant performance  
     advantage.  Use xyz3 when writing slicing functions or coloring  
     functions for slice3.