CenterStage Object Class:  Surface
Subclass of the Root class

The Surface class is one of the basic classes in CenterStage.  It allows
you to create parametric surfaces and specify their domains,
colorations, etc.

In addition to the basic directives, the Surface class supports the
following:

    Function params func [vfunc]

        This directive defines the function that gives the surface 
        parametrically.  The "params" argument is a list of the two 
        parameters to be used in the function, and "func" gives a TCL 
        script that is used to compute the value of the function for any 
        given values of the parameters.  
        
        For example

                Function {u v} {
                   let (x,y,z) = (u,v,u^2-v^2)
                }

        defines a saddle surface in three-space.  The script
        should use the values of the parameters (TCL variables that
        will be set to the correct values before the script is
        executed) to compute values for each of the variables listed
        in the Axes directive (which are {x y z} by default).

        The script can compute its values in any way it wants, either
        individually, as in

                Function {u v} {
                   let x = u+v
                   let y = x^2
                   let z = x + y^3
                }

        or as a triple (as in the example above).  The
        script can use any TCL commands, including if-then, loops,
        even procedure calls.  The script has access to all the
        variables defined by the Setup script, and to the variables
        that are bound to sliders, type-ins and check-boxes.

        CenterStage computes the values of the surface function on the 
        domain grid by using two nested loops:  the outermorst loop runs 
        through the values of the second parameter and the innermost loop 
        runs through the values of the first paramter.  If given, the 
        "vfunc" argument specifies a script that should run every time the 
        outermost loop changes value but before the innermost loop starts.
        This allows you to perform computations that depend only on the 
        second parameter once for each value of that parameter (rather than 
        repeating the computation for every different value of the first 
        parameter as well).  For example, if you are using the second 
        parameter as the parameter of a curve and other parameter to build 
        a surface over that curve using its Frenet frame, you can caompute 
        the frame in the "vfunc" script and save considerable computation 
        time since it will only be computed when the position along the 
        curve changes.
        
        
    Domain {{umin umax udivs} {vmin vmax vdivs}}

	This specifies the range for the parameters and how many divisions 
	to make within each interval.  Thus the domain is a square patch in the 
	domain space, and it is divided into a grid (with the number of divisions 
	specified by udivs and vdivs).          

	The function will be evaluated at the corners of each of the 
	subdivisions of the domain, and a rectangular patch will be used to 
	interpolate between the results of the function at these points.  
	The surface is assumed to be continuous.

        You can specify several domains at once using the form:

            Domain {
              {{um1 uM1 un1} {vm1 vM2 vn2}}
              {{um2 uM2 un2} {vm2 vM2 vn2}}
              ...
            }

        You can specify a different domain style for each domain by
        using the following form:

            Domain { 
              {{um1 uM1 un1} {vm1 vM2 vn2} style1}
              {{um2 uM2 un2} {vm2 vM2 vn2} style2}
              ...
            }

        where "style1", "style2", etc. are each one of Patch,
        Grid, BandsU, BandsV, LinesU, LinesV, Dots, Checks, Spots or Weave.
        For example:

            Domain {
              {{-pi/2 0 10} {-pi/2 0 10}}
              {{0 pi/2 10} {0 pi/2 10} Spots}
            }

        specifies that the first patch will use the DOMAIN menu setting 
        while the second will use the Spots domain style.