Controlling the Plot Domain

"ON" selectors

The primary mechanism for controlling the domain over which plot data are constructed is the "ON" statement, which has many forms:

ON "name"        

ON REGION "name"        

ON REGION number

In three-dimensional problems, the following are also meaningful:

ON LAYER "name"        

ON SURFACE "name"

ON LAYER number

ON SURFACE number

ON equation

The first form selects a boundary path, region, layer or surface depending on the definition of the "name".  (It is actually redundant to specify  SURFACE "name", etc, since the fact that a surface is being specified should be clear from the "name" itself.  Nevertheless, the forms are acceptable.)

In many cases, particularly in 3D, more than one "ON" clause can be used for a single plot, since each "ON" clause adds a restriction to those already in effect.  There is a direct correspondence between the "ON" clauses of a plot statement and the arguments of the various INTEGRAL operators, although some of the allowable integral selections do not have valid corresponding plot options.

In two dimensional geometries, area plots which are not otherwise restricted are assumed to be taken over the entire problem domain.

Contours, Surface Plots, Grid Plots and Vector Plots

Contours. "surfaces" (3D topographic displays), grid plots and vector plots must be taken on some kind of two dimensional data surface, so in 3D problems these plot commands are incomplete without at least one "ON" clause.  This can be an extrusion-surface name,  or a cut-plane equation (it cannot be a projection-plane boundary path).  For example, in a 3D problem,

CONTOUR(...) ON SURFACE 2        

requests a contour plot of data evaluated on the second extrusion surface.

CONTOUR(...) ON SURFACE "top"         

requests a contour plot of data evaluated on the extrusion surface named "top".

CONTOUR(...) ON X=Y         

requests a contour plot of data evaluated on the cut plane where x=y.

In addition to a basic definition of the data surface, "ON" clauses may be used to restrict the display to an arbitrary REGION or LAYER.  In 2D, a REGION restriction will display only that part of the domain which is in the stated region:

CONTOUR(...) ON REGION 2         

requests a contour plot of data evaluated on REGION 2.

Similarly, in 3D,

CONTOUR(...) ON SURFACE 2 ON REGION 2         

requests a contour plot of data evaluated on extrusion surface 2, restricted to that part of the surface lying above REGION 2 of the baseplane projection.

CONTOUR(...) ON SURFACE 2 ON REGION 2 ON LAYER 3 

requests a contour plot of data evaluated on extrusion surface 2, restricted to that part of the surface lying above REGION 2 of the baseplane projection, and with the evaluation taken in layer 3, which is assumed to be bounded by the selected surface.

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Cut Planes in 3D

Contours, surface plots and vector plots can also be specified on cut planes by giving the general formula of the cutting plane:

CONTOUR(...) ON X = expression  

requests a contour plot of data evaluated on the Y-Z plane where X is the specified value.

Cut planes need not be simple coordinate planes:

CONTOUR(...) ON X=Y         

requests a contour plot of data evaluated on the plane containing the z-axis and the 45 degrees line in the XY plane.

The coordinates displayed in oblique cut planes have their origin at the point of closest approach to the origin of the domain coordinates.  The axes are chosen to be aligned with the nearest domain coordinate axes.

Elevation Plots

Elevation plots can be specified by endpoints of a line:

ELEVATION(...) FROM (x1,y1) TO (x2,y2)

ELEVATION(...) FROM (x1,y1,z1) TO (x2,y2,z2)

The plot will be displayed on the straight line connecting the specified endpoints.  These endpoints might span only a small part of the problem domain, or they might exceed the domain dimensions somewhat, in which case the plot line will be truncated to the interior portion.

In 2D geometry only, an elevation plot may be specified by the name of a boundary path, as in

ELEVATION(...) ON "outer_boundary"

These boundary-path elevations can be additionally restricted as to the region in which the evaluation is to be made:

ELEVATION(...) ON "inner_boundary" ON REGION "core"

This form requests that the evaluation of the plot function be made in the region named "core", with the assumption that "core" is one of the regions adjoining the "inner_boundary" path.

Sign of Vector Components

In many cases, boundary-path elevations present normal or tangential components of vectors.  For these applications, the sense of the direction is the same as the sense of the NATURAL boundary condition: 

       The positive normal is outward from the evaluation region.

       The positive tangent is counter-clockwise with respect to the evaluation region.

Plots of the normal components of vectors on extrusion surfaces in 3D follows the same rule:

       The positive normal is outward from the evaluation region.