mfpic-doc.pdf.

4.2 COMMON OBJECTS. 19
lines. Or omit them entirely: well-designed graphs usually don’t need them and almost never should
both horizontals and verticals be used.
The above commands draw their dots and lines within the margins set by the axis margin commands
on page 17.
\plrgrid{〈rsep〉,〈anglesep〉}
\gridarcs{〈rsep〉}
\gridrays{〈anglesep〉}
\plrpatch{〈rmin〉,〈rmax〉,〈rsep〉,〈tmin〉,〈tmax〉,〈tsep〉}
\plrgridpoints[〈size〉]{〈rsep〉,〈anglesep〉}
\plrgrid fills the graph with circular arcs and radial lines. \gridarcs draws only the arcs,
\gridrays only the radial lines. \plrgridpoints places a dot (diameter 〈size〉) at all the places
the rays and arcs would intersect. It takes an optional argument for the size of the dots, the default
being \griddotsize, the same as the \grid command.
The arcs lie on circles centered at (0,0) and the rays would all meet at (0,0) if extended. The
corresponding METAFONT commands actually draw just enough to cover the graph area and then
clip them to the graph boundaries. If you don’t want them clipped, use \plrpatch. Unlike the
rectangular coordinate grid commands, these do not respect the axis margins (rectangular margins
don’t really belong with polar coordinates).
\plrpatch draws arcs with radii starting at 〈rmin〉, stepping by 〈rsep〉 and ending with 〈rmax〉.
Each arc goes from angle 〈tmin〉 to 〈tmax〉. It also draws radial lines with angles starting at 〈tmin〉,
stepping by 〈tsep〉 and ending with 〈tmax〉. Each line goes from radius 〈rmin〉 to 〈rmax〉. If 〈rmax〉−
〈rmin〉 doesn’t happen to be a multiple of 〈rsep〉, the arc with radius 〈rmax〉 is drawn anyway. The
same is true of the line at angle 〈tmax〉, so that the entire boundary is always drawn.
If 〈tsep〉 is larger than 〈tmax〉 − 〈tmin〉, then only the boundary rays will be drawn. If 〈rsep〉 is
larger than 〈rmax〉 − 〈rmin〉, then only the boundary arcs will be drawn.
The color used for rays and arcs is drawcolor, and for dots pointcolor. The advice about
color and use of \gridlines holds for \plrgrid and its relatives as well.
\vectorfield[〈hlen〉]{〈xsp〉,〈ysp〉}{〈formula〉}{〈restriction〉}
\plrvectorfield[〈hlen〉]{〈rsp〉,〈tsp〉}{〈formula〉}{〈restriction〉}
These commande draw a field of vectors (arrows). The optional argument is the length of the
arrowhead, the default being the dimension \headlen, initially 3pt.
For \vectorfield, an arrow is drawn starting from each point (x,y) where x is an integer
multiple of 〈xsp〉 and y is an integer multiple of 〈ysp〉. The vector field is given by 〈formula〉, which
should be a pair-valued expression in the literal variables x and y. Typically that would be a pair
of numeric expressions enclosed in parentheses and separated by a comma. The last argument is
a boolean expression in the literal variables x and y, used to restrict the domain. That is, if the
expression is false for some (x,y), no arrow is drawn at that point. If you do not wish to restrict the
domain, type true for the restriction.
For \plrvectorfield, an arrow is drawn starting from each point with polar coordinates (r,θ)
if r is an integer multiple of 〈rsp〉 and θ is an integer multiple of 〈tsp〉. In this case, the 〈formula〉
must be a pair-valued expression in the literal variables r and t. This should be (or produce) a pair
of x and y coorinates, not a polar coordinate pair. If you have formulas R(r,θ) for the length of each
vector and T (r,θ) for the angle, then the following will convert to (x,y) pairs:
{polar (R(r,t),T(r,t))}
The last argument is as in \vectorfield, except it should depend on the literal variables r and t.