A question about RegionFunction in ver. 6.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg77765] A question about RegionFunction in ver. 6.0*From*: chuck009 <dmilioto at comcast.com>*Date*: Sat, 16 Jun 2007 03:29:59 -0400 (EDT)

I understand RegionFunction allows a specific region of a surface to be plotted. I've checked the documentation and think that's still not going to be enough to provide a nice interface to plot "clean" sheets of multi-functions. Consider the principal sheet of the imaginary component for the function w=(z^2-z^3)^(-1/3): p1 = Plot3D[Evaluate[Im[(z^2 - z^3)^(-1/3) /. z -> x + I y]], {x, -3, 3}, {y, -3, 3}, PlotPoints -> 80, AspectRatio -> 1, PlotRange -> {{-3, 3}, {-3, 3}, {-3, 3}}, BoxRatios -> {1, 1, 1}]; Note how Plot3D produces a jagged boundary at the branch cuts. The following code shows the branch cuts in the plane: sol = Solve[z^2 - z^3 == v, z]; Show[(ParametricPlot[Evaluate[({ Re[#1], Im[#1]} &) /@ (z /. sol)], #1, DisplayFunction -> Identity] &) /@ {{v, -8, -2}, {v, -2, 0}}, DisplayFunction -> $DisplayFunction, PlotRange -> All, Frame -> True, Axes -> False, AspectRatio -> Automatic]; Does anyone feel that the RegionFunction could be adapted to plot the three sectors of this sheet cleanly without the jagged edges? I can plot a clean sheet in ver 5.2, but must create the polygons directly using the data from the branch cuts. It's messy though and lots of code.