       mesh in RegionPlot

• To: mathgroup at smc.vnet.net
• Subject: [mg97017] mesh in RegionPlot
• From: "Cristina Ballantine" <cballant at holycross.edu>
• Date: Mon, 2 Mar 2009 05:22:01 -0500 (EST)

```When plotting the RegionPlot below, some of the mesh lines appear thicker
than the others. The mesh functions are defined in terms of the function f
that describes the region to be plotted and the thicker mesh lines are the
pre-image of the positive real axis under f. I would like this lines to
have the same thickness as the other mesh lines. Any suggestions are very
much appreciated.

Cristina

f[z_] = z^3*(z + 2)/((z - I)^4*(z + 3 - I)^3)

sol := Solve[f'[z] == 0, z]

c3 := z /. Extract[sol, {3}]
c4 := z /. Extract[sol, {4}]

w3 := f[c3]
w4 := f[c4]

r3 := Abs[w3]
r4 := Abs[w4]

plotw4[tmin_, tmax_, c_] :=
RegionPlot[
Abs[f[x + I*y]] > tmin && Abs[f[x + I*y]] < tmax, {x, -10,
10}, {y, -10, 10}, PlotPoints -> 150,
ColorFunction ->
Function[{x, y, z},
With[{bb = f[x + I y]},
Hue[c, Mod[(Arg[bb] - t4)/(2 Pi), 1],
Mod[(Abs[bb] - tmin)/(tmax - tmin), 1] + .4]]],
ColorFunctionScaling -> False,
MeshFunctions -> {Abs[f[#1 + I*#2]] &, Arg[f[#1 + I*#2]] &},
Mesh -> {5, 10}]

With[{tmin = r3, tmax = r4, c = .5}, Show[plotw4[tmin, tmax, c]]]

```

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