Combining a parametric plot with a Graphics3D plot
- To: mathgroup at smc.vnet.net
- Subject: [mg79510] Combining a parametric plot with a Graphics3D plot
- From: chuck009 <dmilioto at comcast.com>
- Date: Sat, 28 Jul 2007 05:32:02 -0400 (EDT)
Hello guys,
I do a lot of work plotting complex contours over the real and imaginary sheets of complex functions. Often though, when I combine both the contour and the sheet, the contour is shown broken-up. The code below shows this problem. It combines the real component of the function:
f[z]=(1+2z}/(1+Exp[z]Sqrt[z])
shown in blue with the path of a contour z=6 Exp[it] shown in red. Note how the red contour is broken-up. Sure would be nice if I could have a plot with the red-contour cleanly trajecting over the surface. I know I can "raise" the contour slightly to reduce the break-up but this often still does not work and also the precision of the plot is reduced. Can anybody suggest a way to integrate both graphics into a single graphics object so that the plot is nice and clean?
I have ver. 5.2. Does ver 6 eliminate this problem?
tophalf = ParametricPlot3D[{Re[z] /. z -> r*Exp[I*t],
Im[z] /. z ->r*Exp[I*t],
Re[(1 + 2*z)/(1 + Exp[z]*Exp[(1/2)*(Log[Abs[z]] +
I*Arg[z])]) /. z ->r*Exp[I*t]], Blue},
{r, 0.3, 6.5}, {t, 0, Pi}, PlotPoints -> {30, 50}]
bothalf = ParametricPlot3D[{Re[z] /. z ->r*Exp[I*t],
Im[z] /. z ->r*Exp[I*t],
Re[(1 + 2*z)/(1 + Exp[z]*Exp[(1/2)*(Log[Abs[z]] +
I*(Arg[z] + 2*Pi))]) /. z ->r*Exp[I*t]],
Blue}, {r, 0.3, 6.5}, {t, Pi, 2*Pi}, PlotPoints -> {30, 50}]
cfunction = {6 Cos[t],6 Sin[t],
Re[(1 + 2*z)/(1 + Exp[z]*Exp[(1/2)*(Log[6] + I*t)]) /.
z ->6 Exp[I*t]] + 0.01};
path1 = ParametricPlot3D[Evaluate[Append[cfunction,
{Red, Thickness[0.01]}]], {t, 0, 2*Pi}]
Show[{tophalf, bothalf, path1}, Lighting -> False]