       RE: Pen Lift for FlybackTrace erasure

• To: mathgroup at smc.vnet.net
• Subject: [mg66850] RE: [mg66830] Pen Lift for FlybackTrace erasure
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 1 Jun 2006 06:55:22 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Oh My!

You can do this in a much simpler manner.

First, why don't you use the ComplexMap standard package?

Needs["Graphics`ComplexMap`"]

CartesianMap[Sin, {-Pi/2, Pi/2}, {-2, 2},
Frame -> True];

Roman Maeder has worked out all the problems of the discontinuities in the
lines. By the way, he shows the code and the development of it in his book
'Programming in Mathematica'.

If you want to plot this yourself, then the best approach is not to use
ListPlot (Throw ListPlot into the ash can!) and not to Flatten your Table
data. Just map Line onto each set of points. Also, the N on your RI
definition does nothing.

z = Complex[x, y];
f[z_] = Sin[z];
RI = {Re[f[z]], Im[f[z]]};

XY = Line /@ Table[RI, {x, -(Pi/2), Pi/2, Pi/10},
{y, -(Pi/2), Pi/2, Pi/60}]//N;
YX = Line /@ Table[RI, {y, -(Pi/2), Pi/2, Pi/10},
{x, -(Pi/2), Pi/2, Pi/60}]//N;

Show[Graphics[
{XY, YX}],
AspectRatio -> Automatic,
Frame -> True];

In the case of Sin, this works pretty well. But if there is a jump
discontinuity in the lines in the domain of the plot then the problem
returns. Maeder's package handles that. The DrawGraphics package has a
routine SplitLineOnDistance that can be used to eliminate these jump lines.

David Park

From: Narasimham [mailto:mathma18 at hotmail.com]
To: mathgroup at smc.vnet.net

Attempting to plot real/imaginary parts of a complex variable function
, {Re,Im}= f [x,y]. But in what follows,

1) How to  ' lift pen '  for suppressing flyback tracer lines
connecting  between  start/end points of  x and  y set curves?

2) How to combine plotting the sets by a single commad like it is in
Plot3D or ParametricPlot3D?     __   TIA

z = Complex[x,y]  ; f[z_]=Sin[z]; RI =  N[  { Re[f[z]],  Im[f[z]] } ];
XY = Flatten[Table[ RI , {x, -Pi/2, Pi/2,Pi/10}, {y, -Pi/2, Pi/2,Pi/60}
],1] ;
xy = ListPlot[XY,PlotJoined->True,AspectRatio->Automatic];

YX=Flatten[Table[ RI , {y, -Pi/2,Pi/2,Pi/10}, {x, -Pi/2, Pi/2,Pi/60}
],1] ;
yx=ListPlot[YX,PlotJoined->True,AspectRatio->Automatic];
Show[xy,yx];

```

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