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Mathematics Graphics and Visualization Wolfram Language

Avoid streamlines to smear in ContourPlot[]?

Gary Palmer

Posted 6 years ago

The image illustrates the problem I am having with ContourPlot[]: lines smear and blot when they get too close together. I tried to reduce the number of streamlines, but the Contours option has no effect, whether I specify a number or real values in curly brackets. (MMA 10.0.0.0 on OS 10.9.5) k = Pi/16; streamline[psi_] := ContourPlot[( -(Exp[x] Sin[y ])/(Exp[2 x] - 2 Exp[x] Cos[y ] + 1)) == psi , {x, -Pi, Pi}, {y, -Pi, Pi}, PlotRange -> All, Background -> White]; psiCurves = Table[streamline[psi], {psi, -Pi, Pi, k}]; Show[psiCurves] Attachments: streamlines_dipole.jpg

POSTED BY: Gary Palmer

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Gary Palmer

Posted 6 years ago

With a slight modifications of Henrik's plot, I was able to obtain the desired effects. I sampled the contours list, inceased the thickness, and increased MaxRecursion. Thanks to all for the almost instantaneous help. k = Pi/21; contours = Table[psi, {psi, -Pi, Pi, 2 k}]; contours = Take[contours, {2, -1, 2}]; sl[x, y] := -(Exp[x] Sin[y])/(Exp[2 x] - 2 Exp[x] Cos[y] + 1); ContourPlot[sl[x, y], {x, -Pi, Pi}, {y, -Pi, Pi}, ContourShading -> None, Contours -> contours, PlotRange -> All, ContourStyle -> Thickness[.004], PerformanceGoal -> "Quality", PlotPoints -> 25, MaxRecursion -> 4, ImageSize -> Large] Attachments: mod_dipole.jpg

POSTED BY: Gary Palmer

Henrik Schachner

Henrik Schachner, Radiation Therapy Center, Weilheim, Germany

Posted 6 years ago

These lines come infinitely close each other, so at some level you will always have that effect as they have finite thickness. Maybe this helps a bit: k = Pi/16; contours = Table[psi, {psi, -Pi, Pi, k}]; sl[x_, y_] := -(Exp[x] Sin[y])/(Exp[2 x] - 2 Exp[x] Cos[y] + 1); ContourPlot[sl[x, y], {x, -Pi, Pi}, {y, -Pi, Pi}, ContourShading -> None, Contours -> contours, PlotRange -> All, ContourStyle -> Thickness[.001], PerformanceGoal -> "Quality", PlotPoints -> 25, MaxRecursion -> 2, ImageSize -> Large]

These lines come infinitely close each other, so at some level you will always have that effect as they have finite thickness. Maybe this helps a bit:

k = Pi/16;
contours = Table[psi, {psi, -Pi, Pi, k}];
sl[x_, y_] := -(Exp[x] Sin[y])/(Exp[2 x] - 2 Exp[x] Cos[y] + 1);

ContourPlot[sl[x, y], {x, -Pi, Pi}, {y, -Pi, Pi}, 
 ContourShading -> None, Contours -> contours, PlotRange -> All, 
 ContourStyle -> Thickness[.001], PerformanceGoal -> "Quality", 
 PlotPoints -> 25, MaxRecursion -> 2, ImageSize -> Large]

POSTED BY: Henrik Schachner

Gary Palmer

Posted 6 years ago

The thin style reduces the extent of smearing, but the plot still shows an irregular clumping at the pole (origin), and the thin lines are not the effect I was looking for. I wanted something more like the following: Attachments: contour_cutout.jpg

POSTED BY: Gary Palmer

Kyle Martin

Kyle Martin, WOLFRAM

Posted 6 years ago

What if you specify `ContourStyle -> Thin`, so that the lines take up less space next to one another? Increasing the size of the output also can help, naturally. k = Pi/16; streamline[psi_] := ContourPlot[(-(Exp[x] Sin[y])/(Exp[2 x] - 2 Exp[x] Cos[y] + 1)) == psi, {x, -Pi, Pi}, {y, -Pi, Pi}, PlotRange -> All, Background -> White, ContourStyle -> Thin]; psiCurves = Table[streamline[psi], {psi, -Pi, Pi, k}]; Show[psiCurves, ImageSize -> Large]

What if you specify ContourStyle -> Thin, so that the lines take up less space next to one another? Increasing the size of the output also can help, naturally.

k = Pi/16;

streamline[psi_] := 
  ContourPlot[(-(Exp[x] Sin[y])/(Exp[2 x] - 2 Exp[x] Cos[y] + 1)) == 
    psi, {x, -Pi, Pi}, {y, -Pi, Pi}, PlotRange -> All, 
   Background -> White, ContourStyle -> Thin];

psiCurves = Table[streamline[psi], {psi, -Pi, Pi, k}];

Show[psiCurves, ImageSize -> Large]

enter image description here