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File:Principle branch of arg on Riemann.png

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Summary

Description
English: The plot is of the surface of arg, coloured by modulus. The thick red lines indicate the cut used to produce the principle branch, and the red hatched section they bracket is the portion of the surface selected.
Date
Source Own work
Author Kan8eDie
Other versions

Mathematica source code

 Show[
 ParametricPlot3D[
  {l Cos[t], l Sin[t], t},
  {t, -2 \[Pi], 2 \[Pi]}, {l, 0, 10},
  ColorFunction -> (Directive[Hue[0.8*#4], 
      Opacity[If[#5 < 0.8, 1, 1 - 5 (#5 - 0.8)]]] &),
  PlotStyle -> {Opacity[0.8], Specularity[White, 50]},
  BoxRatios -> {1, 1, 1},
  PerformanceGoal -> "Quality",
  PlotPoints -> 100,
  Boxed -> False,
  Ticks -> {Automatic, Automatic, Table[i \[Pi], {i, -2, 2}]},
  ImageSize -> 600,
  AxesLabel -> {\[GothicCapitalR], \[GothicCapitalI], Arg[z]},
  MeshFunctions -> {If[Abs[#4] < \[Pi], #5, 0] &},
  MeshStyle -> {Red}
  ],
 ParametricPlot3D[
  Table[{l Cos[t], l Sin[t], t}, {t, -2 \[Pi], 2 \[Pi], \[Pi]/8}],
  {l, 0, 10},
  ColorFunction -> (Directive[
      Opacity[If[#4 < 0.8, 1, 1 - 5 (#4 - 0.8)]]] &),
  PlotStyle -> Directive[Thin]
  ],
 ParametricPlot3D[
  {{-l, 0, -\[Pi] + 0.05}, {-l, 0, \[Pi] + 0.05}},
  {l, 0, 10},
  PlotStyle -> Directive[Thickness[0.01], Red]
  ]
 ]

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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inception

11 February 2008

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Date/TimeThumbnailDimensionsUserComment
current00:44, 11 February 2009Thumbnail for version as of 00:44, 11 February 2009600 × 596 (72 KB)Kan8eDie{{Information |Description={{en|1=The plot is of the surface of arg, coloured by modulus. The thick red lines indicate the cut used to produce the principle branch, and the red hatched section they bracket is the portion of the surface selected. {{mathema

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