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How does Plot work?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115144] How does Plot work?
  • From: Yaroslav Bulatov <yaroslavvb at gmail.com>
  • Date: Sun, 2 Jan 2011 04:56:19 -0500 (EST)

I've read the chapter in Stan Wagon's book on adaptive plotting, and I
still have unanswered questions

1. How does Plot choose initial 50 points?
If they were chosen to split PlotRange into 49 equal intervals, then
the following Plot would coincide with x-axis, but it doesn't
kk = 49;
plot1 = Plot[Sin[2 Pi x], {x, 0, kk}, Mesh -> All, PlotStyle -> Gray,
  MeshStyle -> Directive[Black, Thick], MaxRecursion -> 0,
  PlotPoints -> kk + 1, PlotRangePadding -> 0,
  PlotRange -> {{0, kk}, {-1, 1}}, Axes -> {True, True}]

2. How does adaptive plotting choose to subdivide the regions?
The explanation in the book is that it subdivides if the angle between
two segments is more than 5 degrees, but you can see in this sequence
below that a segment doesn't get subdivided, even it should be
according to the "5 degree rule". This recently caused a user to
wonder why there was a "hole" in his plot (http://stackoverflow.com/
questions/4572183/strange-sinx-graph-in-mathematica)

plot1 = Plot[Sin[x], {x, -42 Pi, 42 Pi}, PlotPoints -> 100,
   PlotStyle -> LightGray];
Table[plot2 =
   Plot[Sin[x], {x, -42 Pi, 42 Pi}, Mesh -> All, MeshStyle -> Thick,
    PlotStyle -> Red, MaxRecursion -> k];
  Show[plot1, plot2, PlotRange -> {{-110, -90}, {-1, 1}},
   PlotLabel -> ("MaxRecursion " <> ToString[k])], {k, 0,
   5}] // GraphicsColumn


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