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MathGroup Archive 2007

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Custom Control of Axes and Plot Labels in 2D and 3D Plots

  • To: mathgroup at smc.vnet.net
  • Subject: [mg82144] Custom Control of Axes and Plot Labels in 2D and 3D Plots
  • From: "David Park" <djmpark at comcast.net>
  • Date: Sat, 13 Oct 2007 03:51:23 -0400 (EDT)

There have been a number of questions concerning the control and placement 
of axis labels and overall plot labels in graphics. I believe that for 2D 
graphics there is a complete solution. For 3D graphics it is possible to 
control the placement of the labels but if the image is rotated it will 
always be possible to obtain overlaps between axis labels and tick marks. 
Nevertheless it should be possible to place axis labels for a satisfactory 
result within range of a recommend viewpoint.

For 2D plots, by using PlotRange, PlotRangePadding, ImagePadding and Text 
statements with Scaled coordinates we can place the various plot labels 
where we wish. The following is an example where the plot labels and axis 
labels have been specifically placed:

Graphics[
 {Circle[],
  Text["x", Scaled[{0.55, -0.06}]],
  Text["y", Scaled[{-0.08, 0.55}]],
  Text[Style["A Custom Plot", Large], Scaled[{0.5, 1.1}]],
  Text["Placing Our Own Labels", Scaled[{0, 1.02}], {-1, 0}]},
 PlotRange -> {{-1, 1}, {-1, 1}},
 PlotRangePadding -> 0.05,
 ImagePadding -> {{35, 20}, {35, 60}},
 Frame -> True]

For a 3D plot the problem is more difficult because of the possibility of 
rotating the image. We can place the plot label using Epilog. For short axes 
labels we can place them just inside the bounding box using Text statements. 
Inside the box they tend to be disentangled from the tick labels. But it is 
always possible to select a viewpoint that can cause overlap. The only 
recourse is to place the axes labels according to the predominate view that 
is wanted. We should probably also set the AxesEdge option to always keep 
the axes with the labels. The SphericalRegion and RotationAction options 
provide a 'jump free' interaction with the mouse.

Graphics3D[
 {Sphere[],
  Text["x", Scaled[{0.5, 0.04, 0.04}]],
  Text["y", Scaled[{0.96, 0.5, 0.04}]],
  Text["z", Scaled[{0.04, 0.04, 0.5}]]},
 PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}},
 Epilog -> {Text[Style["A Custom Plot", Large], Scaled[{0.5, 1.2}]],
   Text["Placing Our Own Labels", Scaled[{0, 1.13}], {-1, 0}]},
 PlotRangePadding -> 0.05,
 ImagePadding -> {{35, 20}, {30, 80}},
 Axes -> True,
 AxesEdge -> {{-1, -1}, {1, -1}, {-1, -1}},
 SphericalRegion -> True, RotationAction -> "Clip"]

With longer axes labels the problem again becomes more difficult because 
there is more chance for overlap of the labels and ticks. The following is 
an attempted solution that works within a selected range of viewpoints.

Graphics3D[
 {Sphere[],
  Text["x axis", Scaled[{0.5, 0.04, 0.04}], {-1, 0}],
  Text["y axis", Scaled[{1.1, 0.5, -0.10}], {-1, 0}],
  Text["z axis", Scaled[{-0.10, -0.10, 0.5}], {0, 0}, {0, 1}]},
 PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}},
 Epilog -> {Text[Style["A Custom Plot", Large], Scaled[{0.5, 1.2}]],
   Text["Placing Our Own Labels", Scaled[{0, 1.13}], {-1, 0}]},
 PlotRangePadding -> 0.05,
 ImagePadding -> {{35, 20}, {30, 80}},
 Axes -> True,
 AxesEdge -> {{-1, -1}, {1, -1}, {-1, -1}},
 SphericalRegion -> True, RotationAction -> "Clip"]

If we can settle for a fixed viewpoint it is even possible to have the 
labels parallel to the axes. (However, I don't think that angled text always 
looks that great on the screen. It may look better printed.)

axisstyle[s_] := Style[s, FontSize -> 14, FontWeight -> "Bold"];
Graphics3D[
 {Sphere[],
  Text[axisstyle["x axis"],
   Scaled[{0.5, 0.04, 0.04}], {0, 0}, {1, -0.4}],
  Text[axisstyle["y axis"],
   Scaled[{1.1, 0.5, -0.10}], {-1, 0}, {1, 1.7}],
  Text[axisstyle["z axis"],
   Scaled[{-0.10, -0.10, 0.5}], {0, 0}, {-0.15, 1}]},
 PlotRange -> {{-1, 1}, {-1, 1}, {-1, 1}},
 Epilog -> {Text[Style["A Custom Plot", Large], Scaled[{0.5, 1.2}]],
   Text["Placing Our Own Labels", Scaled[{0, 1.13}], {-1, 0}]},
 PlotRangePadding -> 0.05,
 ImagePadding -> {{35, 20}, {30, 80}},
 Axes -> True,
 AxesEdge -> {{-1, -1}, {1, -1}, {-1, -1}},
 SphericalRegion -> True, RotationAction -> "Clip"]



-- 
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/




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