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Aligned Axes Labels on Plot3D

• To: mathgroup at smc.vnet.net
• Subject: [mg34014] Aligned Axes Labels on Plot3D
• From: Goyder Dr HGD <H.Goyder at rmcs.cranfield.ac.uk>
• Date: Fri, 26 Apr 2002 03:27:44 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

The axes labels obtained by using AxesLabel in Plot3D are unsatisfactory
because they are always horizontal. In my view the z label looks
particularly odd if it is long. For example (with some size exaggeration)

\!\(\(Plot3D[Sin[x\ y], {x, 0, 4}, {y, 0, 5}, \[IndentingNewLine]\ 
      ColorFunction\  -> \ Hue, 
      TextStyle -> {FontFamily -> "\<Times\>", 
          FontSize -> 
            12}, \[IndentingNewLine]AxesLabel -> \ {StyleForm["\<X-axis / \
(m/s)\>", FontSize -> 18, 
            FontFamily -> "\<Times\>"], \
\[IndentingNewLine]StyleForm[\*"\"\<Y-axis / (m/\!\(s\^2\))\>\"", 
            FontSize -> 18, 
            FontFamily -> "\<Times\>"], \
\[IndentingNewLine]StyleForm["\<Z-axis / (kg/Hz)\>", FontSize -> 18, 
            FontFamily -> "\<Times\>"]}];\)\)

I have used Epilog and Text to produce axes labels that are at an angle and
oriented to lie parallel to the coordinate axes. Thus


\!\(\(Plot3D[Sin[x\ y], {x, 0, 4}, {y, 0, 5}, \[IndentingNewLine]\ 
      ColorFunction\  -> \ Hue, 
      TextStyle -> {FontFamily -> "\<Times\>", 
          FontSize -> 12}, \[IndentingNewLine]PlotRegion -> {{0.1, 1}, {0, 
            1}}, \[IndentingNewLine]Epilog -> \ {\[IndentingNewLine]Text[
            StyleForm["\<X-axis / (m/s)\>", FontSize -> 18, 
              FontFamily -> "\<Times\>"], {0.35, 0.15}, {1, 
              0}, {1, \(-0.36\)}], \[IndentingNewLine]Text[
            StyleForm[\*"\"\<Y-axis / (m/\!\(s\^2\))\>\"", FontSize -> 18, 
              FontFamily -> "\<Times\>"], {0.9, 0.25}, {1, 0}, {1, 
              1.6}], \[IndentingNewLine]Text[
            StyleForm["\<Z-axis / (kg/Hz)\>", FontSize -> 18, 
              FontFamily -> "\<Times\>"], {\(-0.03\), 0.4}, {1, 0}, {\(-1\),

              7}]\[IndentingNewLine]}];\)\)



This works well and prints better than it displays on screen. However, I
have had to position and rotate the labels by hand guessing the direction. I
have also had to shrink the plot using PlotRegion to allow room for the axis
label. 

Has anyone done this automatically? For the direction of the text I need the
2D vector that is the projection of each axis. For the coordinates of the
text I need the 2D vector for the middle of each axis.

Thanks in advance

Hugh Goyder