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Re: Epilog and ListPlot3D

On 7/10/12 at 12:41 AM, gregory.lypny at (Gregory Lypny)

>I'm guessing that Epilog is not an option for ListPointPlot3D.  I
>tried to use it to draw a line from (x1, y1, z1) to (x2, y2, z2) to
>(x3, y3, z3) to emphasize the location of a point at (x3, y3, z3),
>but I got an error.  The Line function works within Graphics3D, so I
>thought it might work the same way in ListPointPlot3D.

Epilog is an option that can be used with ListPointPlot3D as
demonstrated by:

ListPointPlot3D[Table[Sin[j^2 + i], {i, 0, 3, 0.1}, {j, 0, 3, 0.1}],
  Epilog -> {Red, Text[Style["test", 24], {.5, .5}]}]


ListPointPlot3D[Table[Sin[j^2 + i], {i, 0, 3, 0.1}, {j, 0, 3, 0.1}],
  Epilog -> {Red, Line@{{0, 0}, {.5, .5}}}]

But, using it to do what you want isn't the easiest most
intuitive thing to do.

The problem is Epilog renders a 2D graphic. The coordinate
system for the graphic created by Epilog is a 0,1 coordinate
system. So, my second example creates a line running from the
lower left corner of the graphic to the center of the graphic
which you can see when you click on the graphic to rotate it.

Additionally, if you play with the rotation in the first
example, you will see as you rotate the graphic the red "text"
in the center doesn't rotate. And this isn't due to simply
positioning the text at the center of the graphic. Change the
coordinates for the text to {.25,.25} and you will see the label
still doesn't rotate with the graphic.

It is possible (but not easy) to work out the coordinates of the
line you want to drawn. But since it lives in 2D space not the
3D space of the plotted points, I wonder if the effort work out
the correct coordinates for a given view is worth it since any
rotation of the graphic will position your line differently
relative to the plotted points.

If you look up Epilog in the Documentation Center and click on
arrow by more information, you will see the documentation of
coordinates relative to 3D graphics. And if you play with the
examples above you will see the issue I am describing.

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