Prolog in Plot3D should use 3D-coordinates

Ideas
,
1
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2

I have sent this request to Wolfram support.

3

Wolfram Technical Support tells me:

Thank you for contacting Wolfram Technical Support. I understand that
you want to have the Prolog/Epilog option take 3-dimentional
coordinates.

Thank you for taking the time to send your report. Mathematica is
working as designed here.

The Prolog/Epilog options are essentially there to specify the order
of shapes appearing in a graphic. If you specify Prolog in a 3D
graphic, you are stating that the object will always appear behind
every other graphic; because of that, only 2 dimensions are needed to
specify its placement which are scaled (from 0 to 1) to the x and y
coordinates of the graphics window.

For example, if I plot Graphics3D[{Sphere[{0, 0, 0}, 10]}, Prolog →
Disk[{.75, .75}, .1]], I am saying that I want the Disk to appear
always behind the Sphere and at position (.75, .75) in relation to the
graphics window.

If I have missed some essential feature of your report, please let me
know.

Best, Andrew Lewis Wolfram Technology Engineer Technical Support
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4

My answer to technical support:

Hello Andrew
Thanks for your answer. I understand your argument:

“The Prolog/Epilog options are essentially there to specify the order of shapes appearing in a graphic.”

OK. But from my point of view they should be more general: Enhance a graphics with some more graphics. In our case: Enhance some 3D-Plot (or -Chart or the like) with any standard Graphics primitives, and - of course – even 3D primitives. This can currently not be done. (It can be reached with Show or Overlay, but not directly within the 3D-Plot).

For me the sequencing done by Prolog or Epilog does not mean behind or before in space, but drawn before or after (with respect to time) the main 3D-Plot.

“If you specify Prolog in a 3D graphic, you are stating that the object will always appear behind every other graphic; because of that, only 2 dimensions are needed.“

From your point of view this is true since you allow only 2D Prolog/Epilog. From my point of view including 3D Prolog/Epilog, it is not true.

A small Example: You draw some 3D surface with Plot3D and then you want to mark the maxima by a Point, an Arrow and some text (or a Callout). Currently you cannot do that within Plot3D. (Well you could misuse LabelingFunction in some tricky (If {x,y,z} nearest to a maximum, …]) way for that).

I think the restriction to 2D-Prolog/Epilog is far too strict. And I suppose, allowing for 3D as well would be very consistent with the Wolfram graphic language and would not be very difficult for you to implement.

Kind regards
Werner Geiger

5

Wolfram Technical Support, Andrew Lewis, answers:

… Specifying a 3-D point as either a Prolog/Epilog in Plot3D would
make sense programmatically, but it would not make a difference to the
overall graphic when compared with using the Show function with Plot3D
and that same 3-D point.

However, I have sent a suggestion report to the appropriate people in
our development team so this can be considered for future versions of
Mathematica. …

Thanks to Andrew