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I would like to know how one can coax Mathematica to reveal the coordinates of a generic Graphics3D object. Consider, e.g., the unit sphere:

Graphics3D[Sphere[]]

enter image description here

I realise that the first step is probably to generate a discrete mesh of the object using DiscretizeGraphics[], but what next?

enter image description here

EDIT: I apologise, I was vague about what I really wanted. What I really need is the ability to see the coordinates of each point as I am scrolling over it, like in regular 2d plots. Is that possible?

Note: There is already a question on this topic (Seeing coordinates in Graphics3D) from 2016, but it's only meant for line segments, and thus does not serve my purposes.

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2 Answers 2

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Try

pic = DiscretizeGraphics[ Graphics3D[Sphere[]]]


pic["Coordinates"]

gives you all the points of the surface!

More information concerning pic you can fin with pic["Properties"]

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  • $\begingroup$ Thank you. Ideally, would it be possible to display the coordinates of each point as I am scrolling over it? $\endgroup$
    – ap21
    Mar 1, 2021 at 11:24
  • $\begingroup$ In fact, that is really the question I had. Let me edit my question in order to reflect that. Sorry for the confusion; I really appreciate the first step you have provided here. $\endgroup$
    – ap21
    Mar 1, 2021 at 11:29
  • $\begingroup$ @ap21 If you scroll over the 2D image of the sphere how to decide which of the two 3D points is the right one? $\endgroup$
    – Ulrich Neumann
    Mar 1, 2021 at 11:36
  • $\begingroup$ Good point. But I am taking my cue from software like Matlab, where it is possible to scroll over a point in 3d and get its coordinates. I know it is tricky, and one has to play around to get the good coordinates, but if Matlab has a solution, so should Mathematica. That's why I was asking. $\endgroup$
    – ap21
    Mar 1, 2021 at 11:59
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I got the desired results using Ulrich Neumann's answer, and Algohi's answer in How can I add labels to the points in my scatterplot?

I mesh the Graphics3D object, get its coordinates, plot a 3d scatter plot using ListPointPlot3D, and use Tooltip to display its coordinates:

pic = DiscretizeGraphics[ Graphics3D[Sphere[]]]
coords=pic["Coordinates"]
ListPointPlot3D[MapThread[Tooltip, {coords, coords}]]

Show[%, pic]

So, for example, for a sliver of a cone:

enter image description here

I get:

enter image description here

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