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I want to extract data from a plot, more exactly BoundaryDiscretizeRegion[...]. Following Plot, extract data to a file, I use the following codes to make it:

(* Preparation *)
ball = BoundaryDiscretizeRegion@Region[Ball[{0, 0, 0}, 1]];

(* I want to extract the data of ball within Polygon[] *)
Cases[ball, Polygon[data_] :> data, Infinity]
(* ==> {} *)

I wonder why my codes do not work, and how to extract data encapsulated in Polygon[].

Thanks.

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    $\begingroup$ Look up MeshCoordinates and MeshCells. $\endgroup$
    – J. M.'s missing motivation ♦
    Commented Oct 14, 2017 at 13:37
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    $\begingroup$ @J.M. Thanks for your knowledge and warm heart. $\endgroup$
    – PureLine
    Commented Oct 14, 2017 at 14:02
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    $\begingroup$ Just to clarify: this is not a plot, even though it looks like one. It is a BoundaryMeshRegion expression. Take a look at the InputForm of this, as well as Plot's output (which is a Graphics). $\endgroup$
    – Szabolcs
    Commented Oct 14, 2017 at 14:56

2 Answers 2

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There are plenty of data you can extract from your boundary discretized region, for example : 

ball = BoundaryDiscretizeRegion@Region[Ball[{0, 0, 0}, 1]];

MeshPrimitives[ball,0] //Take[#,3]&
MeshPrimitives[ball,1] //Take[#,3]&
MeshPrimitives[ball,2] //Take[#,3]&

{Point[{-0.607062, 0., 0.794654}], Point[{0.894427, 0., 0.447214}],
Point[{0., 0., 1.}]}

{Line[{{0.276393, -0.850651, 0.447214}, {0.204995, -0.829094, 0.520174}}], Line[{{0.204995, -0.829094, 0.520174}, {0.185096, -0.890336, 0.415981}}], Line[{{0.185096, -0.890336, 0.415981}, {0.276393, -0.850651, 0.447214}}]}

{Polygon[{{0.276393, -0.850651, 0.447214}, {0.204995, -0.829094, 0.520174}, {0.185096, -0.890336, 0.415981}}], Polygon[{{0.185096, -0.890336, 0.415981}, {0.204995, -0.829094, 0.520174}, {0.108274, -0.865931, 0.488303}}], Polygon[{{0.185096, -0.890336, 0.415981}, {0.108274, -0.865931, 0.488303}, {0.0871575, -0.92155, 0.378351}}]} 

MeshCoordinates[ball] //Take[#,3]&
MeshCells[ball, 0] //Take[#,3]&
MeshCells[ball, 1] //Take[#,3]&
MeshCells[ball, 2] //Take[#,3]&

{{-0.607062, 0., 0.794654}, {0.894427, 0., 0.447214}, {0., 0., 1.}}

{Point[1], Point[2], Point[3]}

{Line[{7, 38}], Line[{38, 37}], Line[{37, 7}]}

{Polygon[{7, 38, 37}], Polygon[{37, 38, 483}], Polygon[{37, 483, 36}]} 

MeshCellCount[ball, 0] 
MeshCellCount[ball, 1] 
MeshCellCount[ball, 2]

1082

3240

2160

MeshCellIndex[ball, 0] //Take[#,3]&
MeshCellIndex[ball,1] //Take[#,3]&
MeshCellIndex[ball,2] //Take[#,3]&

{{0, 1}, {0, 2}, {0, 3}}

{{1, 1}, {1, 2}, {1, 3}}

{{2, 1}, {2, 2}, {2, 3}} 

PropertyValue[{ball,0},MeshCellMeasure]//Take[#,3]&
PropertyValue[{ball,1},MeshCellMeasure]//Take[#,3]&
PropertyValue[{ball,2},MeshCellMeasure]//Take[#,3]&

{1., 1., 1.}

{0.104334, 0.122485, 0.104334}

{0.00517309, 0.00546982, 0.00557218}

0,1,2 in the Mesh... expressions correspond to the dimensions of the elements you are interested in. There aren't any dimension 3 elements in your example.

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Thanks for @J. M. advice. It's the very answer of my question.

(* extract the indexes of points, which construct the cells of mesh *)
indexOfCells = Cases[MeshCells[reg, 2], Polygon[coord_] :> coord]
(* {{56795, 56753, 56794}, ... {56793, 56752, 56751}} *)

With these data, I can carry out reverse engineering of msome organic texture for the mechanism of robots.

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