RegionMember does not work with RandomPolyhedron or Polyhedron objectHow can I decide whether a closed surface is intersected by a triangle?Region Intersection for MeshRegion objects embedded in 3DThrough does not work with SubtractFitting does not workHandling Self-Intersecting RegionsDetermine whether points lie within a cowVolumes and moments of inertia of meshes in 3DParametricPlot3D coloring based on whether function located inside/outside of another parametric functionBooleanRegion with .stl files does not workInconsistent mesh generation from BoundaryDiscretizeRegion and ToBoundaryMesh at creases
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RegionMember does not work with RandomPolyhedron or Polyhedron object
How can I decide whether a closed surface is intersected by a triangle?Region Intersection for MeshRegion objects embedded in 3DThrough does not work with SubtractFitting does not workHandling Self-Intersecting RegionsDetermine whether points lie within a cowVolumes and moments of inertia of meshes in 3DParametricPlot3D coloring based on whether function located inside/outside of another parametric functionBooleanRegion with .stl files does not workInconsistent mesh generation from BoundaryDiscretizeRegion and ToBoundaryMesh at creases
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
3
$begingroup$
According to the documentation RegionMember should work with regions that are true for ConstantRegionQ. However, the function does not work with simple polyhedra.
Consider:
ConstantRegionQ@RandomPolyhedron[5]
(*True*)
RegionMember@RandomPolyhedron[5]
(* *)
I am using version 12.0. Is this a bug?
And since RegionMember is not working, is there a way to test whether a point lies inside or outside a user defined polyhedra?
An example for a user defined polyhedron (here i have triangulated the individual faces because the vertices of a face does not have to be coplanar):
data = 0.9000000000, 9.803074361, -0.2788974201, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
10.19278579, -0.2270388454, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
10.19278579, -0.2379129589, 0,
9.803074361, -0.3066046725, 0.4500000000,
9.803074361, -0.2935999100, 0,
9.803074361, -0.3066046725, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
9.413362929, -0.3638887807, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
9.413362929, -0.3472567826, 0.9000000000,
9.803074361, -0.2788974201, 0.4500000000,
9.803074361, -0.2935999100, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.4500000000,
9.803074361, -1.293599910, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.4500000000,
9.803074361, -1.293599910, 0.9000000000,
9.803074361, -0.2788974201, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.997930077, -0.7529681327, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -1.227038845, 0.6750000000,
10.19278579, -0.2270388454, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
10.19278579, -0.7324759022, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -1.237912959, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.2250000000,
10.19278579, -1.237912959, 0.1125000000,
9.997930077, -0.7722588157, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.1125000000,
9.997930077, -0.7722588157, 0, 9.803074361, -1.306604673, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0.2250000000,
10.19278579, -0.2379129589, 0.1125000000,
9.997930077, -0.7722588157, 0, 9.803074361, -0.3066046725, 0,
9.803074361, -1.306604673, 0.1125000000,
9.608218645, -0.8352467266, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -1.363888781, 0.2250000000,
9.413362929, -0.3638887807, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.413362929, -0.8555727816, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -1.347256783, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.6750000000,
9.413362929, -1.347256783, 0.7875000000,
9.608218645, -0.8130771013, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -1.278897420, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
9.413362929, -0.3472567826, 0.7875000000,
9.608218645, -0.8130771013;
Polyhedron@data
functions computational-geometry mesh
asked Jul 10 at 3:24
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
$endgroup$
add a comment |
3
$begingroup$
According to the documentation RegionMember should work with regions that are true for ConstantRegionQ. However, the function does not work with simple polyhedra.
Consider:
ConstantRegionQ@RandomPolyhedron[5]
(*True*)
RegionMember@RandomPolyhedron[5]
(* *)
I am using version 12.0. Is this a bug?
And since RegionMember is not working, is there a way to test whether a point lies inside or outside a user defined polyhedra?
An example for a user defined polyhedron (here i have triangulated the individual faces because the vertices of a face does not have to be coplanar):
data = 0.9000000000, 9.803074361, -0.2788974201, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
10.19278579, -0.2270388454, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
10.19278579, -0.2379129589, 0,
9.803074361, -0.3066046725, 0.4500000000,
9.803074361, -0.2935999100, 0,
9.803074361, -0.3066046725, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
9.413362929, -0.3638887807, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
9.413362929, -0.3472567826, 0.9000000000,
9.803074361, -0.2788974201, 0.4500000000,
9.803074361, -0.2935999100, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.4500000000,
9.803074361, -1.293599910, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.4500000000,
9.803074361, -1.293599910, 0.9000000000,
9.803074361, -0.2788974201, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.997930077, -0.7529681327, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -1.227038845, 0.6750000000,
10.19278579, -0.2270388454, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
10.19278579, -0.7324759022, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -1.237912959, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.2250000000,
10.19278579, -1.237912959, 0.1125000000,
9.997930077, -0.7722588157, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.1125000000,
9.997930077, -0.7722588157, 0, 9.803074361, -1.306604673, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0.2250000000,
10.19278579, -0.2379129589, 0.1125000000,
9.997930077, -0.7722588157, 0, 9.803074361, -0.3066046725, 0,
9.803074361, -1.306604673, 0.1125000000,
9.608218645, -0.8352467266, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -1.363888781, 0.2250000000,
9.413362929, -0.3638887807, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.413362929, -0.8555727816, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -1.347256783, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.6750000000,
9.413362929, -1.347256783, 0.7875000000,
9.608218645, -0.8130771013, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -1.278897420, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
9.413362929, -0.3472567826, 0.7875000000,
9.608218645, -0.8130771013;
Polyhedron@data
functions computational-geometry mesh
asked Jul 10 at 3:24
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
$endgroup$
add a comment |
3
3
3
$begingroup$
According to the documentation RegionMember should work with regions that are true for ConstantRegionQ. However, the function does not work with simple polyhedra.
Consider:
ConstantRegionQ@RandomPolyhedron[5]
(*True*)
RegionMember@RandomPolyhedron[5]
(* *)
I am using version 12.0. Is this a bug?
And since RegionMember is not working, is there a way to test whether a point lies inside or outside a user defined polyhedra?
An example for a user defined polyhedron (here i have triangulated the individual faces because the vertices of a face does not have to be coplanar):
data = 0.9000000000, 9.803074361, -0.2788974201, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
10.19278579, -0.2270388454, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
10.19278579, -0.2379129589, 0,
9.803074361, -0.3066046725, 0.4500000000,
9.803074361, -0.2935999100, 0,
9.803074361, -0.3066046725, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
9.413362929, -0.3638887807, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
9.413362929, -0.3472567826, 0.9000000000,
9.803074361, -0.2788974201, 0.4500000000,
9.803074361, -0.2935999100, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.4500000000,
9.803074361, -1.293599910, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.4500000000,
9.803074361, -1.293599910, 0.9000000000,
9.803074361, -0.2788974201, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.997930077, -0.7529681327, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -1.227038845, 0.6750000000,
10.19278579, -0.2270388454, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
10.19278579, -0.7324759022, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -1.237912959, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.2250000000,
10.19278579, -1.237912959, 0.1125000000,
9.997930077, -0.7722588157, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.1125000000,
9.997930077, -0.7722588157, 0, 9.803074361, -1.306604673, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0.2250000000,
10.19278579, -0.2379129589, 0.1125000000,
9.997930077, -0.7722588157, 0, 9.803074361, -0.3066046725, 0,
9.803074361, -1.306604673, 0.1125000000,
9.608218645, -0.8352467266, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -1.363888781, 0.2250000000,
9.413362929, -0.3638887807, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.413362929, -0.8555727816, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -1.347256783, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.6750000000,
9.413362929, -1.347256783, 0.7875000000,
9.608218645, -0.8130771013, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -1.278897420, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
9.413362929, -0.3472567826, 0.7875000000,
9.608218645, -0.8130771013;
Polyhedron@data
functions computational-geometry mesh
asked Jul 10 at 3:24
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
$endgroup$
According to the documentation RegionMember should work with regions that are true for ConstantRegionQ. However, the function does not work with simple polyhedra.
Consider:
ConstantRegionQ@RandomPolyhedron[5]
(*True*)
RegionMember@RandomPolyhedron[5]
(* *)
I am using version 12.0. Is this a bug?
And since RegionMember is not working, is there a way to test whether a point lies inside or outside a user defined polyhedra?
An example for a user defined polyhedron (here i have triangulated the individual faces because the vertices of a face does not have to be coplanar):
data = 0.9000000000, 9.803074361, -0.2788974201, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
10.19278579, -0.2270388454, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
10.19278579, -0.2379129589, 0,
9.803074361, -0.3066046725, 0.4500000000,
9.803074361, -0.2935999100, 0,
9.803074361, -0.3066046725, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
9.413362929, -0.3638887807, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
9.413362929, -0.3472567826, 0.9000000000,
9.803074361, -0.2788974201, 0.4500000000,
9.803074361, -0.2935999100, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.4500000000,
9.803074361, -1.293599910, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.4500000000,
9.803074361, -1.293599910, 0.9000000000,
9.803074361, -0.2788974201, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.997930077, -0.7529681327, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -1.227038845, 0.6750000000,
10.19278579, -0.2270388454, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
10.19278579, -0.7324759022, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -1.237912959, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.2250000000,
10.19278579, -1.237912959, 0.1125000000,
9.997930077, -0.7722588157, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.1125000000,
9.997930077, -0.7722588157, 0, 9.803074361, -1.306604673, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0.2250000000,
10.19278579, -0.2379129589, 0.1125000000,
9.997930077, -0.7722588157, 0, 9.803074361, -0.3066046725, 0,
9.803074361, -1.306604673, 0.1125000000,
9.608218645, -0.8352467266, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -1.363888781, 0.2250000000,
9.413362929, -0.3638887807, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.413362929, -0.8555727816, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -1.347256783, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.6750000000,
9.413362929, -1.347256783, 0.7875000000,
9.608218645, -0.8130771013, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -1.278897420, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
9.413362929, -0.3472567826, 0.7875000000,
9.608218645, -0.8130771013;
Polyhedron@data
functions computational-geometry mesh
functions computational-geometry mesh
asked Jul 10 at 3:24
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
asked Jul 10 at 3:24
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
edited Jul 10 at 6:09
Ali Hashmi
asked Jul 10 at 3:24
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
asked Jul 10 at 3:24
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
asked Jul 10 at 3:24
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
5,9604 gold badges15 silver badges34 bronze badges
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
4
$begingroup$
You could also try:
RegionMember[
BoundaryDiscretizeGraphics@CanonicalizePolyhedron[Polyhedron[data]]]
answered Jul 10 at 14:01
halmirhalmir
11.2k28 silver badges46 bronze badges
$endgroup$
add a comment |
4
$begingroup$
Polyhedrons are a very new data type and it is not unusual that not all possible functions have been overloaded for them.
You can extract the vertex coordinates of a Polyhedron R with R[[1]]; combined with ConvexHullMesh, this allows you to convert the Polyhedron to a MeshRegion and to apply `RandomPoint:
R = RandomPolyhedron[5];
S = ConvexHullMesh[R[[1]]];
RandomMember[S]
With the user-defined "polyhedron", you can do, e.g., this:
R = BoundaryDiscretizeGraphics@Graphics3D[
Polygon[0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
10.19278579, -0.2270388454, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
10.19278579, -0.2379129589, 0,
9.803074361, -0.3066046725, 0.4500000000,
9.803074361, -0.2935999100, 0,
9.803074361, -0.3066046725, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
9.413362929, -0.3638887807, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
9.413362929, -0.3472567826, 0.9000000000,
9.803074361, -0.2788974201, 0.4500000000,
9.803074361, -0.2935999100, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.4500000000,
9.803074361, -1.293599910, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.4500000000,
9.803074361, -1.293599910, 0.9000000000,
9.803074361, -0.2788974201, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.997930077, -0.7529681327, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -1.227038845, 0.6750000000,
10.19278579, -0.2270388454, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
10.19278579, -0.7324759022, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -1.237912959, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.2250000000,
10.19278579, -1.237912959, 0.1125000000,
9.997930077, -0.7722588157, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -1.306604673, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0.2250000000,
10.19278579, -0.2379129589, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0,
9.803074361, -1.306604673, 0.1125000000,
9.608218645, -0.8352467266, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -1.363888781, 0.2250000000,
9.413362929, -0.3638887807, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.413362929, -0.8555727816, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -1.347256783, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.6750000000,
9.413362929, -1.347256783, 0.7875000000,
9.608218645, -0.8130771013, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -1.278897420, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
9.413362929, -0.3472567826, 0.7875000000,
9.608218645, -0.8130771013]
];
RandomMember[R]
PS.: I have no clue at all what this new datatype is supposed to ship what is not already provided MeshRegions.
answered Jul 10 at 3:50
Henrik SchumacherHenrik Schumacher
65.4k5 gold badges94 silver badges180 bronze badges
$endgroup$
$begingroup$
thanks. what about the case if my polyhedron have faces wherein the vertices are not coplanar. What I have done is that I have triangulated those faces and can display a polyhedron successfully. Do you think the approach that you have mentioned above will work for such a polyhedron?
$endgroup$
– Ali Hashmi
Jul 10 at 4:32
$begingroup$
kindly check the example that I posted in the question
$endgroup$
– Ali Hashmi
Jul 10 at 4:43
$begingroup$
thanks. I was working on a solution myself as well. We both reached the same answer :) I will accept your answer however
$endgroup$
– Ali Hashmi
Jul 10 at 5:47
add a comment |
3
$begingroup$
here is a little fix that should work for both cases:
datamodified = data /. 0.4500000000, 9.803074361, -0.2935999100 -> 0.4500000000,
9.803074361, -0.3935999100 (* this will make vertices of one face non-coplanar *)
poly = Polyhedron[datamodified];
points = DeleteDuplicates@Flatten[poly[[1]], 1];
assoc = AssociationThread[points -> Range[Length@points]];
order = Map[Lookup[assoc, #] &, poly[[1]]];
reg = DiscretizeGraphics@Region@Polyhedron[points, order];
RegionMember@reg
answered Jul 10 at 5:42
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
$endgroup$
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
4
$begingroup$
You could also try:
RegionMember[
BoundaryDiscretizeGraphics@CanonicalizePolyhedron[Polyhedron[data]]]
answered Jul 10 at 14:01
halmirhalmir
11.2k28 silver badges46 bronze badges
$endgroup$
add a comment |
4
$begingroup$
You could also try:
RegionMember[
BoundaryDiscretizeGraphics@CanonicalizePolyhedron[Polyhedron[data]]]
answered Jul 10 at 14:01
halmirhalmir
11.2k28 silver badges46 bronze badges
$endgroup$
add a comment |
4
4
4
$begingroup$
You could also try:
RegionMember[
BoundaryDiscretizeGraphics@CanonicalizePolyhedron[Polyhedron[data]]]
answered Jul 10 at 14:01
halmirhalmir
11.2k28 silver badges46 bronze badges
$endgroup$
You could also try:
RegionMember[
BoundaryDiscretizeGraphics@CanonicalizePolyhedron[Polyhedron[data]]]
answered Jul 10 at 14:01
halmirhalmir
11.2k28 silver badges46 bronze badges
answered Jul 10 at 14:01
halmirhalmir
11.2k28 silver badges46 bronze badges
answered Jul 10 at 14:01
halmirhalmir
11.2k28 silver badges46 bronze badges
answered Jul 10 at 14:01
halmirhalmir
11.2k28 silver badges46 bronze badges
11.2k28 silver badges46 bronze badges
add a comment |
add a comment |
4
$begingroup$
Polyhedrons are a very new data type and it is not unusual that not all possible functions have been overloaded for them.
You can extract the vertex coordinates of a Polyhedron R with R[[1]]; combined with ConvexHullMesh, this allows you to convert the Polyhedron to a MeshRegion and to apply `RandomPoint:
R = RandomPolyhedron[5];
S = ConvexHullMesh[R[[1]]];
RandomMember[S]
With the user-defined "polyhedron", you can do, e.g., this:
R = BoundaryDiscretizeGraphics@Graphics3D[
Polygon[0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
10.19278579, -0.2270388454, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
10.19278579, -0.2379129589, 0,
9.803074361, -0.3066046725, 0.4500000000,
9.803074361, -0.2935999100, 0,
9.803074361, -0.3066046725, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
9.413362929, -0.3638887807, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
9.413362929, -0.3472567826, 0.9000000000,
9.803074361, -0.2788974201, 0.4500000000,
9.803074361, -0.2935999100, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.4500000000,
9.803074361, -1.293599910, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.4500000000,
9.803074361, -1.293599910, 0.9000000000,
9.803074361, -0.2788974201, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.997930077, -0.7529681327, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -1.227038845, 0.6750000000,
10.19278579, -0.2270388454, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
10.19278579, -0.7324759022, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -1.237912959, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.2250000000,
10.19278579, -1.237912959, 0.1125000000,
9.997930077, -0.7722588157, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -1.306604673, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0.2250000000,
10.19278579, -0.2379129589, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0,
9.803074361, -1.306604673, 0.1125000000,
9.608218645, -0.8352467266, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -1.363888781, 0.2250000000,
9.413362929, -0.3638887807, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.413362929, -0.8555727816, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -1.347256783, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.6750000000,
9.413362929, -1.347256783, 0.7875000000,
9.608218645, -0.8130771013, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -1.278897420, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
9.413362929, -0.3472567826, 0.7875000000,
9.608218645, -0.8130771013]
];
RandomMember[R]
PS.: I have no clue at all what this new datatype is supposed to ship what is not already provided MeshRegions.
answered Jul 10 at 3:50
Henrik SchumacherHenrik Schumacher
65.4k5 gold badges94 silver badges180 bronze badges
$endgroup$
$begingroup$
thanks. what about the case if my polyhedron have faces wherein the vertices are not coplanar. What I have done is that I have triangulated those faces and can display a polyhedron successfully. Do you think the approach that you have mentioned above will work for such a polyhedron?
$endgroup$
– Ali Hashmi
Jul 10 at 4:32
$begingroup$
kindly check the example that I posted in the question
$endgroup$
– Ali Hashmi
Jul 10 at 4:43
$begingroup$
thanks. I was working on a solution myself as well. We both reached the same answer :) I will accept your answer however
$endgroup$
– Ali Hashmi
Jul 10 at 5:47
add a comment |
4
$begingroup$
Polyhedrons are a very new data type and it is not unusual that not all possible functions have been overloaded for them.
You can extract the vertex coordinates of a Polyhedron R with R[[1]]; combined with ConvexHullMesh, this allows you to convert the Polyhedron to a MeshRegion and to apply `RandomPoint:
R = RandomPolyhedron[5];
S = ConvexHullMesh[R[[1]]];
RandomMember[S]
With the user-defined "polyhedron", you can do, e.g., this:
R = BoundaryDiscretizeGraphics@Graphics3D[
Polygon[0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
10.19278579, -0.2270388454, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
10.19278579, -0.2379129589, 0,
9.803074361, -0.3066046725, 0.4500000000,
9.803074361, -0.2935999100, 0,
9.803074361, -0.3066046725, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
9.413362929, -0.3638887807, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
9.413362929, -0.3472567826, 0.9000000000,
9.803074361, -0.2788974201, 0.4500000000,
9.803074361, -0.2935999100, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.4500000000,
9.803074361, -1.293599910, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.4500000000,
9.803074361, -1.293599910, 0.9000000000,
9.803074361, -0.2788974201, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.997930077, -0.7529681327, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -1.227038845, 0.6750000000,
10.19278579, -0.2270388454, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
10.19278579, -0.7324759022, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -1.237912959, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.2250000000,
10.19278579, -1.237912959, 0.1125000000,
9.997930077, -0.7722588157, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -1.306604673, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0.2250000000,
10.19278579, -0.2379129589, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0,
9.803074361, -1.306604673, 0.1125000000,
9.608218645, -0.8352467266, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -1.363888781, 0.2250000000,
9.413362929, -0.3638887807, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.413362929, -0.8555727816, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -1.347256783, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.6750000000,
9.413362929, -1.347256783, 0.7875000000,
9.608218645, -0.8130771013, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -1.278897420, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
9.413362929, -0.3472567826, 0.7875000000,
9.608218645, -0.8130771013]
];
RandomMember[R]
PS.: I have no clue at all what this new datatype is supposed to ship what is not already provided MeshRegions.
answered Jul 10 at 3:50
Henrik SchumacherHenrik Schumacher
65.4k5 gold badges94 silver badges180 bronze badges
$endgroup$
$begingroup$
thanks. what about the case if my polyhedron have faces wherein the vertices are not coplanar. What I have done is that I have triangulated those faces and can display a polyhedron successfully. Do you think the approach that you have mentioned above will work for such a polyhedron?
$endgroup$
– Ali Hashmi
Jul 10 at 4:32
$begingroup$
kindly check the example that I posted in the question
$endgroup$
– Ali Hashmi
Jul 10 at 4:43
$begingroup$
thanks. I was working on a solution myself as well. We both reached the same answer :) I will accept your answer however
$endgroup$
– Ali Hashmi
Jul 10 at 5:47
add a comment |
4
4
4
$begingroup$
Polyhedrons are a very new data type and it is not unusual that not all possible functions have been overloaded for them.
You can extract the vertex coordinates of a Polyhedron R with R[[1]]; combined with ConvexHullMesh, this allows you to convert the Polyhedron to a MeshRegion and to apply `RandomPoint:
R = RandomPolyhedron[5];
S = ConvexHullMesh[R[[1]]];
RandomMember[S]
With the user-defined "polyhedron", you can do, e.g., this:
R = BoundaryDiscretizeGraphics@Graphics3D[
Polygon[0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
10.19278579, -0.2270388454, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
10.19278579, -0.2379129589, 0,
9.803074361, -0.3066046725, 0.4500000000,
9.803074361, -0.2935999100, 0,
9.803074361, -0.3066046725, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
9.413362929, -0.3638887807, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
9.413362929, -0.3472567826, 0.9000000000,
9.803074361, -0.2788974201, 0.4500000000,
9.803074361, -0.2935999100, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.4500000000,
9.803074361, -1.293599910, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.4500000000,
9.803074361, -1.293599910, 0.9000000000,
9.803074361, -0.2788974201, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.997930077, -0.7529681327, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -1.227038845, 0.6750000000,
10.19278579, -0.2270388454, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
10.19278579, -0.7324759022, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -1.237912959, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.2250000000,
10.19278579, -1.237912959, 0.1125000000,
9.997930077, -0.7722588157, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -1.306604673, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0.2250000000,
10.19278579, -0.2379129589, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0,
9.803074361, -1.306604673, 0.1125000000,
9.608218645, -0.8352467266, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -1.363888781, 0.2250000000,
9.413362929, -0.3638887807, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.413362929, -0.8555727816, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -1.347256783, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.6750000000,
9.413362929, -1.347256783, 0.7875000000,
9.608218645, -0.8130771013, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -1.278897420, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
9.413362929, -0.3472567826, 0.7875000000,
9.608218645, -0.8130771013]
];
RandomMember[R]
PS.: I have no clue at all what this new datatype is supposed to ship what is not already provided MeshRegions.
answered Jul 10 at 3:50
Henrik SchumacherHenrik Schumacher
65.4k5 gold badges94 silver badges180 bronze badges
$endgroup$
Polyhedrons are a very new data type and it is not unusual that not all possible functions have been overloaded for them.
You can extract the vertex coordinates of a Polyhedron R with R[[1]]; combined with ConvexHullMesh, this allows you to convert the Polyhedron to a MeshRegion and to apply `RandomPoint:
R = RandomPolyhedron[5];
S = ConvexHullMesh[R[[1]]];
RandomMember[S]
With the user-defined "polyhedron", you can do, e.g., this:
R = BoundaryDiscretizeGraphics@Graphics3D[
Polygon[0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
10.19278579, -0.2270388454, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
10.19278579, -0.2379129589, 0,
9.803074361, -0.3066046725, 0.4500000000,
9.803074361, -0.2935999100, 0,
9.803074361, -0.3066046725, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.803074361, -0.2935999100, 0.2250000000,
9.413362929, -0.3638887807, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.803074361, -0.2935999100, 0.6750000000,
9.413362929, -0.3472567826, 0.9000000000,
9.803074361, -0.2788974201, 0.4500000000,
9.803074361, -0.2935999100, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.4500000000,
9.803074361, -1.293599910, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.803074361, -1.293599910, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.803074361, -1.293599910, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.4500000000,
9.803074361, -1.293599910, 0.9000000000,
9.803074361, -0.2788974201, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.997930077, -0.7529681327, 0.9000000000,
9.803074361, -1.278897420, 0.6750000000,
10.19278579, -1.227038845, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -1.227038845, 0.6750000000,
10.19278579, -0.2270388454, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.997930077, -0.7529681327, 0.6750000000,
10.19278579, -0.2270388454, 0.6750000000,
10.19278579, -1.227038845, 0.4500000000,
10.19278579, -0.7324759022, 0.6750000000,
10.19278579, -1.227038845, 0.2250000000,
10.19278579, -1.237912959, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -1.237912959, 0.2250000000,
10.19278579, -0.2379129589, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.6750000000,
10.19278579, -0.2270388454, 0.4500000000,
10.19278579, -0.7324759022, 0.2250000000,
10.19278579, -0.2379129589, 0.2250000000,
10.19278579, -1.237912959, 0.1125000000,
9.997930077, -0.7722588157, 0.2250000000,
10.19278579, -1.237912959, 0,
9.803074361, -1.306604673, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -1.306604673, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0.2250000000,
10.19278579, -0.2379129589, 0.1125000000,
9.997930077, -0.7722588157, 0,
9.803074361, -0.3066046725, 0,
9.803074361, -1.306604673, 0.1125000000,
9.608218645, -0.8352467266, 0,
9.803074361, -1.306604673, 0.2250000000,
9.413362929, -1.363888781, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -1.363888781, 0.2250000000,
9.413362929, -0.3638887807, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0,
9.803074361, -0.3066046725, 0.1125000000,
9.608218645, -0.8352467266, 0.2250000000,
9.413362929, -0.3638887807, 0.2250000000,
9.413362929, -1.363888781, 0.4500000000,
9.413362929, -0.8555727816, 0.2250000000,
9.413362929, -1.363888781, 0.6750000000,
9.413362929, -1.347256783, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -1.347256783, 0.6750000000,
9.413362929, -0.3472567826, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.2250000000,
9.413362929, -0.3638887807, 0.4500000000,
9.413362929, -0.8555727816, 0.6750000000,
9.413362929, -0.3472567826, 0.6750000000,
9.413362929, -1.347256783, 0.7875000000,
9.608218645, -0.8130771013, 0.6750000000,
9.413362929, -1.347256783, 0.9000000000,
9.803074361, -1.278897420, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -1.278897420, 0.9000000000,
9.803074361, -0.2788974201, 0.7875000000,
9.608218645, -0.8130771013, 0.9000000000,
9.803074361, -0.2788974201, 0.6750000000,
9.413362929, -0.3472567826, 0.7875000000,
9.608218645, -0.8130771013]
];
RandomMember[R]
PS.: I have no clue at all what this new datatype is supposed to ship what is not already provided MeshRegions.
answered Jul 10 at 3:50
Henrik SchumacherHenrik Schumacher
65.4k5 gold badges94 silver badges180 bronze badges
edited Jul 10 at 17:49
answered Jul 10 at 3:50
Henrik SchumacherHenrik Schumacher
65.4k5 gold badges94 silver badges180 bronze badges
answered Jul 10 at 3:50
Henrik SchumacherHenrik Schumacher
65.4k5 gold badges94 silver badges180 bronze badges
answered Jul 10 at 3:50
Henrik SchumacherHenrik Schumacher
65.4k5 gold badges94 silver badges180 bronze badges
65.4k5 gold badges94 silver badges180 bronze badges
$begingroup$
thanks. what about the case if my polyhedron have faces wherein the vertices are not coplanar. What I have done is that I have triangulated those faces and can display a polyhedron successfully. Do you think the approach that you have mentioned above will work for such a polyhedron?
$endgroup$
– Ali Hashmi
Jul 10 at 4:32
$begingroup$
kindly check the example that I posted in the question
$endgroup$
– Ali Hashmi
Jul 10 at 4:43
$begingroup$
thanks. I was working on a solution myself as well. We both reached the same answer :) I will accept your answer however
$endgroup$
– Ali Hashmi
Jul 10 at 5:47
add a comment |
$begingroup$
thanks. what about the case if my polyhedron have faces wherein the vertices are not coplanar. What I have done is that I have triangulated those faces and can display a polyhedron successfully. Do you think the approach that you have mentioned above will work for such a polyhedron?
$endgroup$
– Ali Hashmi
Jul 10 at 4:32
$begingroup$
kindly check the example that I posted in the question
$endgroup$
– Ali Hashmi
Jul 10 at 4:43
$begingroup$
thanks. I was working on a solution myself as well. We both reached the same answer :) I will accept your answer however
$endgroup$
– Ali Hashmi
Jul 10 at 5:47
$begingroup$
thanks. what about the case if my polyhedron have faces wherein the vertices are not coplanar. What I have done is that I have triangulated those faces and can display a polyhedron successfully. Do you think the approach that you have mentioned above will work for such a polyhedron?
$endgroup$
– Ali Hashmi
Jul 10 at 4:32
$begingroup$
thanks. what about the case if my polyhedron have faces wherein the vertices are not coplanar. What I have done is that I have triangulated those faces and can display a polyhedron successfully. Do you think the approach that you have mentioned above will work for such a polyhedron?
$endgroup$
– Ali Hashmi
Jul 10 at 4:32
$begingroup$
kindly check the example that I posted in the question
$endgroup$
– Ali Hashmi
Jul 10 at 4:43
$begingroup$
kindly check the example that I posted in the question
$endgroup$
– Ali Hashmi
Jul 10 at 4:43
$begingroup$
thanks. I was working on a solution myself as well. We both reached the same answer :) I will accept your answer however
$endgroup$
– Ali Hashmi
Jul 10 at 5:47
$begingroup$
thanks. I was working on a solution myself as well. We both reached the same answer :) I will accept your answer however
$endgroup$
– Ali Hashmi
Jul 10 at 5:47
add a comment |
3
$begingroup$
here is a little fix that should work for both cases:
datamodified = data /. 0.4500000000, 9.803074361, -0.2935999100 -> 0.4500000000,
9.803074361, -0.3935999100 (* this will make vertices of one face non-coplanar *)
poly = Polyhedron[datamodified];
points = DeleteDuplicates@Flatten[poly[[1]], 1];
assoc = AssociationThread[points -> Range[Length@points]];
order = Map[Lookup[assoc, #] &, poly[[1]]];
reg = DiscretizeGraphics@Region@Polyhedron[points, order];
RegionMember@reg
answered Jul 10 at 5:42
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
$endgroup$
add a comment |
3
$begingroup$
here is a little fix that should work for both cases:
datamodified = data /. 0.4500000000, 9.803074361, -0.2935999100 -> 0.4500000000,
9.803074361, -0.3935999100 (* this will make vertices of one face non-coplanar *)
poly = Polyhedron[datamodified];
points = DeleteDuplicates@Flatten[poly[[1]], 1];
assoc = AssociationThread[points -> Range[Length@points]];
order = Map[Lookup[assoc, #] &, poly[[1]]];
reg = DiscretizeGraphics@Region@Polyhedron[points, order];
RegionMember@reg
answered Jul 10 at 5:42
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
$endgroup$
add a comment |
3
3
3
$begingroup$
here is a little fix that should work for both cases:
datamodified = data /. 0.4500000000, 9.803074361, -0.2935999100 -> 0.4500000000,
9.803074361, -0.3935999100 (* this will make vertices of one face non-coplanar *)
poly = Polyhedron[datamodified];
points = DeleteDuplicates@Flatten[poly[[1]], 1];
assoc = AssociationThread[points -> Range[Length@points]];
order = Map[Lookup[assoc, #] &, poly[[1]]];
reg = DiscretizeGraphics@Region@Polyhedron[points, order];
RegionMember@reg
answered Jul 10 at 5:42
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
$endgroup$
here is a little fix that should work for both cases:
datamodified = data /. 0.4500000000, 9.803074361, -0.2935999100 -> 0.4500000000,
9.803074361, -0.3935999100 (* this will make vertices of one face non-coplanar *)
poly = Polyhedron[datamodified];
points = DeleteDuplicates@Flatten[poly[[1]], 1];
assoc = AssociationThread[points -> Range[Length@points]];
order = Map[Lookup[assoc, #] &, poly[[1]]];
reg = DiscretizeGraphics@Region@Polyhedron[points, order];
RegionMember@reg
answered Jul 10 at 5:42
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
answered Jul 10 at 5:42
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
answered Jul 10 at 5:42
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
answered Jul 10 at 5:42
Ali HashmiAli Hashmi
5,9604 gold badges15 silver badges34 bronze badges
5,9604 gold badges15 silver badges34 bronze badges
add a comment |
add a comment |
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