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How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will not work (see "possible issues" in the Mathematica documentation https://reference.wolfram.com/language/ref/RegionIntersection.html).

I know that RegionPlot3D allows logical operators - perhaps there is a way to plot the MeshRegions to a RegionPlot3D and use logical operators to create an intersection?

Something else I thought may work is checking for region membership in all the regions I want to intersect of the tetrahedra making up the mesh region, but RegionMember only checks membership of points.

The types of MeshRegions I am working with are 3D Delaunay, for example

DelaunayMesh@RandomReal[{-1, 1}, {25, 3}]

EDIT: I tried to use this solutionthis solution as suggested in the comments, but it only seems to work for two polyhedra that have the same general shape: only one variable is used for how the vertices should be connected ("faces"). Also, I cannot fully understand the method by which the intersection points were found. It seems to rely on the fact that z convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities (see here). Is there perhaps a simpler way?

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will not work (see "possible issues" in the Mathematica documentation https://reference.wolfram.com/language/ref/RegionIntersection.html).

I know that RegionPlot3D allows logical operators - perhaps there is a way to plot the MeshRegions to a RegionPlot3D and use logical operators to create an intersection?

Something else I thought may work is checking for region membership in all the regions I want to intersect of the tetrahedra making up the mesh region, but RegionMember only checks membership of points.

The types of MeshRegions I am working with are 3D Delaunay, for example

DelaunayMesh@RandomReal[{-1, 1}, {25, 3}]

EDIT: I tried to use this solution as suggested in the comments, but it only seems to work for two polyhedra that have the same general shape: only one variable is used for how the vertices should be connected ("faces"). Also, I cannot fully understand the method by which the intersection points were found. It seems to rely on the fact that z convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities (see here). Is there perhaps a simpler way?

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will not work (see "possible issues" in the Mathematica documentation https://reference.wolfram.com/language/ref/RegionIntersection.html).

I know that RegionPlot3D allows logical operators - perhaps there is a way to plot the MeshRegions to a RegionPlot3D and use logical operators to create an intersection?

Something else I thought may work is checking for region membership in all the regions I want to intersect of the tetrahedra making up the mesh region, but RegionMember only checks membership of points.

The types of MeshRegions I am working with are 3D Delaunay, for example

DelaunayMesh@RandomReal[{-1, 1}, {25, 3}]

EDIT: I tried to use this solution as suggested in the comments, but it only seems to work for two polyhedra that have the same general shape: only one variable is used for how the vertices should be connected ("faces"). Also, I cannot fully understand the method by which the intersection points were found. It seems to rely on the fact that z convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities (see here). Is there perhaps a simpler way?

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Katia
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How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will not work (see "possible issues" in the Mathematica documentation https://reference.wolfram.com/language/ref/RegionIntersection.html).

I know that RegionPlot3D allows logical operators - perhaps there is a way to plot the MeshRegions to a RegionPlot3D and use logical operators to create an intersection?

Something else I thought may work is checking for region membership in all the regions I want to intersect of the tetrahedra making up the mesh region, but RegionMember only checks membership of points.

The types of MeshRegions I am working with are 3D Delaunay, for example

DelaunayMesh@RandomReal[{-1, 1}, {25, 3}]

PSEDIT: Please let me know if you need more informationI tried to help answeruse this solution as suggested in the questioncomments, but it only seems to work for two polyhedra that have the same general shape: only one variable is used for how the vertices should be connected ("faces"). Also, I will editcannot fully understand the post!method by which the intersection points were found. It seems to rely on the fact that z convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities (see here). Is there perhaps a simpler way?

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will not work (see "possible issues" in the Mathematica documentation https://reference.wolfram.com/language/ref/RegionIntersection.html).

I know that RegionPlot3D allows logical operators - perhaps there is a way to plot the MeshRegions to a RegionPlot3D and use logical operators to create an intersection?

Something else I thought may work is checking for region membership in all the regions I want to intersect of the tetrahedra making up the mesh region, but RegionMember only checks membership of points.

The types of MeshRegions I am working with are 3D Delaunay, for example

DelaunayMesh@RandomReal[{-1, 1}, {25, 3}]

PS: Please let me know if you need more information to help answer the question, I will edit the post!

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will not work (see "possible issues" in the Mathematica documentation https://reference.wolfram.com/language/ref/RegionIntersection.html).

I know that RegionPlot3D allows logical operators - perhaps there is a way to plot the MeshRegions to a RegionPlot3D and use logical operators to create an intersection?

Something else I thought may work is checking for region membership in all the regions I want to intersect of the tetrahedra making up the mesh region, but RegionMember only checks membership of points.

The types of MeshRegions I am working with are 3D Delaunay, for example

DelaunayMesh@RandomReal[{-1, 1}, {25, 3}]

EDIT: I tried to use this solution as suggested in the comments, but it only seems to work for two polyhedra that have the same general shape: only one variable is used for how the vertices should be connected ("faces"). Also, I cannot fully understand the method by which the intersection points were found. It seems to rely on the fact that z convex polyhedron can be defined algebraically as the set of solutions to a system of linear inequalities (see here). Is there perhaps a simpler way?

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MarcoB
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How can I create a logical intersection of MeshRegionMeshRegion objects that are three-dimensional? The RegionIntersectionRegionIntersection function will not work (see "possible issues" in the MathematicaMathematica documentation https://reference.wolfram.com/language/ref/RegionIntersection.html).

I know that RegionPlot3DRegionPlot3D allows logical operators - perhaps there is a way to plot the MeshRegionsMeshRegions to a RegionPlot3DRegionPlot3D and use logical operators to create an intersection?

Something else I thought may work is checking for region membership in all the regions I want to intersect of the tetrahedra making up the mesh region, but RegionMemberRegionMember only checks membership of points.

The types of MeshRegionsMeshRegions I am working with are 3D Delaunay, for example DelaunayMesh@RandomReal[{-1, 1}, {25, 3}]

DelaunayMesh@RandomReal[{-1, 1}, {25, 3}]

PS: Please let me know if you need more information to help answer the question, I will edit the post!

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will not work (see "possible issues" in the Mathematica documentation https://reference.wolfram.com/language/ref/RegionIntersection.html).

I know that RegionPlot3D allows logical operators - perhaps there is a way to plot the MeshRegions to a RegionPlot3D and use logical operators to create an intersection?

Something else I thought may work is checking for region membership in all the regions I want to intersect of the tetrahedra making up the mesh region, but RegionMember only checks membership of points.

The types of MeshRegions I am working with are 3D Delaunay, for example DelaunayMesh@RandomReal[{-1, 1}, {25, 3}]

PS: Please let me know if you need more information to help answer the question, I will edit the post!

How can I create a logical intersection of MeshRegion objects that are three-dimensional? The RegionIntersection function will not work (see "possible issues" in the Mathematica documentation https://reference.wolfram.com/language/ref/RegionIntersection.html).

I know that RegionPlot3D allows logical operators - perhaps there is a way to plot the MeshRegions to a RegionPlot3D and use logical operators to create an intersection?

Something else I thought may work is checking for region membership in all the regions I want to intersect of the tetrahedra making up the mesh region, but RegionMember only checks membership of points.

The types of MeshRegions I am working with are 3D Delaunay, for example

DelaunayMesh@RandomReal[{-1, 1}, {25, 3}]

PS: Please let me know if you need more information to help answer the question, I will edit the post!

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Katia
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