ShellRegion

ShellRegion[reg]

gives a solid shell of a 3D region reg.

ShellRegion[reg,t]

gives a solid shell of reg with minimal thickness t.

Details

  • ShellRegion is typically used to hollow out a solid to save material when printing a 3D object.
  • ShellRegion preserves the outer surface of an object.

Examples

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Basic Examples  (2)

Find the shell of a ball:

Find the shell of a mesh region:

Specify a thickness:

Scope  (16)

Basic Uses  (3)

ShellRegion works on solid regions:

Closed surfaces:

Specify a thickness for a shell:

Special Regions  (8)

Find the shell of a Ball:

Cuboid:

Hexahedron:

Parallelepiped:

Prism:

Pyramid:

Simplex:

Tetrahedron:

Formula Regions  (2)

Find the shell of an ImplicitRegion:

Visualize the shell:

A Boolean combination of inequalities:

Visualize the shell:

Mesh Regions  (3)

Find the shell of a BoundaryMeshRegion:

Visualize the shell:

MeshRegion:

Visualize the shell:

A closed surface MeshRegion:

Visualize the shell:

Applications  (5)

Hollow out a 3D model:

A torus:

A molecule:

Find a shell with roughly one quarter the original volume:

Sample points in the region to create a distribution of distances to the boundary:

Find the distance where one quarter of the sampled points are closer to the boundary:

The resulting shell:

Compare the volumes:

Use ShellRegion to save material when printing a 3D object:

The shell requires less material:

Properties & Relations  (3)

ShellRegion preserves the outer surface of an object:

Extract the outer surface:

Compare properties:

Typically, the thickness of the shell is roughly uniform:

Extract the inner and outer surfaces:

Compute distances to the outer surface with RegionDistance:

The shell of Ball is SphericalShell:

Use ShellRegion to compute the shell of other regions:

Possible Issues  (2)

The thickness of a shell may not be uniform:

Different representations of a region can give different shells:

A Ball as an ImplicitRegion:

Wolfram Research (2016), ShellRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/ShellRegion.html.

Text

Wolfram Research (2016), ShellRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/ShellRegion.html.

CMS

Wolfram Language. 2016. "ShellRegion." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ShellRegion.html.

APA

Wolfram Language. (2016). ShellRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ShellRegion.html

BibTeX

@misc{reference.wolfram_2025_shellregion, author="Wolfram Research", title="{ShellRegion}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/ShellRegion.html}", note=[Accessed: 22-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_shellregion, organization={Wolfram Research}, title={ShellRegion}, year={2016}, url={https://reference.wolfram.com/language/ref/ShellRegion.html}, note=[Accessed: 22-February-2025 ]}