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SmoothMesh[mesh]

smooths a mesh region mesh by adjusting cells and keeping the overall shape.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
Method  
"ExplicitLaplacian"  
"ImplicitLaplacian"  
Applications  
See Also
Related Guides
History
Cite this Page

SmoothMesh

SmoothMesh[mesh]

smooths a mesh region mesh by adjusting cells and keeping the overall shape.

Details and Options

  • SmoothMesh is also known as mesh smoothing, denoising, filtering and fairing.
  • SmoothMesh is typically used to improve mesh quality by reducing noise from 3D scanning and reconstruction.
  • SmoothMesh[mesh] returns a mesh region obtained by adjusting cells while improving minimum angle, maximum angle and aspect ratio.
  • SmoothMesh takes the same options as MeshRegion, with the following additions:
  • Method Automaticmethod to use
  • Possible method settings include "ExplicitLaplacian" and "ImplicitLaplacian".

Examples

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Basic Examples  (1)

Smooth a mesh:

Wolfram Language code: ℛ = ResourceData["Beethoven"]
Wolfram Language code: SmoothMesh[ℛ]

Scope  (3)

SmoothMesh works on surfaces:

Wolfram Language code: DiscretizeGraphics[ListPlot3D[Table[Sin[j ^ 2 + i], {i, 0, Pi, Pi / 5}, {j, 0, Pi, Pi / 5}]]]
Wolfram Language code: SmoothMesh[%]

Solids:

Wolfram Language code: BoundaryDiscretizeRegion[Dodecahedron[], MaxCellMeasure -> .01]
Wolfram Language code: SmoothMesh[%]

Apply SmoothMesh multiple times:

Wolfram Language code: ℛ = ResourceData["Beethoven"]; NestList[SmoothMesh, ℛ, 3]

Options  (7)

Method  (7)

"ExplicitLaplacian"  (3)

Update vertex positions directly based on the Laplacian:

Wolfram Language code: SmoothMesh[[image], Method -> "ExplicitLaplacian"]

Use the option "UniformLaplace"True to use a uniform Laplacian:

Wolfram Language code: SmoothMesh[[image], Method -> {"ExplicitLaplacian", "UniformLaplace" -> True}]

Use the option "MaxIterations"->n to specify the maximum number of iterations:

Wolfram Language code: SmoothMesh[[image], Method -> {"ExplicitLaplacian", "MaxIterations" -> 5}]

"ImplicitLaplacian"  (4)

Solve a linear system to update vertex positions:

Wolfram Language code: SmoothMesh[[image], Method -> "ImplicitLaplacian"]

Use the option "UniformLaplace"True to use a uniform Laplacian:

Wolfram Language code: SmoothMesh[[image], Method -> {"ImplicitLaplacian", "UniformLaplace" -> True}]

Use the option "MaxIterations"->n to specify the maximum number of iterations:

Wolfram Language code: SmoothMesh[[image], Method -> {"ImplicitLaplacian", "MaxIterations" -> 5}]

Use the option "TimeStep"->t to controls the extent of smoothing applied in each iteration:

Wolfram Language code: SmoothMesh[[image], Method -> {"ImplicitLaplacian", "TimeStep" -> .05}]

Applications  (1)

Denoise a 3D mesh by smoothing out high-frequency surface variations:

Wolfram Language code: ℛ = [image];

Create a mesh with noise:

Wolfram Language code: noisemesh = MeshRegion[MeshCoordinates[ℛ] + RandomReal[{-0.015, 0.015}, Dimensions[MeshCoordinates[ℛ]]], MeshCells[ℛ, 2]]

Apply SmoothMesh:

Wolfram Language code: SmoothMesh[%]
Wolfram Research (2025), SmoothMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/SmoothMesh.html.

Text

Wolfram Research (2025), SmoothMesh, Wolfram Language function, https://reference.wolfram.com/language/ref/SmoothMesh.html.

CMS

Wolfram Language. 2025. "SmoothMesh." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SmoothMesh.html.

APA

Wolfram Language. (2025). SmoothMesh. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SmoothMesh.html

BibTeX

@misc{reference.wolfram_2026_smoothmesh, author="Wolfram Research", title="{SmoothMesh}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/SmoothMesh.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_smoothmesh, organization={Wolfram Research}, title={SmoothMesh}, year={2025}, url={https://reference.wolfram.com/language/ref/SmoothMesh.html}, note=[Accessed: 13-June-2026]}