RegionDilation

RegionDilation[reg,r]

gives the dilation of the region reg by a disk of radius r centered at the origin.

RegionDilation[reg1,reg2]

gives the dilation of the region reg1 by the region reg2.

RegionDilation[reg1,reg2,{u,v}]

gives the dilation of reg1 scaled by a factor u and reg2 scaled by a factor v.

Details and Options

  • RegionDilation is also known as Minkowski sum, geometric sum or offset.
  • Typically used to construct the union of positions of a region through translation.
  • RegionDilation[reg,r] gives the dilation of the region reg by a disk of radius r.
  • RegionDilation[reg1,reg2] returns the region reg1⊕reg2={a+b|a∈reg1∧b∈reg2}.
  • RegionDilation[reg1,reg2,{u,v}] returns the region u reg1⊕v reg2={u a+v b|a∈reg1∧b∈reg2}.
  • RegionDilation takes the same options as Region.

Examples

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Basic Examples  (4)

Dilation of a disk:

Dilation of Triangle by Disk:

Dilation of Rectangle by Triangle:

Visualize it:

Dilation of two regions:

Visualize it:

Scope  (8)

Special Regions  (4)

Dilation of two lines:

Visualize it:

Dilation of two disks:

Dilation of a rectangle and a disk:

A disk and a circle:

Visualize it:

Dilation of two polygons:

Visualize it:

Formula Regions  (1)

RegionDilation of ImplicitRegion objects:

2D:

Mesh Regions  (1)

Dilation of two BoundaryMeshRegion objects:

In 3D:

Derived Regions  (2)

Dilation of two BooleanRegion objects:

Visualize it:

Dilation of two TransformedRegion objects:

Visualize it:

Possible Issues  (1)

RegionDilation gives an approximate result when the exact result cannot be computed:

Turn on the message:

Wolfram Research (2021), RegionDilation, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionDilation.html.

Text

Wolfram Research (2021), RegionDilation, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionDilation.html.

CMS

Wolfram Language. 2021. "RegionDilation." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/RegionDilation.html.

APA

Wolfram Language. (2021). RegionDilation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionDilation.html

BibTeX

@misc{reference.wolfram_2024_regiondilation, author="Wolfram Research", title="{RegionDilation}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/RegionDilation.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_regiondilation, organization={Wolfram Research}, title={RegionDilation}, year={2021}, url={https://reference.wolfram.com/language/ref/RegionDilation.html}, note=[Accessed: 21-December-2024 ]}