# RegionErosion

RegionErosion[reg,r]

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

RegionErosion[reg1,reg2]

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

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

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

# Details and Options

• RegionErosion is also known as Minkowski difference or geometric difference.
• Typically used to construct the intersection of all positions of a region through translation.
• RegionErosion[reg,r] gives the erosion of the region reg by a disk of radius r.
• RegionErosion[reg1,reg2] returns reg1reg2={d|dreg2reg1} where ab is RegionDilation.
• RegionErosion[reg1,reg2,{u,v}] returns u reg1v reg2={d|dv reg2u reg1}.
• RegionErosion takes the same options as Region.

# Examples

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## Basic Examples(3)

Erosion of a disk:

Visualize it:

Visualize it:

## Scope(5)

### Special Regions(5)

Visualize it:

RegionErosion of Disk and Line:

Visualize it:

Visualize it:

Visualize it:

Visualize it:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_regionerosion, author="Wolfram Research", title="{RegionErosion}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/RegionErosion.html}", note=[Accessed: 21-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_regionerosion, organization={Wolfram Research}, title={RegionErosion}, year={2021}, url={https://reference.wolfram.com/language/ref/RegionErosion.html}, note=[Accessed: 21-July-2024 ]}