RegionDilation
✖
RegionDilation
gives the dilation of the region reg by a disk of radius r centered at the origin.
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+ba∈reg1∧b∈reg2}.
- RegionDilation[reg1,reg2,{u,v}] returns the region u reg1⊕v reg2={u a+v ba∈reg1∧b∈reg2}.
- RegionDilation takes the same options as Region.

Examples
open allclose allBasic Examples (4)Summary of the most common use cases

https://wolfram.com/xid/0g7ijzsssey-7470ib


https://wolfram.com/xid/0g7ijzsssey-5sofxx

Dilation of Rectangle by Triangle:

https://wolfram.com/xid/0g7ijzsssey-zfeyxd


https://wolfram.com/xid/0g7ijzsssey-fuvyxr


https://wolfram.com/xid/0g7ijzsssey-i47t61


https://wolfram.com/xid/0g7ijzsssey-9btejp

Scope (8)Survey of the scope of standard use cases
Special Regions (4)

https://wolfram.com/xid/0g7ijzsssey-1opzvd


https://wolfram.com/xid/0g7ijzsssey-igwg55


https://wolfram.com/xid/0g7ijzsssey-hl5gpm

https://wolfram.com/xid/0g7ijzsssey-tsw7u5

Dilation of a rectangle and a disk:

https://wolfram.com/xid/0g7ijzsssey-dpwalb


https://wolfram.com/xid/0g7ijzsssey-dq7yx6

https://wolfram.com/xid/0g7ijzsssey-of250


https://wolfram.com/xid/0g7ijzsssey-h9631g

https://wolfram.com/xid/0g7ijzsssey-b76l3e

https://wolfram.com/xid/0g7ijzsssey-unxw

Formula Regions (1)
RegionDilation of ImplicitRegion objects:

https://wolfram.com/xid/0g7ijzsssey-crtuk1

https://wolfram.com/xid/0g7ijzsssey-p5g6yh


https://wolfram.com/xid/0g7ijzsssey-gc5987

https://wolfram.com/xid/0g7ijzsssey-fbwnu3


https://wolfram.com/xid/0g7ijzsssey-3s8ugb

Mesh Regions (1)
Dilation of two BoundaryMeshRegion objects:

https://wolfram.com/xid/0g7ijzsssey-bep0zh

https://wolfram.com/xid/0g7ijzsssey-evjawf


https://wolfram.com/xid/0g7ijzsssey-3h9218

https://wolfram.com/xid/0g7ijzsssey-5r3i0z

Derived Regions (2)
Dilation of two BooleanRegion objects:

https://wolfram.com/xid/0g7ijzsssey-fzcaz8

https://wolfram.com/xid/0g7ijzsssey-d19z6l

https://wolfram.com/xid/0g7ijzsssey-b3gvca

Dilation of two TransformedRegion objects:

https://wolfram.com/xid/0g7ijzsssey-fdpyhr

https://wolfram.com/xid/0g7ijzsssey-hj2g71

https://wolfram.com/xid/0g7ijzsssey-c2ee5

Possible Issues (1)Common pitfalls and unexpected behavior
RegionDilation gives an approximate result when the exact result cannot be computed:

https://wolfram.com/xid/0g7ijzsssey-qh1w39


https://wolfram.com/xid/0g7ijzsssey-w3t8yg

https://wolfram.com/xid/0g7ijzsssey-l6k8sb


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.
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.
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
Wolfram Language. (2021). RegionDilation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/RegionDilation.html
BibTeX
@misc{reference.wolfram_2025_regiondilation, author="Wolfram Research", title="{RegionDilation}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/RegionDilation.html}", note=[Accessed: 06-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_regiondilation, organization={Wolfram Research}, title={RegionDilation}, year={2021}, url={https://reference.wolfram.com/language/ref/RegionDilation.html}, note=[Accessed: 06-June-2025
]}