# InverseTransformedRegion

InverseTransformedRegion[reg,f,n]

represents the inverse transformed region , where reg is a region and f is a function.

# Examples

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## Basic Examples(2)

The inverse transform of a rotated rectangle:

The inverse image of a disk through :

## Scope(22)

### Special Regions(9)

Some inverse transformed regions are computed explicitly:

Visualize the transformation:

The inverse image of the unit cuboid through a linear-fractional transformation:

Visualize the transformation:

The inverse transform of a translated unit Disk:

Visualize it:

The inverse transform of a sheared unit Rectangle:

Visualize it:

The inverse transform of a rotated Triangle:

Visualize it:

The inverse transform of a scaled Circle:

The inverse image of the unit cube through a rotation transform:

Visualize it:

An inverse transform of a rectangle by a linear transformation :

Visualize it:

Map points from a Triangle embedded in 2D into 3D by a nonlinear transformation :

Visualize it:

### Formula Regions(4)

The inverse transform of a sheared ParametricRegion:

Visualize it:

The inverse transform of a rotated ParametricRegion:

Visualize it:

The inverse transform of a sheared ImplicitRegion:

Visualize it:

The inverse transform of a scaled ImplicitRegion:

Visualize it:

### Mesh Regions(2)

An inverse transform of BoundaryMeshRegion objects is a BoundaryMeshRegion:

2D:

3D:

An inverse transform of MeshRegion objects is a MeshRegion:

2D:

3D:

### Derived Regions(5)

The inverse transform of a reflected TransformedRegion:

Visualize it:

The inverse transform of a rotated RegionDifference:

Visualize it:

The inverse transform of a scaled RegionBoundary:

Visualize it:

The inverse transform of a reflected RegionProduct:

Visualize it:

The inverse transform of a RegionUnion by a nonlinear transformation :

Visualize it:

### Geographic Regions(2)

InverseTransformedRegion works on polygons of geographic entities:

Polygons with GeoPosition:

Polygons with GeoPositionXYZ:

Polygons with GeoPositionENU:

Polygons with GeoGridPosition:

Wolfram Research (2014), InverseTransformedRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseTransformedRegion.html.

#### Text

Wolfram Research (2014), InverseTransformedRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseTransformedRegion.html.

#### CMS

Wolfram Language. 2014. "InverseTransformedRegion." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseTransformedRegion.html.

#### APA

Wolfram Language. (2014). InverseTransformedRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseTransformedRegion.html

#### BibTeX

@misc{reference.wolfram_2024_inversetransformedregion, author="Wolfram Research", title="{InverseTransformedRegion}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/InverseTransformedRegion.html}", note=[Accessed: 06-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_inversetransformedregion, organization={Wolfram Research}, title={InverseTransformedRegion}, year={2014}, url={https://reference.wolfram.com/language/ref/InverseTransformedRegion.html}, note=[Accessed: 06-August-2024 ]}