TransformedRegion

TransformedRegion[reg,f]

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

Details and Options

Examples

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Basic Examples  (2)

A rotated rectangle:

A disk transformed by :

Scope  (24)

Special Regions  (10)

Some transformed regions are computed explicitly:

Visualize the transformation:

A linear-fractional transformation of the unit ball:

Visualize the transformation:

Translate a unit Disk:

Point membership test:

Conditions for point membership:

Shear a unit Rectangle:

Compute the RegionBounds:

Rotate a standard Triangle:

Region remains constant and bounded:

Scale a Circle:

Compute the ArcLength:

A disk transformed by a nonlinear transformation :

Express the same point mapping using Indexed:

Compute the RegionMeasure:

Map points from a 3D Cuboid into 2D by a nonlinear transformation :

Geometric and embedding dimension:

Compute the RegionCentroid:

Visualize:

Signed distance from a point:

Rotate a 3D Cuboid:

Distance from a point:

Nearest point in the region:

Nearest points:

Integrate over a rotated unit cube:

Optimize:

Solve equations:

Formula Regions  (6)

Shear a ParametricRegion:

Compute the ArcLength:

Nearest point on the region from a given point:

A rotated ParametricRegion:

Compute the Area:

Compute the RegionBounds:

RegionDistance:

Shear an ImplicitRegion:

Region remains unbounded:

Point membership test:

Conditions for point membership:

Scale an ImplicitRegion:

Compute the Volume:

Integrate over the region:

Optimize:

Solve equations:

An ImplicitRegion transformed by a nonlinear transformation :

Express the same point mapping using Indexed:

Compute the RegionMeasure:

Map points from a 3D ball into 2D by a nonlinear transformation :

Geometric and embedding dimension:

Compute the RegionCentroid:

Visualize:

Mesh Regions  (3)

Rotate a BoundaryMeshRegion:

Transformed region is still BoundaryMeshRegionQ:

Point membership test:

Compute the RegionCentroid:

Visualize it:

Compute the Area:

Integrate over the region:

Shear a MeshRegion:

Transformed region is still MeshRegionQ:

Compute the Volume:

Compute the RegionBounds:

RegionDistance from a point:

Integrate over the region:

Scale a lower-dimensional MeshRegion:

Compute the ArcLength:

Nearest point on the region from a given point:

Derived Regions  (5)

Transform a TransformedRegion:

Compute the Volume:

Integrate over the region:

Optimize:

Solve equations:

Transform a RegionDifference:

Compute the Area:

Compute the RegionBounds:

SignedRegionDistance from a given point:

Transform a RegionBoundary:

Compute the ArcLength:

Nearest point on the region from a given point:

Transform a RegionProduct:

Compute the Volume:

Compute the RegionBounds:

RegionDistance from a point:

Transform a RegionUnion by a nonlinear transformation :

Express the same point mapping using Indexed:

Compute the RegionBounds:

Applications  (2)

Any triangle is an affine transformation of the standard triangle:

The transformation is given by , where A=TemplateBox[{{{, {{{p, _, 1}, -, {p, _, 0}}, ,, ..., ,, {{p, _, 3}, -, {p, _, 0}}}, }}}, Transpose]:

Compare original and transformed unit triangle:

Find the perspective transformation of a unit Cuboid with center :

Visualize the region:

Compute the Volume:

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

Text

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

BibTeX

@misc{reference.wolfram_2021_transformedregion, author="Wolfram Research", title="{TransformedRegion}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/TransformedRegion.html}", note=[Accessed: 17-June-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_transformedregion, organization={Wolfram Research}, title={TransformedRegion}, year={2014}, url={https://reference.wolfram.com/language/ref/TransformedRegion.html}, note=[Accessed: 17-June-2021 ]}

CMS

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

APA

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