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:

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:

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:

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: