# RegionConvert

RegionConvert[reg,form]

converts the region representation reg to the specified form.

# Details

• RegionConvert will produce an expression equivalent to expr.
• RegionConvert is typically used for comparing regions with different representations or to get a representation suitable for different functions, e.g. optimization expects implicit forms of region constraints, whereas integration over a region expects the parametric form of a region.
• The following forms can be used for converting between region representations:
•  "Implicit" implicit representation "Mesh" mesh representation "Parametric" parametric representation "Spline" spline representation

# Examples

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## Basic Examples(2)

Convert the unit disk to the implicit form:

Parametric form:

Convert a cube to the implicit form:

Parametric form:

## Scope(11)

### Special Regions(5)

Convert Rectangle to the implicit form:

Parametric form:

Visualize it:

Convert DiskSegment to the implicit form:

Parametric form:

Visualize it:

Convert CapsuleShape to the implicit form:

Parametric form:

Visualize it:

Convert Hyperplane to the implicit form:

Parametric form:

Visualize it:

Represent Sphere as a B-spline surface:

Visualize it, along with the control points:

### Formula Regions(2)

Convert an ImplicitRegion object to the implicit form:

Convert a ParametricRegion object to the implicit form:

### Mesh Regions(2)

Convert a MeshRegion object to the implicit form:

A mesh region with disconnected components:

Convert a BoundaryMeshRegion object to the implicit form:

A boundary mesh region with disconnected components:

### Derived Regions(2)

Convert a BooleanRegion object to the implicit form:

Visualize it:

Convert a TransformedRegion object to the implicit form:

Visualize it:

## Applications(3)

Compute the area of an annulus using its implicit form:

Compare:

Compute the volume of a ball using its implicit form:

Compare:

Find the projection of an implicit region on the plane in :

Visualize the projection:

## Properties & Relations(3)

Use CanonicalizePolygon to convert a region representation to a polygon form:

Use CanonicalizePolyhedron to convert a region representation to a polyhedron form:

Use DiscretizeRegion to convert a region into a mesh:

Wolfram Research (2021), RegionConvert, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionConvert.html (updated 2024).

#### Text

Wolfram Research (2021), RegionConvert, Wolfram Language function, https://reference.wolfram.com/language/ref/RegionConvert.html (updated 2024).

#### CMS

Wolfram Language. 2021. "RegionConvert." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/RegionConvert.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_regionconvert, author="Wolfram Research", title="{RegionConvert}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/RegionConvert.html}", note=[Accessed: 14-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_regionconvert, organization={Wolfram Research}, title={RegionConvert}, year={2024}, url={https://reference.wolfram.com/language/ref/RegionConvert.html}, note=[Accessed: 14-September-2024 ]}