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

open allclose all

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: 30-December-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: 30-December-2024 ]}