ParametricRegion

ParametricRegion[{f1,,fn},{u1,,um}]

represents a region in given by the points {f1,,fn} for parameters ui.

ParametricRegion[{f1,,fn},{{u1,a1,b1},}]

constrains parameters to an interval a1u1b1 etc.

ParametricRegion[{{f1,,fn},cond},]

constrains parameters to satisfy the condition cond.

Examples

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Basic Examples(2)

Specify a circle as a ParametricRegion:

Specify a disk:

The region between two parabolas:

Scope(20)

Purely Parametric Description(10)

Parametrically described region:

Embedding dimension:

Geometric dimension:

Point membership test:

Get conditions for point membership:

Area and centroid:

Distance from a point:

Signed distance from a point:

Nearest point in the region:

Nearest points:

The set of points above a parabola is not bounded:

Integrate over an implicitly defined region:

Optimize over an implicitly defined region:

Solve equations in an implicitly defined region:

Mixed Implicit and Parametric Description(10)

A region given in a mixed implicit and parametric description:

Embedding dimension:

Geometric dimension:

Point membership test:

Get conditions for point membership:

Area and centroid:

Distance from a point:

Signed distance from a point:

Nearest point in the region:

Nearest points:

is bounded but not convex:

Integrate over :

Optimize over :

Solve equations and inequalities in :

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_parametricregion, author="Wolfram Research", title="{ParametricRegion}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/ParametricRegion.html}", note=[Accessed: 12-August-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_parametricregion, organization={Wolfram Research}, title={ParametricRegion}, year={2014}, url={https://reference.wolfram.com/language/ref/ParametricRegion.html}, note=[Accessed: 12-August-2024 ]}