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 a1≤u1≤b1 etc.

ParametricRegion[{{f1,…,fn},cond},…]

constrains parameters to satisfy the condition cond.

Details

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:

ℛ is bounded but not convex:

Integrate over ℛ:

Optimize over ℛ:

Solve equations and inequalities in ℛ:

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: 02-November-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: 02-November-2024 ]}