ImplicitRegion [cond,{x1,…,xn}]
represents a region in that satisfies the conditions cond.
ImplicitRegion [cond,{{x1,a1,b1},…}]
represents a region in that satisfies the conditions cond as well as etc.
ImplicitRegion
ImplicitRegion [cond,{x1,…,xn}]
represents a region in that satisfies the conditions cond.
ImplicitRegion [cond,{{x1,a1,b1},…}]
represents a region in that satisfies the conditions cond as well as etc.
Details
- The value of xi in ImplicitRegion [cond,{x1,…,xn}] is taken to be localized, as in Block .
- ImplicitRegion [cond,{{x1,a1,b1},…}] is equivalent to ImplicitRegion [cond∧a1≤x1≤b1∧⋯,{x1,…}].
- ImplicitRegion can be used in functions such as RegionDistance , Reduce , and Integrate .
Examples
open all close allBasic Examples (1)
Specify a disk as an ImplicitRegion :
A circle:
Scope (27)
Regions in 1D (3)
A 0D region is a set of discrete points:
Find the points:
A purely 1D region is a union of (possibly unbounded) segments:
Find the segments:
A region with 1D and 0D components:
Find the components:
Compute the length:
Regions in 2D (5)
A 0D region is a set of discrete points:
Find the points:
A purely 1D region is a curve:
Plot it:
A higher-degree algebraic curve:
Plot it:
A 2D region with two connected components:
Plot it:
A 2D region with lower-dimensional components:
Plot it:
Regions in 3D (7)
A 0D region is a set of discrete points:
Find the points:
A purely 1D region is a curve; conic curves are intersections of a cone and a plane:
An ellipse:
A parabola:
A hyperbola:
A higher-degree algebraic curve:
Plot it:
The curve is an intersection of two surfaces:
A purely 2D region is a surface:
Plot it:
A higher-degree algebraic surface:
Plot it:
A purely 3D region is a solid:
Plot it:
A higher-degree algebraic solid:
Plot it:
Regions in D (2)
A ball in :
Intersect with a 3D affine space and project on :
Plot it:
A torus embedded in :
Compute the area of the torus:
Embed the torus in using the mapping :
Plot it:
Properties (10)
Implicitly described region:
Plot it:
Embedding dimension:
Geometric dimension:
Point membership test:
Plot it:
Get conditions for point membership:
Area and centroid:
Plot it:
Distance from a point:
Plot it:
Signed distance from a point:
Plot it:
Nearest point in the region:
Plot it:
Nearest points:
A trifolium is bounded:
Plot it:
Integrate over an implicitly defined region:
Optimize over an implicitly defined region:
Solve equations in an implicitly defined region:
Applications (1)
Find the projection of an implicit region on the plane in :
Visualize the region:
Visualize the projection:
Related Guides
History
Text
Wolfram Research (2014), ImplicitRegion, Wolfram Language function, https://reference.wolfram.com/language/ref/ImplicitRegion.html.
CMS
Wolfram Language. 2014. "ImplicitRegion." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ImplicitRegion.html.
APA
Wolfram Language. (2014). ImplicitRegion. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ImplicitRegion.html
BibTeX
@misc{reference.wolfram_2025_implicitregion, author="Wolfram Research", title="{ImplicitRegion}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/ImplicitRegion.html}", note=[Accessed: 16-November-2025]}
BibLaTeX
@online{reference.wolfram_2025_implicitregion, organization={Wolfram Research}, title={ImplicitRegion}, year={2014}, url={https://reference.wolfram.com/language/ref/ImplicitRegion.html}, note=[Accessed: 16-November-2025]}