WOLFRAM

Region[reg]

represents a geometric region.

Region[reg,options]

gives a region that uses the specified options.

Details and Options

Examples

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Basic Examples  (3)Summary of the most common use cases

A unit disk:

Out[1]=1

A MeshRegion is a Region with an additional mesh structure:

Out[1]=1
Out[2]=2

Region represents the underlying three-dimensional point set without the mesh structure:

Out[3]=3

Style a Region:

Out[1]=1

Scope  (35)Survey of the scope of standard use cases

Regions  (14)

Regions in 1D  (3)

A strictly 0D Region is a point set:

Out[1]=1

A strictly 1D Region is a collection of line segments:

Out[1]=1

A Region can combine elements of different dimensions:

Out[1]=1

Regions in 2D  (5)

A strictly 0D Region is a point set:

Out[1]=1

A strictly 1D Region is a collection of line segments:

Out[1]=1

A strictly 2D Region is a collection of polygonal faces:

Out[1]=1

A Region can combine elements of different dimensions:

Out[1]=1

Polygons with GeoGridPosition:

Out[1]=1

Regions in 3D  (6)

A strictly 0D Region is a point set:

Out[1]=1

A strictly 1D Region is a collection of line segments:

Out[1]=1

A strictly 2D Region is a collection of polygonal faces:

Out[1]=1

A strictly 3D Region is a collection of polyhedral volumes:

Out[1]=1

Polyhedral volume cells include Cone, Cuboid, Pyramid etc.:

Out[2]=2

A Region can combine elements of different dimensions:

Out[1]=1

PolygonCoordinates works on polygons of geographic entities:

Out[1]=1

Polygons with GeoPosition:

Out[2]=2

Polygons with GeoPositionXYZ:

Out[3]=3

Polygons with GeoPositionENU:

Out[4]=4

Presentation  (8)

Use a monochrome theme:

Out[1]=1

Use a detailed theme:

Out[1]=1

Use a business theme:

Out[1]=1

Use a marketing theme:

Out[1]=1

Use a minimal theme:

Out[1]=1

Use a scientific theme:

Out[1]=1

Use a web theme:

Out[1]=1

Use a classic theme:

Out[1]=1

Properties  (8)

Embedding dimension:

Out[2]=2

Geometric dimension:

Out[3]=3

Point membership test:

Out[2]=2

Visualize it:

Out[4]=4

Measure is ArcLength for a 1D region, Area for a 2D region and Volume for a 3D region:

Out[1]=1
Out[2]=2
Out[3]=3

Compute the centroids of each:

Out[4]=4

Distance from a point:

Out[2]=2

Visualize it:

Out[3]=3

Signed distance from a point:

Out[2]=2

Visualize it:

Out[3]=3

Nearest point in the region:

Out[2]=2

A Region is always bounded:

Out[2]=2

Get its bounds:

Out[3]=3

Integrate over a Region:

Out[2]=2

Wrappers  (5)

Use wrappers on a Region:

Out[1]=1

Wrappers can be nested:

Out[1]=1

Add interactive behavior with wrappers such as Tooltip:

Out[1]=1

Any object can be used in the tooltip:

Out[2]=2

Use Button to trigger actions when clicking a Region:

Out[1]=1

Use PopupWindow to provide information drilldown:

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Options  (96)Common values & functionality for each option

AlignmentPoint  (1)

Specify the position to be aligned in 3D Inset, using coordinates:

Out[1]=1
Out[2]=2

AspectRatio  (1)

Use numerical values for AspectRatio:

Out[1]=1

Axes  (2)

Draw all the axes:

Out[1]=1

Draw the axis but not the axis:

Out[1]=1

AxesEdge  (2)

Choose the bounding box edges automatically to draw the axes:

Out[1]=1

Choose the bounding box edges automatically to draw the axes:

Out[1]=1

AxesLabel  (2)

Place a label for the axis:

Out[1]=1

Specify a label for each axis:

Out[1]=1

AxesOrigin  (2)

Determine where the axes cross automatically:

Out[1]=1

Specify the axes' origin explicitly:

Out[1]=1

AxesStyle  (2)

Specify the overall axes style, including the ticks and the tick labels:

Out[1]=1

Specify the style of each axis:

Out[1]=1

Background  (1)

Specify a background color:

Out[1]=1

BaselinePosition  (3)

Align the center of a graphic with the baseline of the text:

Out[1]=1

Specify the baseline of a graphic as a fraction of the height by using Scaled:

Out[1]=1

Use the axis of a graphic as the baseline:

Out[1]=1

BaseStyle  (2)

Set the starting style:

Out[1]=1

Set multiple starting styles:

Out[1]=1

Boxed  (2)

Draw the edges of the bounding box:

Out[1]=1

Do not draw the edges of the bounding box:

Out[1]=1

BoxRatios  (2)

Specify the ratios between the bounding box edges:

Out[1]=1

Use the actual coordinate values for the ratios:

Out[1]=1

BoxStyle  (1)

Use dashed lines for the bounding box:

Out[1]=1

Epilog  (1)

Draw a disk above the graphic, including the axes:

Out[1]=1

FaceGrids  (4)

Put grids on every face of a 3D graphic:

Out[1]=1

Put grids on both faces:

Out[1]=1

Put face grids on the plane:

Out[1]=1

On the plane, put grid lines on , and :

Out[1]=1

FaceGridsStyle  (1)

Specify the overall style of face grids:

Out[1]=1

Frame  (2)

Draw a frame around the whole graphic:

Out[1]=1

Draw a frame on the left and right edges:

Out[1]=1

FrameLabel  (2)

Specify frame labels for the bottom and left edges:

Out[1]=1

Specify labels for each edge:

Out[1]=1

FrameStyle  (2)

Specify the overall frame style:

Out[1]=1

Specify the style of each frame edge:

Out[1]=1

FrameTicks  (3)

Put a frame, but no ticks:

Out[1]=1

Tick mark labels on the bottom and left frame edges:

Out[1]=1

Frame ticks on the bottom and right edges:

Out[1]=1

FrameTicksStyle  (2)

Specify frame tick and frame tick label style:

Out[1]=1

Specify frame tick style for each edge:

Out[1]=1

GridLines  (3)

Put grids across a 2D graphic:

Out[1]=1

Draw grid lines at specific positions:

Out[1]=1

Specify the style of each grid:

Out[1]=1

GridLinesStyle  (1)

Specify the overall grid style:

Out[1]=1

ImageMargins  (3)

Allow no margins outside of ImageSize:

Out[1]=1

Have 20-point margins on all sides:

Out[1]=1

Draw grid lines at specific positions:

Out[1]=1

ImagePadding  (4)

Leave no padding outside the plot range:

Out[1]=1

Leave enough padding for all objects and labels that are present:

Out[1]=1

Specify the same padding for all sides in printer's points:

Out[1]=1

Specify the same padding for all sides in printer's points:

Out[1]=1

ImageSize  (3)

Use predefined symbolic sizes:

Out[1]=1

Use an explicit image width:

Out[1]=1

Use an explicit image width and height:

Out[1]=1

LabelStyle  (1)

Specify the overall style of all the label-like elements:

Out[1]=1

Lighting  (4)

Ambient light is uniformly applied to all the surfaces in the scene:

Out[1]=1

Directional lights with different colors:

Out[1]=1

Point lights with different colors:

Out[1]=1

Spotlights with different colors:

Out[1]=1

PlotLabel  (2)

Display a label on the top of the graphic in TraditionalForm:

Out[1]=1

Use Style and other typesetting functions to modify how the label appears:

Out[1]=1

PlotRange  (3)

Display all objects:

Out[1]=1

Explicitly choose and ranges:

Out[1]=1

Force clipping at the PlotRange:

Out[2]=2

PlotRange->s is equivalent to PlotRange->{{-s,s},{-s,s}}:

Out[1]=1

PlotRangeClipping  (2)

Allow graphics objects to spread beyond PlotRange:

Out[1]=1

Clip all graphics objects at PlotRange:

Out[1]=1

PlotRangePadding  (3)

Include 1 coordinate unit of padding on all sides:

Out[1]=1

Include padding using Scaled coordinates:

Out[1]=1

Specify different padding on each side:

Out[1]=1

PlotRegion  (3)

The contents of a graphic use the whole region:

Out[1]=1

Limit the contents of the graphic to the middle half of the region in each direction:

Out[1]=1

ImagePadding can also be used to add padding around a graphic:

Out[1]=1

PlotTheme  (3)

Base Themes  (2)

Use a common base theme:

Out[1]=1

Use a monochrome theme:

Out[1]=1

Feature Themes  (1)

Use a theme to draw sampled points from mesh cells:

Out[1]=1

Prolog  (1)

Define a simple graphic to use as a background:

Use it in multiple mesh regions:

Out[2]=2
Out[3]=3

RotateLabel  (2)

Specify that vertical frame labels should be rotated:

Out[1]=1

Specify that vertical frame labels should not be rotated:

Out[1]=1

SphericalRegion  (2)

Make a sequence of images be consistently sized, independent of orientation:

Out[1]=1

Without SphericalRegion, each image is made as big as possible:

Out[1]=1

Ticks  (3)

Draw the axes but no tick marks:

Out[1]=1

Place tick marks automatically:

Out[1]=1

Draw tick marks at specific positions:

Out[1]=1

TicksStyle  (2)

Specify the styles of the ticks and tick labels:

Out[1]=1

Specify the styles of and axis ticks separately:

Out[1]=1

ViewAngle  (1)

Use a specific angle for a simulated camera:

Out[1]=1

ViewCenter  (1)

Place the top-right corner of the object at the center of the final image:

Out[1]=1

ViewMatrix  (1)

Orthographic view of a mesh region from the negative direction:

Out[1]=1

ViewPoint  (3)

Specify the view point using the special scaled coordinates:

Out[1]=1

Use symbolic view points:

Out[1]=1

Specify orthographic views:

Out[1]=1

ViewRange  (2)

By default, the range is sufficient to include all the objects:

Out[1]=1

Specify the minimum and maximum distances from the camera to be included:

Out[1]=1

ViewVector  (1)

Specify the view vectors using ordinary coordinates:

Out[1]=1

ViewVertical  (2)

Use the axis direction as the vertical direction in the final image:

Out[1]=1

Various views of vertical directions:

Out[1]=1

Properties & Relations  (2)Properties of the function, and connections to other functions

Region can have any geometric dimension:

Out[5]=5

RegionQ can be used to test whether a region is a Region:

Out[1]=1
Out[2]=2
Wolfram Research (2017), Region, Wolfram Language function, https://reference.wolfram.com/language/ref/Region.html (updated 2017).
Wolfram Research (2017), Region, Wolfram Language function, https://reference.wolfram.com/language/ref/Region.html (updated 2017).

Text

Wolfram Research (2017), Region, Wolfram Language function, https://reference.wolfram.com/language/ref/Region.html (updated 2017).

Wolfram Research (2017), Region, Wolfram Language function, https://reference.wolfram.com/language/ref/Region.html (updated 2017).

CMS

Wolfram Language. 2017. "Region." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Region.html.

Wolfram Language. 2017. "Region." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Region.html.

APA

Wolfram Language. (2017). Region. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Region.html

Wolfram Language. (2017). Region. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Region.html

BibTeX

@misc{reference.wolfram_2025_region, author="Wolfram Research", title="{Region}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Region.html}", note=[Accessed: 09-July-2025 ]}

@misc{reference.wolfram_2025_region, author="Wolfram Research", title="{Region}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Region.html}", note=[Accessed: 09-July-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_region, organization={Wolfram Research}, title={Region}, year={2017}, url={https://reference.wolfram.com/language/ref/Region.html}, note=[Accessed: 09-July-2025 ]}

@online{reference.wolfram_2025_region, organization={Wolfram Research}, title={Region}, year={2017}, url={https://reference.wolfram.com/language/ref/Region.html}, note=[Accessed: 09-July-2025 ]}