# DiskSegment

DiskSegment[{x,y},r,{θ1,θ2}]

represents the disk segment from angle θ1 to θ2 in a disk centered at {x,y} of radius r.

DiskSegment[{x,y},{rx,ry},{θ1,θ2}]

represents the ellipse segment from angle θ1 to θ2 in an axis-aligned ellipse with semiaxes lengths rx and ry.

# Details and Options

• DiskSegment can be used as a geometric region and a graphics primitive.
• DiskSegment represents the filled segment part of Disk with the same arguments.
• Angles are measured in radians counterclockwise from the positive x direction.
• DiskSegment can be used in Graphics.
• In graphics, the point {x,y} can be Dynamic expressions.
• Graphics rendering is affected by directives such as FaceForm, EdgeForm, and color.

# Examples

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## Basic Examples(5)

Half of a unit disk:

A disk segment:

A segment of an elliptical disk:

Differently styled disk segments:

Get the Area of a disk segment (half disk):

The area of an ellipse segment:

## Scope(17)

### Graphics(7)

#### Specification(4)

Specify centers:

Specify the angle:

An elliptical disk segment:

#### Styling(2)

Color directives specify the face colors of disk segments:

FaceForm and EdgeForm can be used to specify the styles of the interiors and boundaries:

Boundaries of a disk segment:

#### Coordinates(1)

Points can be Dynamic:

### Regions(10)

Embedding dimension:

Geometric dimension:

Point membership test:

Get conditions for point membership:

Area:

Centroid:

Distance from a point:

Signed distance from a point:

Nearest point in the region:

Nearest points:

An ellipse segment is bounded:

Get its range:

Integrate over an ellipse segment:

Optimize over an ellipse segment:

Solve equations in an ellipse segment:

## Applications(5)

Plot a function over a disk segment:

Create a 3D disk segment extrusion with RegionProduct:

To show the region difference between a disk and a regular polygon, a set of disk segments may be used. First you get a set of arcs:

However, some of arcs are not increasing angle ranges, so in those cases is added to the second angle to make it increasing:

Finally, visualize:

A lens can be modeled as two adjacent disk segments. Create a rightward-facing lens segment of height and radius of , centered on the origin:

For the leftward-facing part of the lens, you need to switch the position and switch the direction of the arc:

Now make a function that will construct a pair of disk segments for given height and radii, and visualize it for a range of radius values:

You can find an approximate measure of a region by finding the fraction of random points within a region of known volume that fall within the region whose measure you seek. Use a disk segment as an example:

This region can be contained within the region and , which has an area of 16. Generate a list of random points within this general region:

Find the percent of these random points that fall within the disk segment:

The area of the region (the disk segment) should be close to that ratio times the area over which the random points are distributed. Compare this approximation to the actual value:

## Properties & Relations(4)

DiskSegment can be represented by a FilledCurve:

A disk segment may result from the RegionIntersection of a Disk and another region:

ImplicitRegion can represent any DiskSegment:

ParametricRegion can represent a DiskSegment:

## Neat Examples(3)

Random disk segment collections:

A family of disk segments:

Digital petals:

Wolfram Research (2015), DiskSegment, Wolfram Language function, https://reference.wolfram.com/language/ref/DiskSegment.html.

#### Text

Wolfram Research (2015), DiskSegment, Wolfram Language function, https://reference.wolfram.com/language/ref/DiskSegment.html.

#### CMS

Wolfram Language. 2015. "DiskSegment." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DiskSegment.html.

#### APA

Wolfram Language. (2015). DiskSegment. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiskSegment.html

#### BibTeX

@misc{reference.wolfram_2024_disksegment, author="Wolfram Research", title="{DiskSegment}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/DiskSegment.html}", note=[Accessed: 12-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_disksegment, organization={Wolfram Research}, title={DiskSegment}, year={2015}, url={https://reference.wolfram.com/language/ref/DiskSegment.html}, note=[Accessed: 12-June-2024 ]}