Circle

Circle[{x,y},r]

represents a circle of radius r centered at {x,y}.

Circle[{x,y}]

gives a circle of radius 1.

Circle[{x,y},{rx,ry}]

gives an axis-aligned ellipse with semiaxes lengths rx and ry.

Circle[{x,y},,{θ1,θ2}]

gives a circular or ellipse arc from angle θ1 to θ2.

Details

  • Circle with its different parameter settings is also known as arc, circular arc, semicircle, and ellipse.
  • Circle can be used as a geometric region and a graphics primitive.
  • Circle[] is equivalent to Circle[{0,0}]. »
  • Circle represents the curve .
  • Angles are measured in radians counterclockwise from the positive x direction.
  • Circle can be used in Graphics.
  • In graphics, the point {x,y} and radii r and {rx,ry} can be Scaled, Offset, ImageScaled, and Dynamic expressions.
  • Graphics rendering is affected by directives such as Thickness, Dashing, and color.

Background & Context

  • Circle is a graphics and geometry primitive that represents a circle, ellipse, or circular/elliptical arc in the plane. In particular, Circle[{x,y},r] represents the circle of radius r in centered at {x,y}, Circle[{x,y},{rx,ry}] represents the axis-aligned filled ellipse in with center {x,y} and semiaxis lengths rx and ry, and Circle[{x,y},,{θ1,θ2}] represents the (potentially elliptical) arc centered at {x,y} ranging between angles θ1 and θ2 measured in radians counterclockwise from the positive axis. The shorthand form Circle[{x,y}] is equivalent to Circle[{x,y},1], while Circle[] autoevaluates to Circle[{0,0},1].
  • Circle objects can be formatted by placing them inside a Graphics expression. Note that while abstract circles have dimension 1 and zero thickness, for convenience, formatted Circle objects are rendered by default with finite thickness. The appearance of Circle objects in graphics can be modified by specifying thickness directives such as Thickness, AbsoluteThickness, Thick and Thin; dashing directives such as Dashing, AbsoluteDashing, Dashed, Dotted and DotDashed; color directives such as Red; the transparency directive Opacity; and the style option Antialiasing.
  • Circle may also serve as a region specification over which a computation should be performed. For example, Integrate[1,{x, y}Circle[{0,0},r]] and ArcLength[Circle[{x,y},r]] both return the perimeter .
  • CirclePoints may be used to give the positions of equally spaced points around a circle.
  • Circle is related to a number of other symbols. Circle represents the boundary of a disk, as can be computed using RegionBoundary[Disk[{x,y},r]]. Cylinder and Sphere may be thought of as higher-dimensional analogs of circles. Circle[{x,y},r] may be alternately represented using Sphere[{x,y},r], ImplicitRegion[(x-u)2+(y-v)2r2,{u,v}] or ParametricRegion[{x+r Cos[t],y+r Sin[t]},{t,0,2π}]. Precomputed properties of the circle and its variants in standard position are available using PlaneCurveData["entity","property"] or EntityValue[Entity["PlaneCurve","entity"],"property"], where "entity" is one of "Circle", "CircularArc", "Ellipse", "Semicircle", etc.

Examples

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Basic Examples  (5)

A unit circle:

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A circular arc:

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An ellipse:

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Differently styled circles:

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ArcLength of a circle:

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Length or circular arc:

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Scope  (23)

Applications  (8)

Properties & Relations  (10)

Possible Issues  (2)

Neat Examples  (4)

See Also

Disk  RoundingRadius  Rotate  Cylinder  Sphere  CirclePoints

Introduced in 1991
(2.0)
| Updated in 2014
(10.0)