CirclePoints
Details
- For positive integer n, CirclePoints[n] generates a list of vertices for a regular n-sided polygon, oriented so its base is horizontal.
- In CirclePoints[n], n does not have to be an exact integer. The angles between successive vectors are always .
- Unless explicitly given as a Quantity object, the angle θ1 is assumed to be in radians, counterclockwise starting from the axis. (Multiply by Degree to convert from degrees.)
- If the angle θ1 is not given, it is assumed to be π/n-π/2, so that for integer n the vectors correspond to a regular polygon with its base horizontal.
- All arguments of CirclePoints except n can be symbolic. They can also be Quantity objects.
Examples
open allclose allBasic Examples (3)Summary of the most common use cases
Scope (6)Survey of the scope of standard use cases
Corners of a centered square with horizontal and vertical sides:
https://wolfram.com/xid/0rswwyniu-9h1zsa
https://wolfram.com/xid/0rswwyniu-z2pf8e
Four unitary vectors aligned with the axes:
https://wolfram.com/xid/0rswwyniu-7srgdn
Displace them to a different point:
https://wolfram.com/xid/0rswwyniu-x2otro
The four corners of an arbitrary square, at any point and any size or orientation:
https://wolfram.com/xid/0rswwyniu-jyo4kf
Use a Quantity radius:
https://wolfram.com/xid/0rswwyniu-hwdwdw
Specify the initial angle as a Quantity object:
https://wolfram.com/xid/0rswwyniu-ojbhta
Draw polygons, with their lowest side oriented horizontally by default:
https://wolfram.com/xid/0rswwyniu-h658hl
Draw them all together, with opacity:
https://wolfram.com/xid/0rswwyniu-48azw2
Properties & Relations (2)Properties of the function, and connections to other functions
CirclePoints returns pairs that can be reinterpreted as real and imaginary parts of the roots of unity:
https://wolfram.com/xid/0rswwyniu-5hvjyg
https://wolfram.com/xid/0rswwyniu-em154p
https://wolfram.com/xid/0rswwyniu-1afeq5
CirclePoints is equivalent to a collection of AngleVector calls:
https://wolfram.com/xid/0rswwyniu-tong5y
https://wolfram.com/xid/0rswwyniu-k3qzwj
Interactive Examples (1)Examples with interactive outputs
https://wolfram.com/xid/0rswwyniu-kcuc25
Neat Examples (2)Surprising or curious use cases
Combine Fold and CirclePoints:
https://wolfram.com/xid/0rswwyniu-s9fmxe
Combine CirclePoints with BezierCurve:
https://wolfram.com/xid/0rswwyniu-m3ze2e
https://wolfram.com/xid/0rswwyniu-d63t6
Text
Wolfram Research (2015), CirclePoints, Wolfram Language function, https://reference.wolfram.com/language/ref/CirclePoints.html.
CMS
Wolfram Language. 2015. "CirclePoints." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CirclePoints.html.
APA
Wolfram Language. (2015). CirclePoints. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CirclePoints.html