Isotoxal 2n-gon inner radius

isotoxal_2ngon_inner_radius() computes the inner radius of an isotoxal 2n-gon polygon. star_inner_radius() is an alias.

Usage

isotoxal_2ngon_inner_radius(
  n,
  outer_radius = 1,
  ...,
  alpha = NULL,
  beta_ext = NULL,
  d = NULL
)

star_inner_radius(
  n,
  outer_radius = 1,
  ...,
  alpha = NULL,
  beta_ext = NULL,
  d = NULL
)

Arguments

n

The number of outer vertices.

outer_radius

The outer radius of the isotoxal 2n-gon.

...

Ignored.

alpha

The interior angle of an outer vertex. Will be coerced by degrees().

beta_ext

The exterior angle of an inner vertex. Will be coerced by degrees().

d

The density aka winding number of the regular star polygon (outline) in which case this star is represented by |n/d|.

Value

A numeric vector

Details

Isotoxal 2n-gon polygons are polygons with:

• 2n vertices alternating between n "outer" vertices evenly spaced on one circle and n "inner" vertices evenly spaced on smaller circle with the same center.

• Each edge of the polygon is of the same length.

• The outer vertices all have the same interior angle alpha and the inner vertices all have the same interior angle beta.

• They are a generalization of (the outlines of) concave simple "star" polygons that also includes convex polygons with an even number of vertices.

See also

isotoxal_2ngon_polygon2d() to construct an isotoxal 2n-gon Polygon2D object. https://en.wikipedia.org/wiki/Isotoxal_figure#Isotoxal_polygons and https://en.wikipedia.org/wiki/Star_polygon#Isotoxal_star_simple_polygons for more information on isotoxal polygons.

Examples

# |8/3| star has outer vertex internal angle 45 degrees
# and inner vertex external angle 90 degrees
isotoxal_2ngon_inner_radius(8, d = 3)
#> [1] 0.5411961
isotoxal_2ngon_inner_radius(8, alpha = 45)
#> [1] 0.5411961
isotoxal_2ngon_inner_radius(8, beta_ext = 90)
#> [1] 0.5411961