A circle is defined by a center and a radius (given as the squared radius due to the inexactness of square roots). In 3 dimensions a circle is a disc and thus have an orientation given by an orthogonal direction. If the radius is 0 the circle is considered degenerate.

circle(..., default_dim = 2) is_circle(x) as_circle(x)

... | Various input. See the Constructor section. |
---|---|

default_dim | The dimensionality when constructing an empty vector |

x | A circle vector or an object to convert to it |

An `euclid_circle`

vector

**2 dimensional circles**

Providing one point and one numeric vector will construct circles centered at the point with the

**squared**radius given by the numeric.Providing two points will construct circles centered between the two points with a radius of half the distance between the two points.

Providing three point vectors will construct the unique circle that pass through the three points.

**3 dimensional circles**

Providing three point vectors will construct the unique circle that pass through the three points.

Providing a point, a numeric, and a plane will construct a circle centered on the point with the squared radius given by the numeric and the orientation given by the plane. The point must lie on the plane

Providing a point, a numeric, and a vector will construct a circle centered on the point with the squared radius given by the numeric and the orientation orthogonal to the vector

Providing two spheres will construct a circle given by the intersection of the two spheres. The spheres must intersect

Providing a sphere and a plane will construct a circle given by the intersection of the sphere and the plane. The sphere and plane must intersect.

## 2 Dimensions point1 <- point(runif(5), runif(5)) point2 <- point(runif(5), runif(5)) point3 <- point(runif(5), runif(5)) number <- exact_numeric(1:5) # Construction with center and radius circ <- circle(point1, number) circ#> <2D circles [5]> #> [1] <x:0.301, y:0.949, r2:1> <x:0.636, y:0.18, r2:2> <x:0.479, y:0.217, r2:3> #> [4] <x:0.432, y:0.68, r2:4> <x:0.706, y:0.499, r2:5># integers and numerics are converted automatically circle(point1, 1:5)#> <2D circles [5]> #> [1] <x:0.301, y:0.949, r2:1> <x:0.636, y:0.18, r2:2> <x:0.479, y:0.217, r2:3> #> [4] <x:0.432, y:0.68, r2:4> <x:0.706, y:0.499, r2:5># You are free to name the input for readability circle(center = point1, radius = number)#> <2D circles [5]> #> [1] <x:0.301, y:0.949, r2:1> <x:0.636, y:0.18, r2:2> <x:0.479, y:0.217, r2:3> #> [4] <x:0.432, y:0.68, r2:4> <x:0.706, y:0.499, r2:5># Construction with 2 points circle(point1, point2)#> <2D circles [5]> #> [1] <x:0.471, y:0.97, r2:0.0295> <x:0.648, y:0.575, r2:0.156> #> [3] <x:0.288, y:0.303, r2:0.0441> <x:0.599, y:0.571, r2:0.0398> #> [5] <x:0.738, y:0.407, r2:0.00943># Construction with 3 points circle(point1, point2, point3)#> <2D circles [5]> #> [1] <x:0.506, y:0.687, r2:0.111> <x:0.068, y:0.593, r2:0.493> #> [3] <x:0.289, y:0.307, r2:0.0441> <x:0.65, y:0.648, r2:0.0483> #> [5] <x:0.485, y:0.32, r2:0.081>## 3 Dimensions point1 <- point(runif(5), runif(5), runif(5)) point2 <- point(runif(5), runif(5), runif(5)) point3 <- point(runif(5), runif(5), runif(5)) circ <- circle(point1, point2, point3) circle(point1, number, as_vec(point2))#> <3D circles [5]> #> [1] <x:0.57, y:0.542, z:0.0281, r2:1, dx:0.56, dy:0.261, dz:0.213> #> [2] <x:0.336, y:0.545, z:0.466, r2:2, dx:0.857, dy:0.29, dz:0.672> #> [3] <x:0.596, y:0.279, z:0.39, r2:3, dx:0.385, dy:0.48, dz:0.0586> #> [4] <x:0.192, y:0.447, z:0.0201, r2:4, dx:0.528, dy:0.92, dz:0.997> #> [5] <x:0.948, y:0.372, z:0.377, r2:5, dx:0.601, dy:0.401, dz:0.149>#> <3D euclid_planes [5]> #> [1] <a:-0.16, b:-0.00572, c:-0.0174, d:0.0947> #> [2] <a:0.169, b:0.234, c:-0.139, d:-0.119> #> [3] <a:0.0689, b:-0.0344, c:-0.0649, d:-0.00619> #> [4] <a:-0.0436, b:-0.17, c:0.0972, d:0.0822> #> [5] <a:0.105, b:0.137, c:-0.142, d:-0.0965>#> <3D euclid_spheres [5]> #> [1] <x:0.537, y:0.541, z:0.33, r2:0.0922> <x:0.611, y:0.291, z:0.375, r2:0.149> #> [3] <x:0.549, y:0.467, z:0.24, r2:0.0602> <x:1.07, y:0.431, z:0.387, r2:0.902> #> [5] <x:0.706, y:0.571, z:0.39, r2:0.0983>