A plane splits the euclidean space in two by all the points that satisfy the plane equation ax + by + cz + d = 0. As can be seen this is an extension of the concept of lines in 2 dimensions though lines can also exist in three dimensions.

plane(...)

is_plane(x)

as_plane(x)

## Arguments

... Various input. See the Constructor section. A vector of planes or an object to convert to it

## Value

An euclid_plane vector

## Constructors

3 dimensional planes

• Providing 4 numberics will construct planes with coefficients from the 4 numerics in the order given.

• Providing 3 points will construct planes passing through the three points

• Providing a point and vector will construct planes that goes through the point and are orthogonal to the vector

• Providing a point and a direction will construct planes that goes through the point and are orthogonal to the direction

• Providing a point and a line will construct planes that goes through the point and 2 points on the line

• Providing a point and a ray will construct planes that goes through the point and 2 points on the ray

• Providing a point and a segment will construct planes that goes through the point and the two points making up the segment

• Providing a circle will construct planes that contains the circle

• Providing a triangle will construct planes that contains the triangle

## Examples

# Construction
p <- plane(sample(10, 2), sample(10, 2), sample(10, 2), sample(10, 2))
p
#> <3D euclid_planes >
#>  <a:1, b:9, c:5, d:7>  <a:8, b:7, c:2, d:10>