Vector of planes

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.

Usage

plane(...)

is_plane(x)

as_plane(x)

Arguments

...

Various input. See the Constructor section.

x

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

See also

Other Geometries: circle(), direction(), iso_cube(), iso_rect(), line(), point(), ray(), segment(), sphere(), tetrahedron(), triangle(), vec(), weighted_point()

Other Surfaces: circle(), iso_rect(), triangle()

Examples

# Construction
p <- plane(sample(10, 2), sample(10, 2), sample(10, 2), sample(10, 2))
p
#> <3D euclid_planes [2]>
#> [1] <a:2, b:6, c:9, d:1> <a:4, b:7, c:8, d:7>