ostk.mathematics.geometry.d3.object.Plane

class Plane(

self: ostk.mathematics.geometry.d3.object.Plane,

point: ostk.mathematics.geometry.d3.object.Point,

normal_vector: numpy.ndarray[numpy.float64[3, 1]],

)

Bases: Object

Create a 3D plane from a point and normal vector.

Parameters:

• point (Point) -- A point on the plane.

• normal_vector (numpy.array) -- The normal vector to the plane.

Example

>>> point = Point(0.0, 0.0, 0.0)
>>> normal = numpy.array([0.0, 0.0, 1.0])
>>> plane = Plane(point, normal)

Methods

apply_transformation	Apply a transformation to the plane.
as_cone	Convert the object to a cone.
as_ellipsoid	Convert the object to an ellipsoid.
as_line	Convert the object to a line.
as_line_string	Convert the object to a line string.
as_plane	Convert the object to a plane.
as_point	Convert the object to a point.
as_point_set	Convert the object to a point set.
as_polygon	Convert the object to a polygon.
as_pyramid	Convert the object to a pyramid.
as_ray	Convert the object to a ray.
as_segment	Convert the object to a segment.
as_sphere	Convert the object to a sphere.
contains	Overloaded function.
get_normal_vector	Get the normal vector of the plane.
get_point	Get a reference point on the plane.
intersection_with	Overloaded function.
intersects	Overloaded function.
is_cone	Check if the object is a cone.
is_defined	Check if the plane is defined.
is_ellipsoid	Check if the object is an ellipsoid.
is_line	Check if the object is a line.
is_line_string	Check if the object is a line string.
is_plane	Check if the object is a plane.
is_point	Check if the object is a point.
is_point_set	Check if the object is a point set.
is_polygon	Check if the object is a polygon.
is_pyramid	Check if the object is a pyramid.
is_ray	Check if the object is a ray.
is_segment	Check if the object is a segment.
is_sphere	Check if the object is a sphere.
undefined	Create an undefined plane.

apply_transformation(

self: ostk.mathematics.geometry.d3.object.Plane,

transformation: ostk::mathematics::geometry::d3::Transformation,

) → None

Apply a transformation to the plane.

Parameters:

transformation (Transformation) -- The transformation to apply.

Returns:

The transformed plane.

Return type:

Plane

Example

>>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
>>> transformation = Transformation.identity()
>>> transformed = plane.apply_transformation(transformation)

as_cone(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::Cone

Convert the object to a cone.

Returns:

The cone.

Return type:

Cone

as_ellipsoid(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::Ellipsoid

Convert the object to an ellipsoid.

Returns:

The ellipsoid.

Return type:

Ellipsoid

as_line(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::Line

Convert the object to a line.

Returns:

The line.

Return type:

Line

as_line_string(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::LineString

Convert the object to a line string.

Returns:

The line string.

Return type:

LineString

as_plane(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::Plane

Convert the object to a plane.

Returns:

The plane.

Return type:

Plane

as_point(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::Point

Convert the object to a point.

Returns:

The point.

Return type:

Point

as_point_set(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::PointSet

Convert the object to a point set.

Returns:

The point set.

Return type:

PointSet

as_polygon(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::Polygon

Convert the object to a polygon.

Returns:

The polygon.

Return type:

Polygon

as_pyramid(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::Pyramid

Convert the object to a pyramid.

Returns:

The pyramid.

Return type:

Pyramid

as_ray(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::Ray

Convert the object to a ray.

Returns:

The ray.

Return type:

Ray

as_segment(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::Segment

Convert the object to a segment.

Returns:

The segment.

Return type:

Segment

as_sphere(

self: ostk.mathematics.geometry.d3.Object,

) → ostk::mathematics::geometry::d3::object::Sphere

Convert the object to a sphere.

Returns:

The sphere.

Return type:

Sphere

contains(*args, **kwargs)

Overloaded function.

1. contains(self: ostk.mathematics.geometry.d3.object.Plane, point: ostk.mathematics.geometry.d3.object.Point) -> bool

   Check if the plane contains a point.

   Args:

   point (Point): The point to check.

   Returns:

   bool: True if the plane contains the point, False otherwise.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> plane.contains(Point(1.0, 1.0, 0.0))  # True (z=0 plane)
   

2. contains(self: ostk.mathematics.geometry.d3.object.Plane, point_set: ostk.mathematics.geometry.d3.object.PointSet) -> bool

   Check if the plane contains a point set.

   Args:

   point_set (PointSet): The point set to check.

   Returns:

   bool: True if the plane contains all points in the set, False otherwise.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> points = PointSet([Point(1.0, 1.0, 0.0), Point(2.0, 2.0, 0.0)])
   >>> plane.contains(points)  # True
   

3. contains(self: ostk.mathematics.geometry.d3.object.Plane, line: ostk.mathematics.geometry.d3.object.Line) -> bool

   Check if the plane contains a line.

   Args:

   line (Line): The line to check.

   Returns:

   bool: True if the plane contains the entire line, False otherwise.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> line = Line(Point(0.0, 0.0, 0.0), numpy.array([1.0, 0.0, 0.0]))
   >>> plane.contains(line)  # True (line lies in z=0 plane)
   

4. contains(self: ostk.mathematics.geometry.d3.object.Plane, ray: ostk.mathematics.geometry.d3.object.Ray) -> bool

   Check if the plane contains a ray.

   Args:

   ray (Ray): The ray to check.

   Returns:

   bool: True if the plane contains the entire ray, False otherwise.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> ray = Ray(Point(0.0, 0.0, 0.0), numpy.array([1.0, 0.0, 0.0]))
   >>> plane.contains(ray)  # True
   

5. contains(self: ostk.mathematics.geometry.d3.object.Plane, segment: ostk.mathematics.geometry.d3.object.Segment) -> bool

   Check if the plane contains a segment.

   Args:

   segment (Segment): The segment to check.

   Returns:

   bool: True if the plane contains the entire segment, False otherwise.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> segment = Segment(Point(0.0, 0.0, 0.0), Point(1.0, 0.0, 0.0))
   >>> plane.contains(segment)  # True
   

get_normal_vector(

self: ostk.mathematics.geometry.d3.object.Plane,

) → numpy.ndarray[numpy.float64[3, 1]]

Get the normal vector of the plane.

Returns:

The normal vector to the plane.

Return type:

Vector3d

Example

>>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
>>> normal = plane.get_normal_vector()  # [0.0, 0.0, 1.0]

get_point(

self: ostk.mathematics.geometry.d3.object.Plane,

) → ostk.mathematics.geometry.d3.object.Point

Get a reference point on the plane.

Returns:

A point on the plane.

Return type:

Point

Example

>>> plane = Plane(Point(1.0, 2.0, 3.0), numpy.array([0.0, 0.0, 1.0]))
>>> point = plane.get_point()

intersection_with(*args, **kwargs)

Overloaded function.

1. intersection_with(self: ostk.mathematics.geometry.d3.object.Plane, point: ostk.mathematics.geometry.d3.object.Point) -> ostk::mathematics::geometry::d3::Intersection

   Compute the intersection of the plane with a point.

   Args:

   point (Point): The point to intersect with.

   Returns:

   Intersection: The intersection result.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> intersection = plane.intersection_with(Point(1.0, 1.0, 0.0))
   

2. intersection_with(self: ostk.mathematics.geometry.d3.object.Plane, point_set: ostk.mathematics.geometry.d3.object.PointSet) -> ostk::mathematics::geometry::d3::Intersection

   Compute the intersection of the plane with a point set.

   Args:

   point_set (PointSet): The point set to intersect with.

   Returns:

   Intersection: The intersection result.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> points = PointSet([Point(1.0, 1.0, 0.0), Point(2.0, 2.0, 1.0)])
   >>> intersection = plane.intersection_with(points)
   

3. intersection_with(self: ostk.mathematics.geometry.d3.object.Plane, line: ostk.mathematics.geometry.d3.object.Line) -> ostk::mathematics::geometry::d3::Intersection

   Compute the intersection of the plane with a line.

   Args:

   line (Line): The line to intersect with.

   Returns:

   Intersection: The intersection result (point or line if coplanar).

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> line = Line(Point(0.0, 0.0, -1.0), numpy.array([0.0, 0.0, 1.0]))
   >>> intersection = plane.intersection_with(line)
   

4. intersection_with(self: ostk.mathematics.geometry.d3.object.Plane, ray: ostk.mathematics.geometry.d3.object.Ray) -> ostk::mathematics::geometry::d3::Intersection

   Compute the intersection of the plane with a ray.

   Args:

   ray (Ray): The ray to intersect with.

   Returns:

   Intersection: The intersection result.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> ray = Ray(Point(0.0, 0.0, -1.0), numpy.array([0.0, 0.0, 1.0]))
   >>> intersection = plane.intersection_with(ray)
   

5. intersection_with(self: ostk.mathematics.geometry.d3.object.Plane, segment: ostk.mathematics.geometry.d3.object.Segment) -> ostk::mathematics::geometry::d3::Intersection

   Compute the intersection of the plane with a segment.

   Args:

   segment (Segment): The segment to intersect with.

   Returns:

   Intersection: The intersection result.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> segment = Segment(Point(0.0, 0.0, -1.0), Point(0.0, 0.0, 1.0))
   >>> intersection = plane.intersection_with(segment)
   

intersects(*args, **kwargs)

Overloaded function.

1. intersects(self: ostk.mathematics.geometry.d3.object.Plane, point: ostk.mathematics.geometry.d3.object.Point) -> bool

   Check if the plane intersects with a point.

   Args:

   point (Point): The point to check.

   Returns:

   bool: True if the plane intersects the point, False otherwise.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> plane.intersects(Point(1.0, 1.0, 0.0))  # True
   

2. intersects(self: ostk.mathematics.geometry.d3.object.Plane, point_set: ostk.mathematics.geometry.d3.object.PointSet) -> bool

   Check if the plane intersects with a point set.

   Args:

   point_set (PointSet): The point set to check.

   Returns:

   bool: True if the plane intersects the point set, False otherwise.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> points = PointSet([Point(1.0, 1.0, 0.0), Point(2.0, 2.0, 0.0)])
   >>> plane.intersects(points)  # True
   

3. intersects(self: ostk.mathematics.geometry.d3.object.Plane, line: ostk.mathematics.geometry.d3.object.Line) -> bool

   Check if the plane intersects with a line.

   Args:

   line (Line): The line to check.

   Returns:

   bool: True if the plane intersects the line, False otherwise.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> line = Line(Point(0.0, 0.0, -1.0), numpy.array([0.0, 0.0, 1.0]))
   >>> plane.intersects(line)  # True
   

4. intersects(self: ostk.mathematics.geometry.d3.object.Plane, ray: ostk.mathematics.geometry.d3.object.Ray) -> bool

   Check if the plane intersects with a ray.

   Args:

   ray (Ray): The ray to check.

   Returns:

   bool: True if the plane intersects the ray, False otherwise.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> ray = Ray(Point(0.0, 0.0, -1.0), numpy.array([0.0, 0.0, 1.0]))
   >>> plane.intersects(ray)  # True
   

5. intersects(self: ostk.mathematics.geometry.d3.object.Plane, segment: ostk.mathematics.geometry.d3.object.Segment) -> bool

   Check if the plane intersects with a segment.

   Args:

   segment (Segment): The segment to check.

   Returns:

   bool: True if the plane intersects the segment, False otherwise.

   Example:

   >>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
   >>> segment = Segment(Point(0.0, 0.0, -1.0), Point(0.0, 0.0, 1.0))
   >>> plane.intersects(segment)  # True
   

is_cone(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a cone.

Returns:

True if the object is a cone.

Return type:

bool

is_defined(self: ostk.mathematics.geometry.d3.object.Plane) → bool

Check if the plane is defined.

Returns:

True if the plane is defined, False otherwise.

Return type:

bool

Example

>>> plane = Plane(Point(0.0, 0.0, 0.0), numpy.array([0.0, 0.0, 1.0]))
>>> plane.is_defined()  # True

is_ellipsoid(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is an ellipsoid.

Returns:

True if the object is an ellipsoid.

Return type:

bool

is_line(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a line.

Returns:

True if the object is a line.

Return type:

bool

is_line_string(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a line string.

Returns:

True if the object is a line string.

Return type:

bool

is_plane(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a plane.

Returns:

True if the object is a plane.

Return type:

bool

is_point(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a point.

Returns:

True if the object is a point.

Return type:

bool

is_point_set(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a point set.

Returns:

True if the object is a point set.

Return type:

bool

is_polygon(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a polygon.

Returns:

True if the object is a polygon.

Return type:

bool

is_pyramid(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a pyramid.

Returns:

True if the object is a pyramid.

Return type:

bool

is_ray(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a ray.

Returns:

True if the object is a ray.

Return type:

bool

is_segment(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a segment.

Returns:

True if the object is a segment.

Return type:

bool

is_sphere(self: ostk.mathematics.geometry.d3.Object) → bool

Check if the object is a sphere.

Returns:

True if the object is a sphere.

Return type:

bool

static undefined() → ostk.mathematics.geometry.d3.object.Plane

Create an undefined plane.

Returns:

An undefined plane.

Return type:

Plane

Example

>>> undefined_plane = Plane.undefined()
>>> undefined_plane.is_defined()  # False