ostk.mathematics.geometry.d3.object.Pyramid¶

class Pyramid( self: ostk.mathematics.geometry.d3.object.Pyramid, base: ostk.mathematics.geometry.d3.object.Polygon, apex: ostk.mathematics.geometry.d3.object.Point, )¶

Bases: Object

A pyramid in 3D space.

A Pyramid is defined by a polygonal base and an apex point, with triangular lateral faces connecting the base edges to the apex.

Construct a pyramid from a base polygon and apex point.

Parameters:

base (Polygon) -- The polygonal base of the pyramid.
apex (Point) -- The apex point of the pyramid.

Example

>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)])
>>> apex = Point(0.0, 0.0, 1.0)
>>> pyramid = Pyramid(base, apex)

Methods

`apply_transformation`	Apply a transformation to the pyramid.
`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_apex`	Get the apex point of the pyramid.
`get_base`	Get the base polygon of the pyramid.
`get_lateral_face_at`	Get the lateral face at a given index.
`get_lateral_face_count`	Get the number of lateral faces.
`get_rays_of_lateral_face_at`	Get rays from the apex through a specific lateral face.
`get_rays_of_lateral_faces`	Get rays from the apex through all lateral faces.
`intersection_with`	Overloaded function.
`intersects`	Check if the pyramid intersects an ellipsoid.
`is_cone`	Check if the object is a cone.
`is_defined`	Check if the pyramid 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 pyramid.

apply_transformation( self: ostk.mathematics.geometry.d3.object.Pyramid, transformation: ostk::mathematics::geometry::d3::Transformation, ) → None¶

Apply a transformation to the pyramid.

Parameters:: transformation (Transformation) -- The transformation to apply.

Example

>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)])
>>> apex = Point(0.0, 0.0, 1.0)
>>> pyramid = Pyramid(base, apex)
>>> transformation = Transformation.identity()
>>> pyramid.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.

contains(self: ostk.mathematics.geometry.d3.object.Pyramid, point: ostk.mathematics.geometry.d3.object.Point) -> bool
Check if the pyramid contains a point.
Args:
point (Point): The point to check.

Returns:
bool: True if the pyramid contains the point.

Example:
>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)]) >>> apex = Point(0.0, 0.0, 1.0) >>> pyramid = Pyramid(base, apex) >>> pyramid.contains(Point(0.5, 0.5, 0.5))
contains(self: ostk.mathematics.geometry.d3.object.Pyramid, point_set: ostk.mathematics.geometry.d3.object.PointSet) -> bool
Check if the pyramid contains all points in a point set.
Args:
point_set (PointSet): The point set to check.

Returns:
bool: True if the pyramid contains all points.

Example:
>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)]) >>> apex = Point(0.0, 0.0, 1.0) >>> pyramid = Pyramid(base, apex) >>> pyramid.contains(PointSet([Point(0.5, 0.5, 0.5), Point(0.6, 0.6, 0.6)]))
contains(self: ostk.mathematics.geometry.d3.object.Pyramid, segment: ostk.mathematics.geometry.d3.object.Segment) -> bool
Check if the pyramid contains a segment.
Args:
segment (Segment): The segment to check.

Returns:
bool: True if the pyramid contains the segment.

Example:
>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)]) >>> apex = Point(0.0, 0.0, 1.0) >>> pyramid = Pyramid(base, apex) >>> pyramid.contains(Segment(Point(0.5, 0.5, 0.5), Point(0.6, 0.6, 0.6)))
contains(self: ostk.mathematics.geometry.d3.object.Pyramid, ellipsoid: ostk.mathematics.geometry.d3.object.Ellipsoid) -> bool
Check if the pyramid contains an ellipsoid.
Args:
ellipsoid (Ellipsoid): The ellipsoid to check.

Returns:
bool: True if the pyramid contains the ellipsoid.

Example:
>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)]) >>> apex = Point(0.0, 0.0, 1.0) >>> pyramid = Pyramid(base, apex) >>> pyramid.contains(Ellipsoid(Point(0.0, 0.0, 0.0), 1.0, 1.0, 1.0))

get_apex( self: ostk.mathematics.geometry.d3.object.Pyramid, ) → ostk.mathematics.geometry.d3.object.Point¶

Get the apex point of the pyramid.

Returns:: The apex point.
Return type:: Point

Example

>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)])
>>> apex = Point(0.0, 0.0, 1.0)
>>> pyramid = Pyramid(base, apex)
>>> pyramid.get_apex()

get_base( self: ostk.mathematics.geometry.d3.object.Pyramid, ) → ostk.mathematics.geometry.d3.object.Polygon¶

Get the base polygon of the pyramid.

Returns:: The base polygon.
Return type:: Polygon

Example

>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)])
>>> apex = Point(0.0, 0.0, 1.0)
>>> pyramid = Pyramid(base, apex)
>>> pyramid.get_base()

get_lateral_face_at( self: ostk.mathematics.geometry.d3.object.Pyramid, index: int, ) → ostk.mathematics.geometry.d3.object.Polygon¶

Get the lateral face at a given index.

Parameters:: index (int) -- The index of the lateral face.
Returns:: The lateral face polygon.
Return type:: Polygon

Example

>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)])
>>> apex = Point(0.0, 0.0, 1.0)
>>> pyramid = Pyramid(base, apex)
>>> pyramid.get_lateral_face_at(0)

get_lateral_face_count(self: ostk.mathematics.geometry.d3.object.Pyramid) → int¶

Get the number of lateral faces.

Returns:: The number of lateral faces.
Return type:: int

Example

>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)])
>>> apex = Point(0.0, 0.0, 1.0)
>>> pyramid = Pyramid(base, apex)
>>> pyramid.get_lateral_face_count()

get_rays_of_lateral_face_at( self: ostk.mathematics.geometry.d3.object.Pyramid, lateral_face_index: int, ray_count: int = 2, ) → list[ostk.mathematics.geometry.d3.object.Ray]¶

Get rays from the apex through a specific lateral face.

Parameters:

lateral_face_index (int) -- The index of the lateral face.
ray_count (int) -- The number of rays to generate (default: 2).

Returns:

Array of rays.

Return type:

list[Ray]

Example

>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)])
>>> apex = Point(0.0, 0.0, 1.0)
>>> pyramid = Pyramid(base, apex)
>>> pyramid.get_rays_of_lateral_face_at(0)

get_rays_of_lateral_faces( self: ostk.mathematics.geometry.d3.object.Pyramid, ray_count: int = 0, ) → list[ostk.mathematics.geometry.d3.object.Ray]¶

Get rays from the apex through all lateral faces.

Parameters:: ray_count (int, optional) -- The number of rays per face. Defaults to 0.
Returns:: Array of rays.
Return type:: list[Ray]

Example

>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)])
>>> apex = Point(0.0, 0.0, 1.0)
>>> pyramid = Pyramid(base, apex)
>>> pyramid.get_rays_of_lateral_faces(ray_count=1)

intersection_with(*args, **kwargs)¶

Overloaded function.

intersection_with(self: ostk.mathematics.geometry.d3.object.Pyramid, sphere: ostk.mathematics.geometry.d3.object.Sphere, only_in_sight: bool = False, discretization_level: int = 40) -> ostk::mathematics::geometry::d3::Intersection
Compute the intersection of the pyramid with a sphere.
Args:
sphere (Sphere): The sphere to intersect with. only_in_sight (bool): Only compute intersection in sight of the apex. discretization_level (int): The level of discretization for the computation.

Returns:
Intersection: The intersection result.

Example:
>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)]) >>> apex = Point(0.0, 0.0, 1.0) >>> pyramid = Pyramid(base, apex) >>> pyramid.intersection_with(Sphere(Point(0.0, 0.0, 0.0), 1.0))
intersection_with(self: ostk.mathematics.geometry.d3.object.Pyramid, ellipsoid: ostk.mathematics.geometry.d3.object.Ellipsoid, only_in_sight: bool = False, discretization_level: int = 40) -> ostk::mathematics::geometry::d3::Intersection
Compute the intersection of the pyramid with an ellipsoid.
Args:
ellipsoid (Ellipsoid): The ellipsoid to intersect with. only_in_sight (bool): Only compute intersection in sight of the apex. discretization_level (int): The level of discretization for the computation.

Returns:
Intersection: The intersection result.

Example:
>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)]) >>> apex = Point(0.0, 0.0, 1.0) >>> pyramid = Pyramid(base, apex) >>> pyramid.intersection_with(Ellipsoid(Point(0.0, 0.0, 0.0), 1.0, 1.0, 1.0))

intersects( self: ostk.mathematics.geometry.d3.object.Pyramid, ellipsoid: ostk.mathematics.geometry.d3.object.Ellipsoid, discretization_level: int = 40, ) → bool¶

Check if the pyramid intersects an ellipsoid.

Parameters:

ellipsoid (Ellipsoid) -- The ellipsoid to check intersection with.
discretization_level (int) -- The level of discretization for the check.

Returns:

True if the pyramid intersects the ellipsoid.

Return type:

bool

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.Pyramid) → bool¶

Check if the pyramid is defined.

Returns:: True if the pyramid is defined.
Return type:: bool

Example

>>> base = Polygon([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)])
>>> apex = Point(0.0, 0.0, 1.0)
>>> pyramid = Pyramid(base, apex)
>>> pyramid.is_defined()

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.Pyramid¶

Create an undefined pyramid.

Returns:: An undefined pyramid.
Return type:: Pyramid

Example

>>> undefined_pyramid = Pyramid.undefined()
>>> undefined_pyramid.is_defined()  # False