ostk.mathematics.geometry.d3.object.Sphere¶

class Sphere( self: ostk.mathematics.geometry.d3.object.Sphere, center: ostk.mathematics.geometry.d3.object.Point, radius: ostk.core.type.Real, )¶

Bases: Object

Create a 3D sphere with center and radius.

Parameters:

center (Point) -- The center point of the sphere.
radius (float) -- The radius of the sphere.

Example

>>> center = Point(0.0, 0.0, 0.0)
>>> sphere = Sphere(center, 1.0)

Methods

`apply_transformation`	Apply a transformation to the sphere in place.
`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_center`	Get the center point of the sphere.
`get_radius`	Get the radius of the sphere.
`intersection_with`	Overloaded function.
`intersects`	Overloaded function.
`is_cone`	Check if the object is a cone.
`is_defined`	Check if the sphere 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.
`is_unitary`	Check if the sphere is a unit sphere (radius = 1).
`undefined`	Create an undefined sphere.
`unit`	Create a unit sphere (radius = 1) at a given center.

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

Apply a transformation to the sphere in place.

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

Example

>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0)
>>> transformation = Translation([1.0, 0.0, 0.0])
>>> sphere.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.Sphere, point: ostk.mathematics.geometry.d3.object.Point) -> bool
Check if the sphere contains a point.
Args:
point (Point): The point to check.

Returns:
bool: True if the sphere contains the point, False otherwise.

Example:
>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0) >>> sphere.contains(Point(0.5, 0.5, 0.5)) # True
contains(self: ostk.mathematics.geometry.d3.object.Sphere, point_set: ostk.mathematics.geometry.d3.object.PointSet) -> bool
Check if the sphere contains a point set.
Args:
point_set (PointSet): The point set to check.

Returns:
bool: True if the sphere contains the point set, False otherwise.

Example:
>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0) >>> sphere.contains(PointSet([Point(0.5, 0.5, 0.5), Point(1.0, 1.0, 1.0)])) # True

get_center( self: ostk.mathematics.geometry.d3.object.Sphere, ) → ostk.mathematics.geometry.d3.object.Point¶

Get the center point of the sphere.

Returns:: The center point of the sphere.
Return type:: Point

Example

>>> sphere = Sphere(Point(1.0, 2.0, 3.0), 1.0)
>>> center = sphere.get_center()  # Point(1.0, 2.0, 3.0)

get_radius( self: ostk.mathematics.geometry.d3.object.Sphere, ) → ostk.core.type.Real¶

Get the radius of the sphere.

Returns:: The radius of the sphere.
Return type:: float

Example

>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 2.5)
>>> radius = sphere.get_radius()  # 2.5

intersection_with(*args, **kwargs)¶

Overloaded function.

intersection_with(self: ostk.mathematics.geometry.d3.object.Sphere, line: ostk.mathematics.geometry.d3.object.Line) -> ostk::mathematics::geometry::d3::Intersection
Check if the sphere intersects a line.
Args:
line (Line): The line to check intersection with.

Returns:
bool: True if the sphere intersects the line.

Example:
>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0) >>> sphere.intersection_with(Line(Point(1.0, 0.0, 0.0), Point(0.0, 1.0, 0.0))) # True
intersection_with(self: ostk.mathematics.geometry.d3.object.Sphere, ray: ostk.mathematics.geometry.d3.object.Ray, only_in_sight: bool = False) -> ostk::mathematics::geometry::d3::Intersection
Check if the sphere intersects a ray.
Args:
ray (Ray): The ray to check intersection with. only_in_sight (bool, optional): If true, only return intersection points that are in sight. Defaults to False.

Returns:
bool: True if the sphere intersects the ray.

Example:
>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0) >>> sphere.intersection_with(Ray(Point(1.0, 0.0, 0.0), Point(0.0, 1.0, 0.0))) # True

intersects(*args, **kwargs)¶

Overloaded function.

intersects(self: ostk.mathematics.geometry.d3.object.Sphere, point: ostk.mathematics.geometry.d3.object.Point) -> bool
Check if the sphere intersects a point.
Args:
point (Point): The point to check intersection with.

Returns:
bool: True if the sphere intersects the point.

Example:
>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0) >>> sphere.intersects(Point(1.0, 0.0, 0.0)) # True
intersects(self: ostk.mathematics.geometry.d3.object.Sphere, point_set: ostk.mathematics.geometry.d3.object.PointSet) -> bool
Check if the sphere intersects a point set.
Args:
point_set (PointSet): The point set to check intersection with.

Returns:
bool: True if the sphere intersects the point set.

Example:
>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0) >>> sphere.intersects(PointSet([Point(1.0, 0.0, 0.0), Point(0.0, 1.0, 0.0)])) # True
intersects(self: ostk.mathematics.geometry.d3.object.Sphere, line: ostk.mathematics.geometry.d3.object.Line) -> bool
Check if the sphere intersects a line.
Args:
line (Line): The line to check intersection with.

Returns:
bool: True if the sphere intersects the line.

Example:
>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0) >>> sphere.intersects(Line(Point(1.0, 0.0, 0.0), Point(0.0, 1.0, 0.0))) # True
intersects(self: ostk.mathematics.geometry.d3.object.Sphere, ray: ostk.mathematics.geometry.d3.object.Ray) -> bool
Check if the sphere intersects a ray.
Args:
ray (Ray): The ray to check intersection with.

Returns:
bool: True if the sphere intersects the ray.

Example:
>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0) >>> sphere.intersects(Ray(Point(1.0, 0.0, 0.0), Point(0.0, 1.0, 0.0))) # True
intersects(self: ostk.mathematics.geometry.d3.object.Sphere, segment: ostk.mathematics.geometry.d3.object.Segment) -> bool
Check if the sphere intersects a segment.
Args:
segment (Segment): The segment to check intersection with.

Returns:
bool: True if the sphere intersects the segment.

Example:
>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0) >>> sphere.intersects(Segment(Point(1.0, 0.0, 0.0), Point(0.0, 1.0, 0.0))) # True
intersects(self: ostk.mathematics.geometry.d3.object.Sphere, plane: ostk.mathematics.geometry.d3.object.Plane) -> bool
Check if the sphere intersects a plane.
Args:
plane (Plane): The plane to check intersection with.

Returns:
bool: True if the sphere intersects the plane.

Example:
>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0) >>> sphere.intersects(Plane(Point(1.0, 0.0, 0.0), Vector3d(0.0, 0.0, 1.0))) # 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.Sphere) → bool¶

Check if the sphere is defined.

Returns:: True if the sphere is defined, False otherwise.
Return type:: bool

Example

>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0)
>>> sphere.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

is_unitary(self: ostk.mathematics.geometry.d3.object.Sphere) → bool¶

Check if the sphere is a unit sphere (radius = 1).

Returns:: True if the sphere has unit radius, False otherwise.
Return type:: bool

Example

>>> sphere = Sphere(Point(0.0, 0.0, 0.0), 1.0)
>>> sphere.is_unitary()  # True

static undefined() → ostk.mathematics.geometry.d3.object.Sphere¶

Create an undefined sphere.

Returns:: An undefined sphere.
Return type:: Sphere

Example

>>> undefined_sphere = Sphere.undefined()
>>> undefined_sphere.is_defined()  # False

static unit( center: ostk.mathematics.geometry.d3.object.Point, ) → ostk.mathematics.geometry.d3.object.Sphere¶

Create a unit sphere (radius = 1) at a given center.

Parameters:: center (Point) -- The center point of the unit sphere.
Returns:: A unit sphere centered at the given point.
Return type:: Sphere

Example

>>> center = Point(1.0, 2.0, 3.0)
>>> unit_sphere = Sphere.unit(center)
>>> unit_sphere.get_radius()  # 1.0