ostk.mathematics.geometry.d3.object.Point¶

class Point( self: ostk.mathematics.geometry.d3.object.Point, first_coordinate: ostk.core.type.Real, second_coordinate: ostk.core.type.Real, third_coordinate: ostk.core.type.Real, )¶

Bases: Object

Create a 3D point with specified coordinates.

Parameters:

first_coordinate (float) -- The x-coordinate.
second_coordinate (float) -- The y-coordinate.
third_coordinate (float) -- The z-coordinate.

Example

>>> point = Point(1.0, 2.0, 3.0)
>>> point.x()  # 1.0
>>> point.y()  # 2.0
>>> point.z()  # 3.0

Methods

`apply_transformation`	Apply a transformation to the point.
`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.
`as_vector`	Convert the point to a 3D vector.
`contains`	Check if this object contains another object.
`distance_to`	Calculate the distance to another point.
`intersects`	Check if this object intersects another object.
`is_cone`	Check if the object is a cone.
`is_defined`	Check if the point 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_near`	Check if this point is near another point within tolerance.
`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.
`origin`	Create a point at the origin (0, 0, 0).
`to_string`	Convert the point to a string representation.
`undefined`	Create an undefined point.
`vector`	Create a point from a 3D vector.
`x`	Get the x-coordinate of the point.
`y`	Get the y-coordinate of the point.
`z`	Get the z-coordinate of the point.

__add__( self: ostk.mathematics.geometry.d3.object.Point, arg0: numpy.ndarray[numpy.float64[3, 1]], ) → ostk.mathematics.geometry.d3.object.Point¶

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

Apply a transformation to the point.

Parameters:: transformation (Transformation) -- The transformation to apply.
Returns:: The transformed point.
Return type:: Point

Example

>>> point = Point(1.0, 2.0, 3.0)
>>> transformation = Transformation.identity()
>>> transformed = point.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

as_vector( self: ostk.mathematics.geometry.d3.object.Point, ) → numpy.ndarray[numpy.float64[3, 1]]¶

Convert the point to a 3D vector.

Returns:: The point as a 3D vector.
Return type:: Vector3d

Example

>>> point = Point(1.0, 2.0, 3.0)
>>> vector = point.as_vector()  # numpy.array([1.0, 2.0, 3.0])

contains( self: ostk.mathematics.geometry.d3.Object, arg0: ostk.mathematics.geometry.d3.Object, ) → bool¶

Check if this object contains another object.

Parameters:: object (Object) -- The object to check containment of.
Returns:: True if this object contains the other object.
Return type:: bool

Example

>>> object = Cone(Point(1.0, 2.0, 3.0), [0.0, 0.0, 1.0], Angle.degrees(30.0))
>>> other_object = Point(1.0, 2.0, 3.1)
>>> object.contains(other_object)  # True

distance_to( self: ostk.mathematics.geometry.d3.object.Point, point: ostk.mathematics.geometry.d3.object.Point, ) → ostk.core.type.Real¶

Calculate the distance to another point.

Parameters:: point (Point) -- The other point.
Returns:: The distance between the points.
Return type:: float

Example

>>> point1 = Point(0.0, 0.0, 0.0)
>>> point2 = Point(3.0, 4.0, 0.0)
>>> point1.distance_to(point2)  # 5.0

intersects( self: ostk.mathematics.geometry.d3.Object, arg0: ostk.mathematics.geometry.d3.Object, ) → bool¶

Check if this object intersects another object.

Parameters:: object (Object) -- The object to check intersection with.
Returns:: True if the objects intersect.
Return type:: bool

Example

>>> object = Cone(Point(1.0, 2.0, 3.0), [0.0, 0.0, 1.0], Angle.degrees(30.0))
>>> other_object = Point(1.0, 2.0, 3.1)
>>> object.intersects(other_object)  # 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.Point) → bool¶

Check if the point is defined.

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

Example

>>> point = Point(1.0, 2.0, 3.0)
>>> point.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_near( self: ostk.mathematics.geometry.d3.object.Point, point: ostk.mathematics.geometry.d3.object.Point, tolerance: ostk.core.type.Real, ) → bool¶

Check if this point is near another point within tolerance.

Parameters:

point (Point) -- The point to compare with.
tolerance (float) -- The tolerance for comparison.

Returns:

True if points are within tolerance, False otherwise.

Return type:

bool

Example

>>> point1 = Point(1.0, 2.0, 3.0)
>>> point2 = Point(1.1, 2.1, 3.1)
>>> point1.is_near(point2, 0.2)  # True

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 origin() → ostk.mathematics.geometry.d3.object.Point¶

Create a point at the origin (0, 0, 0).

Returns:: A point at coordinates (0, 0, 0).
Return type:: Point

Example

>>> origin = Point.origin()
>>> origin.x()  # 0.0
>>> origin.y()  # 0.0
>>> origin.z()  # 0.0

to_string( self: ostk.mathematics.geometry.d3.object.Point, precision: ostk.core.type.Integer = Undefined, ) → ostk.core.type.String¶

Convert the point to a string representation.

Parameters:: precision (int, optional) -- Number of decimal places. Defaults to DEFAULT_PRECISION.
Returns:: String representation of the point.
Return type:: str

Example

>>> point = Point(1.123456, 2.345678, 3.567890)
>>> point.to_string(3)  # "[1.123, 2.346, 3.568]"

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

Create an undefined point.

Returns:: An undefined point.
Return type:: Point

Example

>>> undefined_point = Point.undefined()
>>> undefined_point.is_defined()  # False

static vector( vector: numpy.ndarray[numpy.float64[3, 1]], ) → ostk.mathematics.geometry.d3.object.Point¶

Create a point from a 3D vector.

Parameters:: vector (numpy.array) -- The vector to convert to a point.
Returns:: A point with coordinates from the vector.
Return type:: Point

Example

>>> vector = numpy.array([1.0, 2.0, 3.0])
>>> point = Point.vector(vector)  # Point(1.0, 2.0, 3.0)

x(self: ostk.mathematics.geometry.d3.object.Point) → ostk.core.type.Real¶

Get the x-coordinate of the point.

Returns:: The x-coordinate.
Return type:: float

Example

>>> point = Point(1.0, 2.0, 3.0)
>>> point.x()  # 1.0

y(self: ostk.mathematics.geometry.d3.object.Point) → ostk.core.type.Real¶

Get the y-coordinate of the point.

Returns:: The y-coordinate.
Return type:: float

Example

>>> point = Point(1.0, 2.0, 3.0)
>>> point.y()  # 2.0

z(self: ostk.mathematics.geometry.d3.object.Point) → ostk.core.type.Real¶

Get the z-coordinate of the point.

Returns:: The z-coordinate.
Return type:: float

Example

>>> point = Point(1.0, 2.0, 3.0)
>>> point.z()  # 3.0