ostk.mathematics.geometry.d3.object.Polygon¶

class Polygon( self: ostk.mathematics.geometry.d3.object.Polygon, polygon: ostk.mathematics.geometry.d2.object.Polygon, origin: ostk.mathematics.geometry.d3.object.Point, x_axis: numpy.ndarray[numpy.float64[3, 1]], y_axis: numpy.ndarray[numpy.float64[3, 1]], )¶

Bases: Object

A polygon in 3D space.

A Polygon is a planar figure defined by a 2D polygon and its position and orientation in 3D space.

Construct a 3D polygon from a 2D polygon and coordinate frame.

Parameters:

polygon (Polygon2d) -- The 2D polygon.
origin (Point) -- The origin of the polygon in 3D space.
x_axis (numpy.ndarray) -- The x-axis direction of the polygon's local frame.
y_axis (numpy.ndarray) -- The y-axis direction of the polygon's local frame.

Example

>>> polygon2d = Polygon2d([Point2d(0.0, 0.0), Point2d(1.0, 0.0), Point2d(1.0, 1.0), Point2d(0.0, 1.0)])
>>> origin = Point(0.0, 0.0, 0.0)
>>> x_axis = numpy.array([1.0, 0.0, 0.0])
>>> y_axis = numpy.array([0.0, 1.0, 0.0])
>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)

Methods

`apply_transformation`	Apply a transformation to the polygon 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`	Check if this object contains another object.
`get_edge_at`	Get the edge at a given index.
`get_edge_count`	Get the number of edges in the polygon.
`get_normal_vector`	Get the normal vector of the polygon's plane.
`get_origin`	Get the origin point of the polygon.
`get_polygon2d`	Get the 2D polygon representation.
`get_vertex_at`	Get the vertex at a given index.
`get_vertex_count`	Get the number of vertices in the polygon.
`get_vertices`	Get all vertices of the polygon.
`get_x_axis`	Get the x-axis direction of the polygon's local frame.
`get_y_axis`	Get the y-axis direction of the polygon's local frame.
`intersects`	Check if this object intersects another object.
`is_cone`	Check if the object is a cone.
`is_defined`	Check if the polygon 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 another polygon is near this one within a 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.
`undefined`	Create an undefined polygon.

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

Apply a transformation to the polygon in place.

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

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> transformation = Transformation.identity()
>>> polygon.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( 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

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

Get the edge at a given index.

Parameters:: index (int) -- The index of the edge.
Returns:: The edge segment.
Return type:: Segment

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.get_edge_at(0)

get_edge_count(self: ostk.mathematics.geometry.d3.object.Polygon) → int¶

Get the number of edges in the polygon.

Returns:: The number of edges.
Return type:: int

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.get_edge_count()

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

Get the normal vector of the polygon's plane.

Returns:: The normal vector.
Return type:: numpy.ndarray

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.get_normal_vector()

get_origin( self: ostk.mathematics.geometry.d3.object.Polygon, ) → ostk.mathematics.geometry.d3.object.Point¶

Get the origin point of the polygon.

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

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.get_origin()

get_polygon2d( self: ostk.mathematics.geometry.d3.object.Polygon, ) → ostk.mathematics.geometry.d2.object.Polygon¶

Get the 2D polygon representation.

Returns:: The 2D polygon.
Return type:: Polygon2d

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.get_polygon2d()

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

Get the vertex at a given index.

Parameters:: index (int) -- The index of the vertex.
Returns:: The vertex point.
Return type:: Point

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.get_vertex_at(0)

get_vertex_count(self: ostk.mathematics.geometry.d3.object.Polygon) → int¶

Get the number of vertices in the polygon.

Returns:: The number of vertices.
Return type:: int

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.get_vertex_count()

get_vertices( self: ostk.mathematics.geometry.d3.object.Polygon, ) → list[ostk.mathematics.geometry.d3.object.Point]¶

Get all vertices of the polygon.

Returns:: Array of vertex points.
Return type:: list[Point]

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.get_vertices()

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

Get the x-axis direction of the polygon's local frame.

Returns:: The x-axis vector.
Return type:: numpy.ndarray

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.get_x_axis()

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

Get the y-axis direction of the polygon's local frame.

Returns:: The y-axis vector.
Return type:: numpy.ndarray

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.get_y_axis()

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.Polygon) → bool¶

Check if the polygon is defined.

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

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.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_near( self: ostk.mathematics.geometry.d3.object.Polygon, polygon: ostk.mathematics.geometry.d3.object.Polygon, tolerance: ostk.core.type.Real, ) → bool¶

Check if another polygon is near this one within a tolerance.

Parameters:

polygon (Polygon) -- The polygon to compare against.
tolerance (float) -- The maximum distance for polygons to be considered near.

Returns:

True if the polygons are near each other.

Return type:

bool

Example

>>> polygon = Polygon(polygon2d, origin, x_axis, y_axis)
>>> polygon.is_near(polygon, 0.0)

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.Polygon¶

Create an undefined polygon.

Returns:: An undefined polygon.
Return type:: Polygon

Example

>>> undefined_polygon = Polygon.undefined()
>>> undefined_polygon.is_defined()  # False