Parabola

class compas.geometry.Parabola[source]

Bases: Conic

A parabola is defined by a plane and a major and minor axis. The origin of the coordinate frame is the center of the parabola.

The parabola in this implementation is based on the equation y = a * x**2. Therefore it will have the y axis of the coordinate frame as its axis of symmetry.

Parameters:

focalfloat: The focal length of the parabola.
framecompas.geometry.Frame: The coordinate frame of the parabola.
namestr, optional: The name of the parabola.

Attributes:

framecompas.geometry.Frame: The coordinate frame of the parabola.
transformationTransformation, read-only: The transformation from the local coordinate system of the parabola (frame) to the world coordinate system.
focalfloat: The focal length of the parabola.
planecompas.geometry.Plane, read-only: The plane of the parabola.
latuscompas.geometry.Point, read-only: The latus rectum of the parabola.
eccentricityfloat, read-only: The eccentricity of a parabola is between 0 and 1.
focuscompas.geometry.Point, read-only: The focus point of the parabola.
directixcompas.geometry.Line, read-only: The directix is the line perpendicular to the y axis of the parabola frame at a distance d = + major / eccentricity from the origin of the parabola frame.
is_closedbool, read-only: False.
is_periodicbool, read-only: False.

See also

compas.geometry.Ellipse, compas.geometry.Hyperbola, compas.geometry.Circle

Examples

Construct a parabola in the world XY plane.

>>> from compas.geometry import Frame, Parabola
>>> parabola = Parabola(focal=3, frame=Frame.worldXY())
>>> parabola = Parabola(focal=3)

Construct a parabola such that the Z axis of its frame aligns with a given line.

>>> from compas.geometry import Frame, Line, Plane, Parabola
>>> line = Line([0, 0, 0], [1, 1, 1])
>>> plane = Plane(line.end, line.direction)
>>> frame = Frame.from_plane(plane)
>>> parabola = Parabola(focal=3, frame=frame)

Visualize the parabola with the COMPAS viewer.

>>> from compas_viewer import Viewer  
>>> viewer = Viewer()  
>>> viewer.scene.add(line)  
>>> viewer.scene.add(parabola)  
>>> viewer.scene.add(parabola.frame)  
>>> viewer.show()  

Methods

`normal_at`	Normal at a specific normalized parameter.
`point_at`	Point at the parameter.
`tangent_at`	Tangent vector at the parameter.

Inherited Methods

`ToString`	Converts the instance to a string.
`aabb`	Compute the axis-aligned bounding box of the curve.
`closest_point`	Compute the closest point on the curve to a given point.
`compute_aabb`	Compute the axis-aligned bounding box of the geometry.
`compute_obb`	Compute the oriented bounding box of the geometry.
`copy`	Make an independent copy of the data object.
`curvature_at`	Compute the curvature vector of the curve at a parameter.
`divide_by_count`	Compute the curve parameters that divide the curve into a specific number of equal length segments.
`divide_by_length`	Compute the curve parameters that divide the curve into segments of specified length.
`fair`
`frame_at`	Compute the local frame of the curve at a parameter.
`from_json`	Construct an object of this type from a JSON file.
`from_jsonstring`	Construct an object of this type from a JSON string.
`from_native`	Construct a parametric curve from a native curve geometry.
`from_obj`	Load a curve from an OBJ file.
`from_step`	Load a curve from a STP file.
`length`	Compute the length of the curve.
`offset`
`reverse`	Reverse the parametrisation of the curve.
`reversed`	Reverse a copy of the curve.
`rotate`	Rotate the geometry.
`rotated`	Returns a rotated copy of this geometry.
`scale`	Scale the geometry.
`scaled`	Returns a scaled copy of this geometry.
`sha256`	Compute a hash of the data for comparison during version control using the sha256 algorithm.
`smooth`
`split`
`to_json`	Convert an object to its native data representation and save it to a JSON file.
`to_jsonstring`	Convert an object to its native data representation and save it to a JSON string.
`to_obj`	Write the curve geometry to an OBJ file.
`to_points`	Convert the curve to a list of points.
`to_polygon`	Convert the curve to a polygon.
`to_polyline`	Convert the curve to a polyline.
`to_step`	Write the curve geometry to a STP file.
`transform`	Transform the local coordinate system of the curve.
`transformed`	Returns a transformed copy of this geometry.
`translate`	Translate the geometry.
`translated`	Returns a translated copy of this geometry.
`trim`
`validate_data`	Validate the data against the object's data schema.