Ellipse

class compas.geometry.Ellipse[source]

Bases: Conic

An ellipse is a curve defined by a coordinate system and a major and minor axis.

The centre of the ellipse is at the origin of the coordinate system. The major axis is parallel to the local x-axis. The minor axis is parallel to the local y-axis. The parameter domain of an ellipse is [0, 2*pi]. Moving along the ellipse in the parameter direction corresponds to moving counter-clockwise around the origin of the local coordinate system.

Parameters:

majorfloat: The major of the ellipse.
minorfloat: The minor of the ellipse.
framecompas.geometry.Frame, optional: The local coordinate system of the ellipse. The default value is None, in which case the ellipse is constructed in the XY plane of the world coordinate system.
namestr, optional: The name of the ellipse.

Attributes:

framecompas.geometry.Frame: The coordinate frame of the ellipse.
transformationTransformation, read-only: The transformation from the local coordinate system of the ellipse (frame) to the world coordinate system.
majorfloat: The major of the ellipse.
minorfloat: The minor of the ellipse.
planecompas.geometry.Plane, read-only: The plane of the ellipse.
areafloat, read-only: The area of the ellipse.
circumferencefloat, read-only: The length of the circumference of the ellipse.
semifocalfloat, read-only: The semi-focal distance of the ellipse. This is the distance from the center of the ellipse to the focus points.
focalfloat, read-only: The distance between the two focus points.
eccentricityfloat, read-only: The eccentricity of the ellipse. This is the ratio between the semifocal length to the length of the semi-major axis.
focus1compas.geometry.Point, read-only: The first focus point of the ellipse.
focus2compas.geometry.Point, read-only: The second focus point of the ellipse.
directix1compas.geometry.Line, read-only: The first directix of the ellipse. The directix is perpendicular to the major axis and passes through a point at a distance major **2 / semifocal along the positive xaxis from the center of the ellipse.
directix2compas.geometry.Line, read-only: The second directix of the ellipse. The directix is perpendicular to the major axis and passes through a point at a distance major **2 / semifocal along the negative xaxis from the center of the ellipse.
is_closedbool, read-only: True.
is_periodicbool, read-only: True.
is_circlebool, read-only: True if the ellipse is a circle.

See also

compas.geometry.Circle, compas.geometry.Hyperbola, compas.geometry.Parabola

Examples

Construct an ellipse in the world XY plane.

>>> from compas.geometry import Frame, Ellipse
>>> ellipse = Ellipse(major=3, minor=2, frame=Frame.worldXY())
>>> ellipse = Ellipse(major=3, minor=2)

Construct an ellipse such that its normal aligns with a given line.

>>> from compas.geometry import Line, Frame, Plane, Ellipse
>>> line = Line([0, 0, 0], [1, 1, 1])
>>> plane = Plane(line.end, line.direction)
>>> ellipse = Ellipse.from_plane_major_minor(plane, 3, 2)
>>> ellipse = Ellipse(major=3, minor=2, frame=Frame.from_plane(plane))

Visualise the line, ellipse, and frame of the ellipse with the COMPAS viewer.

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

Methods

`from_plane_major_minor`	Construct a ellipse from a point and major and minor axis lengths.
`from_point_major_minor`	Construct a ellipse from a point and major and minor axis lengths.
`normal_at`	Compute the normal at a specific parameter.
`point_at`	Compute the point at a specific parameter.
`tangent_at`	Compute the tangent at a specific 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.