Hyperbola

class compas.geometry.Hyperbola[source]

Bases: Conic

A hyperbola is defined by a coordinate frame and a major and minor axis.

It is implemented using the equation

\[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\]

and with parametric form

\[\begin{split}x(t) &= a \times \sec(t) \\ y(t) &= b \times \tan(t)\end{split}\]

This means that the center of the hyperbola is at the center of the coordinate frame, the vertices of the left and right branches are at (0, -a) and (0, +a) respectively, the linear eccentricity is math::sqrt{a^2 + b^2}, and the eccentricity math::fraq{sqrt{a^2 + b^2}}{a}.

Parameters:

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

Attributes:

framecompas.geometry.Frame: The coordinate frame of the hyperbola.
transformationTransformation, read-only: The transformation from the local coordinate system of the hyperbola (frame) to the world coordinate system.
majorfloat: The major radius of the hyperbola.
minorfloat: The minor radius of the hyperbola.
planecompas.geometry.Plane, read-only: The plane of the hyperbola.
semifocalfloat, read-only: The distance between the center and the focus points.
focalfloat, read-only: The distance between the two focus points.
eccentricityfloat, read-only: This is the ratio between the semifocal length to the length of the semi-major axis. The eccentricity of a hyperbola is a number higher than 1.
vertex1compas.geometry.Point, read-only: The first vertex of the hyperbola is on the positive x axis.
vertex2compas.geometry.Point, read-only: The second vertex of the hyperbola is on the negative x axis.
focus1compas.geometry.Point, read-only: The first focus of the hyperbola is on the positive x axis.
focus2compas.geometry.Point, read-only: The second focus of the hyperbola is on the negative x axis.
asymptote1compas.geometry.Line, read-only: The first asymptote of the hyperbola.
asymptote2compas.geometry.Line, read-only: The second asymptote of the hyperbola.
is_closedbool, read-only: False.
is_periodicbool, read-only: False.

See also

compas.geometry.Circle, compas.geometry.Ellipse, compas.geometry.Parabola

Examples

Construct a hyperbola in the world XY plane.

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

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

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

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

>>> from compas_viewer import Viewer          
>>> viewer = Viewer()                         
>>> viewer.scene.add(line)                    
>>> viewer.scene.add(hyperbola)               
>>> viewer.scene.add(hyperbola.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.