Arc

class compas.geometry.Arc[source]

Bases: Curve

An arc is a segment of a circle, and is defined by a coordinate system, radius, and start and end angles.

The centre of the underlying circle is at the origin of the coordinate system. The start and end angles are measured from the positive X axis towards the positive Y axis.

The parametrisation of the arc is normalised with respect to the arc angle. The value t=0.0 corresponds to the start angle of the arc. The value t=1.0 corresponds to the end angle of the arc. The value t=0.5 corresponds to the angle halfway between start and end.

Transformations of the arc are performed by transforming the local coordinate system.

Parameters:

radiusfloat: Radius of the arc’s circle.
start_anglefloat: The angle in radians of the start of this Arc.
end_anglefloat: The angle in radians of the end of this Arc.
framecompas.geometry.Frame, optional: Local coordinate system of the arc. Defaults to the world XY plane.
namestr, optional: The name of the arc.

See also

compas.geometry.Circle

Examples

Construct a semicircular arc in the XY plane, with radius 1.0, and compute its length.

>>> from math import pi
>>> from compas.geometry import Arc
>>> arc = Arc(radius=1.0, start_angle=0.0, end_angle=pi)
>>> arc.length == 1.0 * pi
True

Construct a quarter arc in the 3rd quadrant of a frame aligned with the world ZX plane at a distance of 1.0 from the world origin along the world Y axis.

>>> from math import pi
>>> from compas.geometry import Frame
>>> from compas.geometry import Arc
>>> frame = Frame([0.0, 1.0, 0.0], [0.0, 0.0, 1.0], [1.0, 0.0, 0.0])
>>> arc = Arc(radius=1.0, start_angle=pi, end_angle=pi * 1.5, frame=frame)
>>> arc.length == 1.0 * pi * 0.5
True

Visualize the arc using the viewer.

>>> from compas_viewer import Viewer   
>>> viewer = Viewer()                     
>>> viewer.scene.add(arc.to_polyline(n=20))  
>>> viewer.scene.add(arc.frame)              
>>> viewer.show()                       

Visualize only part of the arc.

>>> from compas_viewer import Viewer                        
>>> viewer = Viewer()                                          
>>> viewer.scene.add(arc.to_polyline(n=20, domain=(0.25, 0.75)))  
>>> viewer.scene.add(arc.frame)                                   
>>> viewer.show()                                            

Attributes:

framecompas.geometry.Frame: The coordinate frame of the arc.
transformationTransformation, read-only: The transformation from the local coordinate system of the arc (frame) to the world coordinate system.
radiusfloat: The radius of the circle.
start_anglefloat: The start angle of the arc.
end_anglefloat: The end angle of the arc.
circlecompas.geometry.Circle, read-only: The underlying circle.
planecompas.geometry.Plane, read-only: The plane of the arc.
diameterfloat, read-only: The diameter of the underlying circle.
lengthfloat, read-only: Compute the length of the curve.
anglefloat, read-only: The sweep angle in radians between start angle and end angle.
circumferencefloat, read-only: The circumference of the underlying circle.
is_closedbool, read-only: False.
is_periodicbool, read-only: False.

Methods

`from_circle`	Creates an Arc from a circle and start and end angles.
`normal_at`	Construct a normal vector to the arc at a specific parameter.
`point_at`	Returns the point at the specified parameter.
`tangent_at`	Construct a tangent on the circle 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_obj`	Load a curve from an OBJ file.
`from_step`	Load a curve from a STP file.
`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.