Arcs of circles and ellipses

class sage.plot.arc.Arc(x, y, r1, r2, angle, s1, s2, options)[source]

Bases: GraphicPrimitive

Primitive class for the Arc graphics type. See arc? for information about actually plotting an arc of a circle or an ellipse.

INPUT:

  • x, y – coordinates of the center of the arc

  • r1, r2 – lengths of the two radii

  • angle – angle of the horizontal with width

  • sector – sector of angle

  • options – dictionary of valid plot options to pass to constructor

EXAMPLES:

Note that the construction should be done using arc:

sage: from math import pi
sage: from sage.plot.arc import Arc
sage: print(Arc(0,0,1,1,pi/4,pi/4,pi/2,{}))
Arc with center (0.0,0.0) radii (1.0,1.0) angle 0.78539816339... inside the sector (0.78539816339...,1.5707963267...)

>>> from sage.all import *
>>> from math import pi
>>> from sage.plot.arc import Arc
>>> print(Arc(Integer(0),Integer(0),Integer(1),Integer(1),pi/Integer(4),pi/Integer(4),pi/Integer(2),{}))
Arc with center (0.0,0.0) radii (1.0,1.0) angle 0.78539816339... inside the sector (0.78539816339...,1.5707963267...)

from math import pi
from sage.plot.arc import Arc
print(Arc(0,0,1,1,pi/4,pi/4,pi/2,{}))
bezier_path()[source]

Return self as a Bezier path.

This is needed to concatenate arcs, in order to create hyperbolic polygons.

EXAMPLES:

sage: from sage.plot.arc import Arc
sage: op = {'alpha':1,'thickness':1,'rgbcolor':'blue','zorder':0,
....:     'linestyle':'--'}
sage: Arc(2,3,2.2,2.2,0,2,3,op).bezier_path()
Graphics object consisting of 1 graphics primitive

sage: from math import pi
sage: a = arc((0,0),2,1,0,(pi/5,pi/2+pi/12), linestyle='--', color='red')
sage: b = a[0].bezier_path()
sage: b[0]
Bezier path from (1.133..., 0.8237...) to (-0.2655..., 0.9911...)

>>> from sage.all import *
>>> from sage.plot.arc import Arc
>>> op = {'alpha':Integer(1),'thickness':Integer(1),'rgbcolor':'blue','zorder':Integer(0),
...     'linestyle':'--'}
>>> Arc(Integer(2),Integer(3),RealNumber('2.2'),RealNumber('2.2'),Integer(0),Integer(2),Integer(3),op).bezier_path()
Graphics object consisting of 1 graphics primitive

>>> from math import pi
>>> a = arc((Integer(0),Integer(0)),Integer(2),Integer(1),Integer(0),(pi/Integer(5),pi/Integer(2)+pi/Integer(12)), linestyle='--', color='red')
>>> b = a[Integer(0)].bezier_path()
>>> b[Integer(0)]
Bezier path from (1.133..., 0.8237...) to (-0.2655..., 0.9911...)

from sage.plot.arc import Arc
op = {'alpha':1,'thickness':1,'rgbcolor':'blue','zorder':0,
    'linestyle':'--'}
Arc(2,3,2.2,2.2,0,2,3,op).bezier_path()
from math import pi
a = arc((0,0),2,1,0,(pi/5,pi/2+pi/12), linestyle='--', color='red')
b = a[0].bezier_path()
b[0]
get_minmax_data()[source]

Return a dictionary with the bounding box data.

The bounding box is computed as minimal as possible.

EXAMPLES:

An example without angle:

sage: p = arc((-2, 3), 1, 2)
sage: d = p.get_minmax_data()
sage: d['xmin']
-3.0
sage: d['xmax']
-1.0
sage: d['ymin']
1.0
sage: d['ymax']
5.0

>>> from sage.all import *
>>> p = arc((-Integer(2), Integer(3)), Integer(1), Integer(2))
>>> d = p.get_minmax_data()
>>> d['xmin']
-3.0
>>> d['xmax']
-1.0
>>> d['ymin']
1.0
>>> d['ymax']
5.0

p = arc((-2, 3), 1, 2)
d = p.get_minmax_data()
d['xmin']
d['xmax']
d['ymin']
d['ymax']

The same example with a rotation of angle \(\pi/2\):

sage: from math import pi
sage: p = arc((-2, 3), 1, 2, pi/2)
sage: d = p.get_minmax_data()
sage: d['xmin']
-4.0
sage: d['xmax']
0.0
sage: d['ymin']
2.0
sage: d['ymax']
4.0

>>> from sage.all import *
>>> from math import pi
>>> p = arc((-Integer(2), Integer(3)), Integer(1), Integer(2), pi/Integer(2))
>>> d = p.get_minmax_data()
>>> d['xmin']
-4.0
>>> d['xmax']
0.0
>>> d['ymin']
2.0
>>> d['ymax']
4.0

from math import pi
p = arc((-2, 3), 1, 2, pi/2)
d = p.get_minmax_data()
d['xmin']
d['xmax']
d['ymin']
d['ymax']
plot3d()[source]
sage.plot.arc.arc(center, r1, r2=None, angle=0.0, sector=(0.0, 6.283185307179586), alpha=1, thickness=1, linestyle='solid', zorder=5, rgbcolor='blue', aspect_ratio=1.0, **options)[source]

An arc (that is a portion of a circle or an ellipse).

Type arc.options to see all options.

INPUT:

  • center – 2-tuple of real numbers; position of the center

  • r1, r2 – positive real numbers; radii of the ellipse. If only r1 is set, then the two radii are supposed to be equal and this function returns an arc of circle.

  • angle – real number; angle between the horizontal and the axis that corresponds to r1

  • sector – 2-tuple (default: (0,2*pi)); angles sector in which the arc will be drawn

OPTIONS:

  • alpha – float (default: 1) – transparency

  • thickness – float (default: 1) – thickness of the arc

  • color, rgbcolor – string or 2-tuple (default: 'blue'); the color of the arc

  • linestyle – string (default: 'solid'); the style of the line, which is one of 'dashed', 'dotted', 'solid', 'dashdot', or '--', ':', '-', '-.', respectively

EXAMPLES:

Plot an arc of circle centered at (0,0) with radius 1 in the sector \((\pi/4,3*\pi/4)\):

sage: from math import pi
sage: arc((0,0), 1, sector=(pi/4,3*pi/4))
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> from math import pi
>>> arc((Integer(0),Integer(0)), Integer(1), sector=(pi/Integer(4),Integer(3)*pi/Integer(4)))
Graphics object consisting of 1 graphics primitive

from math import pi
arc((0,0), 1, sector=(pi/4,3*pi/4))
../../_images/arc-1.svg

Plot an arc of an ellipse between the angles 0 and \(\pi/2\):

sage: arc((2,3), 2, 1, sector=(0,pi/2))
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> arc((Integer(2),Integer(3)), Integer(2), Integer(1), sector=(Integer(0),pi/Integer(2)))
Graphics object consisting of 1 graphics primitive

arc((2,3), 2, 1, sector=(0,pi/2))
../../_images/arc-2.svg

Plot an arc of a rotated ellipse between the angles 0 and \(\pi/2\):

sage: arc((2,3), 2, 1, angle=pi/5, sector=(0,pi/2))
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> arc((Integer(2),Integer(3)), Integer(2), Integer(1), angle=pi/Integer(5), sector=(Integer(0),pi/Integer(2)))
Graphics object consisting of 1 graphics primitive

arc((2,3), 2, 1, angle=pi/5, sector=(0,pi/2))
../../_images/arc-3.svg

Plot an arc of an ellipse in red with a dashed linestyle:

sage: arc((0,0), 2, 1, 0, (0,pi/2), linestyle='dashed', color='red')
Graphics object consisting of 1 graphics primitive
sage: arc((0,0), 2, 1, 0, (0,pi/2), linestyle='--', color='red')
Graphics object consisting of 1 graphics primitive

>>> from sage.all import *
>>> arc((Integer(0),Integer(0)), Integer(2), Integer(1), Integer(0), (Integer(0),pi/Integer(2)), linestyle='dashed', color='red')
Graphics object consisting of 1 graphics primitive
>>> arc((Integer(0),Integer(0)), Integer(2), Integer(1), Integer(0), (Integer(0),pi/Integer(2)), linestyle='--', color='red')
Graphics object consisting of 1 graphics primitive

arc((0,0), 2, 1, 0, (0,pi/2), linestyle='dashed', color='red')
arc((0,0), 2, 1, 0, (0,pi/2), linestyle='--', color='red')
../../_images/arc-4.svg

The default aspect ratio for arcs is 1.0:

sage: arc((0,0), 1, sector=(pi/4,3*pi/4)).aspect_ratio()
1.0

>>> from sage.all import *
>>> arc((Integer(0),Integer(0)), Integer(1), sector=(pi/Integer(4),Integer(3)*pi/Integer(4))).aspect_ratio()
1.0

arc((0,0), 1, sector=(pi/4,3*pi/4)).aspect_ratio()

It is not possible to draw arcs in 3D:

sage: A = arc((0,0,0), 1)
Traceback (most recent call last):
...
NotImplementedError

>>> from sage.all import *
>>> A = arc((Integer(0),Integer(0),Integer(0)), Integer(1))
Traceback (most recent call last):
...
NotImplementedError

A = arc((0,0,0), 1)