class, y, r, options)

Bases: sage.plot.primitive.GraphicPrimitive

Primitive class for the Circle graphics type. See circle? for information about actually plotting circles.


  • x - \(x\)-coordinate of center of Circle
  • y - \(y\)-coordinate of center of Circle
  • r - radius of Circle object
  • options - dict of valid plot options to pass to constructor


Note this should normally be used indirectly via circle:

sage: from import Circle
sage: C = Circle(2,3,5,{'zorder':2})
sage: C
Circle defined by (2.0,3.0) with r=5.0
sage: C.options()['zorder']
sage: C.r


We test creating a circle:

sage: C = circle((2,3), 5)

Returns a dictionary with the bounding box data.


sage: p = circle((3, 3), 1)
sage: d = p.get_minmax_data()
sage: d['xmin']
sage: d['ymin']
plot3d(z=0, **kwds)

Plots a 2D circle (actually a 50-gon) in 3D, with default height zero.


  • z - optional 3D height above \(xy\)-plane.


sage: circle((0,0), 1).plot3d()

This example uses this method implicitly, but does not pass the optional parameter z to this method:

sage: sum([circle((random(),random()), random()).plot3d(z=random()) for _ in range(20)])

These examples are explicit, and pass z to this method:

sage: C = circle((2,pi), 2, hue=.8, alpha=.3, fill=True)
sage: c = C[0]
sage: d = c.plot3d(z=2)
sage: d.texture.opacity
sage: C = circle((2,pi), 2, hue=.8, alpha=.3, linestyle='dotted')
sage: c = C[0]
sage: d = c.plot3d(z=2)
sage: d.jmol_repr(d.testing_render_params())[0][-1]
'color $line_1 translucent 0.7 [204,0,255]', radius, edgecolor='blue', legend_color=None, facecolor='blue', clip=True, linestyle='solid', thickness=1, zorder=5, aspect_ratio=1.0, alpha=1, legend_label=None, fill=False, **options)

Return a circle at a point center = \((x,y)\) (or \((x,y,z)\) and parallel to the \(xy\)-plane) with radius = \(r\). Type circle.options to see all options.


  • alpha - default: 1
  • fill - default: False
  • thickness - default: 1
  • linestyle - default: 'solid' (2D plotting only) The style of the line, which is one of 'dashed', 'dotted', 'solid', 'dashdot', or '--', ':', '-', '-.', respectively.
  • edgecolor - default: ‘blue’ (2D plotting only)
  • facecolor - default: ‘blue’ (2D plotting only, useful only if fill=True)
  • rgbcolor - 2D or 3D plotting. This option overrides edgecolor and facecolor for 2D plotting.
  • legend_label - the label for this item in the legend
  • legend_color - the color for the legend label


The default color is blue, the default linestyle is solid, but this is easy to change:

sage: c = circle((1,1), 1)
sage: c
sage: c = circle((1,1), 1, rgbcolor=(1,0,0), linestyle='-.')
sage: c

We can also use this command to plot three-dimensional circles parallel to the \(xy\)-plane:

sage: c = circle((1,1,3), 1, rgbcolor=(1,0,0))
sage: c
sage: type(c)
<class 'sage.plot.plot3d.base.TransformGroup'>

To correct the aspect ratio of certain graphics, it is necessary to show with a figsize of square dimensions:


Here we make a more complicated plot, with many circles of different colors:

sage: g = Graphics()
sage: step=6; ocur=1/5; paths=16;
sage: PI = math.pi    # numerical for speed -- fine for graphics
sage: for r in range(1,paths+1):
...       for x,y in [((r+ocur)*math.cos(n), (r+ocur)*math.sin(n)) for n in srange(0, 2*PI+PI/step, PI/step)]:
...           g += circle((x,y), ocur, rgbcolor=hue(r/paths))
...       rnext = (r+1)^2
...       ocur = (rnext-r)-ocur
sage:^2, xmax=(paths+1)^2, ymin=-(paths+1)^2, ymax=(paths+1)^2, figsize=[6,6])

Note that the rgbcolor option overrides the other coloring options. This produces red fill in a blue circle:

sage: circle((2,3), 1, fill=True, edgecolor='blue')

This produces an all-green filled circle:

sage: circle((2,3), 1, fill=True, edgecolor='blue', rgbcolor='green')

The option hue overrides all other options, so be careful with its use. This produces a purplish filled circle:

sage: circle((2,3), 1, fill=True, edgecolor='blue', rgbcolor='green', hue=.8)

And circles with legends:

sage: circle((4,5), 1, rgbcolor='yellow', fill=True, legend_label='the sun').show(xmin=0, ymin=0)
sage: circle((4,5), 1, legend_label='the sun', legend_color='yellow').show(xmin=0, ymin=0)

Extra options will get passed on to show(), as long as they are valid:

sage: circle((0, 0), 2, figsize=[10,10]) # That circle is huge!
sage: circle((0, 0), 2).show(figsize=[10,10]) # These are equivalent


We cannot currently plot circles in more than three dimensions:

sage: circle((1,1,1,1), 1, rgbcolor=(1,0,0))
Traceback (most recent call last):
ValueError: The center of a plotted circle should have two or three coordinates.

The default aspect ratio for a circle is 1.0:

sage: P = circle((1,1), 1)
sage: P.aspect_ratio()

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