Points

TESTS:

sage: E = EllipticCurve('37a')
sage: P = E(0,0)
sage: def get_points(n): return sum([point(list(i*P)[:2], pointsize=3) for i in range(-n,n) if i != 0 and (i*P)[0] < 3])
sage: sum([get_points(15*n).plot3d(z=n) for n in range(1,10)])
class sage.plot.point.Point(xdata, ydata, options)

Primitive class for the point graphics type. See point?, point2d? or point3d? for information about actually plotting points.

INPUT:

  • xdata - list of x values for points in Point object
  • ydata - list of y values for points in Point object
  • options - dict of valid plot options to pass to constructor

EXAMPLES:

Note this should normally be used indirectly via point and friends:

sage: from sage.plot.point import Point
sage: P = Point([1,2],[2,3],{'alpha':.5})
sage: P
Point set defined by 2 point(s)
sage: P.options()['alpha']
0.500000000000000
sage: P.xdata
[1, 2]

TESTS:

We test creating a point:

sage: P = point((3,3))
__getitem__(i)

Returns tuple of coordinates of point.

EXAMPLES:

sage: P=point([(0,0), (1,1), (2,3)])
sage: p=P[0]; p
Point set defined by 3 point(s)
sage: p[1]
(1.0, 1.0)
__init__(xdata, ydata, options)

Initializes base class Point.

EXAMPLES:

sage: P = point((3,4))
sage: P[0].xdata
[3.0]
sage: P[0].options()['alpha']
1
_allowed_options()

Return the allowed options for the Point class.

EXAMPLES:

sage: P = point((3,4))
sage: P[0]._allowed_options()['pointsize']
'How big the point is.'
_plot3d_options(options=None)

Translate 2D plot options into 3D plot options.

EXAMPLES:

sage: A=point((1,1),pointsize=22)
sage: a=A[0];a
Point set defined by 1 point(s)
sage: b=a.plot3d()
sage: b.size
22
sage: b=a.plot3d(size=3)
sage: b.size
3
_render_on_subplot(subplot)

TESTS:

We check to make sure that #2076 is fixed by verifying all the points are red:

sage: point(((1,1), (2,2), (3,3)), rgbcolor=hue(1), pointsize=30) 
_repr_()

String representation of Point primitive.

EXAMPLES:

sage: P=point([(0,0), (1,1)])
sage: p=P[0]; p
Point set defined by 2 point(s)
plot3d(z=0, **kwds)

Plots a two-dimensional point in 3-D, with default height zero.

INPUT:

  • z - optional 3D height above xy-plane. May be a list if self is a list of points.

EXAMPLES:

One point:

sage: A=point((1,1))
sage: a=A[0];a
Point set defined by 1 point(s)
sage: b=a.plot3d()

One point with a height:

sage: A=point((1,1))
sage: a=A[0];a
Point set defined by 1 point(s)
sage: b=a.plot3d(z=3)
sage: b.loc[2]
3.0

Multiple points:

sage: P=point([(0,0), (1,1)])
sage: p=P[0]; p
Point set defined by 2 point(s)
sage: q=p.plot3d(size=22)

Multiple points with different heights:

sage: P=point([(0,0), (1,1)])
sage: p=P[0]
sage: q=p.plot3d(z=[2,3])
sage: q.all[0].loc[2]
2.0
sage: q.all[1].loc[2]
3.0

Note that keywords passed must be valid point3d options:

sage: A=point((1,1),pointsize=22)
sage: a=A[0];a
Point set defined by 1 point(s)
sage: b=a.plot3d()
sage: b.size
22
sage: b=a.plot3d(pointsize=23) # only 2D valid option
sage: b.size
22
sage: b=a.plot3d(size=23) # correct keyword
sage: b.size
23

TESTS:

Heights passed as a list should have same length as number of points:

sage: P=point([(0,0), (1,1), (2,3)])
sage: p=P[0]
sage: q=p.plot3d(z=2)
sage: q.all[1].loc[2]
2.0
sage: q=p.plot3d(z=[2,-2])
...
ValueError: Incorrect number of heights given
sage.plot.point.point(points, **kwds)

Returns either a 2-dimensional or 3-dimensional point or sum of points.

INPUT:

  • points - either a single point (as a tuple) or a list of points.

For information regarding additional arguments, see either point2d? or point3d?.

EXAMPLES:

sage: point((1,2))
sage: point((1,2,3))
sage: point([(0,0), (1,1)])
sage: point([(0,0,1), (1,1,1)])

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

sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)], frame=True)
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent
sage.plot.point.point2d(*args, **kwds)

A point of size pointsize defined by point = (x,y). Point takes either a single tuple of coordinates or a list of tuples.

Type point2d.options to see all options.

EXAMPLES:

A purple point from a single tuple or coordinates:

sage: point((0.5, 0.5), rgbcolor=hue(0.75))

If you need a 2D point to live in 3-space later, this is possible:

sage: A=point((1,1))
sage: a=A[0];a
Point set defined by 1 point(s)
sage: b=a.plot3d(z=3)

This is also true with multiple points:

sage: P=point([(0,0), (1,1)])
sage: p=P[0]
sage: q=p.plot3d(z=[2,3])

Here are some random larger red points, given as a list of tuples:

sage: point(((0.5, 0.5), (1, 2), (0.5, 0.9), (-1, -1)), rgbcolor=hue(1), pointsize=30)

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

sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)], frame=True)
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent
sage.plot.point.points(points, **kwds)

Returns either a 2-dimensional or 3-dimensional point or sum of points.

INPUT:

  • points - either a single point (as a tuple) or a list of points.

For information regarding additional arguments, see either point2d? or point3d?.

EXAMPLES:

sage: point((1,2))
sage: point((1,2,3))
sage: point([(0,0), (1,1)])
sage: point([(0,0,1), (1,1,1)])

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

sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)], frame=True)
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent

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