# Points¶

TESTS:

sage: E = EllipticCurve('37a')
sage: P = E(0,0)
sage: def get_points(n): return sum([point(list(i*P)[:2], size=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)])
Graphics3d Object

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: point((3,3))
Graphics object consisting of 1 graphics primitive

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),size=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])
Traceback (most recent call last):
...
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), a list of points, a single complex number, or a list of complex numbers.

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

EXAMPLES:

sage: point((1,2))
Graphics object consisting of 1 graphics primitive

sage: point((1,2,3))
Graphics3d Object

sage: point([(0,0), (1,1)])
Graphics object consisting of 1 graphics primitive

sage: point([(0,0,1), (1,1,1)])
Graphics3d Object


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)
Graphics object consisting of 1 graphics primitive
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent


TESTS:

One can now use iterators (trac ticket #13890):

sage: point(iter([(1,1,1)]))
Graphics3d Object
sage: point(iter([(1,2),(3,5)]))
Graphics object consisting of 1 graphics primitive

sage.plot.point.point2d(points, legend_color=None, faceted=False, rgbcolor=(0, 0, 1), marker='o', markeredgecolor=None, aspect_ratio='automatic', alpha=1, legend_label=None, size=10, **options)

A point of size size defined by point = $$(x,y)$$.

INPUT:

• points - either a single point (as a tuple), a list of points, a single complex number, or a list of complex numbers.
• alpha – How transparent the point is.
• faceted – If True color the edge of the point. (only for 2D plots)
• hue – The color given as a hue.
• legend_color – The color of the legend text
• legend_label – The label for this item in the legend.
• marker – the marker symbol for 2D plots only (see documentation of plot() for details)
• markeredgecolor – the color of the marker edge (only for 2D plots)
• rgbcolor – The color as an RGB tuple.
• size – How big the point is (i.e., area in points^2=(1/72 inch)^2).
• zorder – The layer level in which to draw

EXAMPLES:

A purple point from a single tuple or coordinates:

sage: point((0.5, 0.5), rgbcolor=hue(0.75))
Graphics object consisting of 1 graphics primitive


Points with customized markers and edge colors:

sage: r = [(random(), random()) for _ in range(10)]
sage: point(r, marker='d', markeredgecolor='red', size=20)
Graphics object consisting of 1 graphics primitive


Passing an empty list returns an empty plot:

sage: point([])
Graphics object consisting of 0 graphics primitives
sage: import numpy; point(numpy.array([]))
Graphics object consisting of 0 graphics primitives


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), size=30)
Graphics object consisting of 1 graphics primitive


And an example with a legend:

sage: point((0,0), rgbcolor='black', pointsize=40, legend_label='origin')
Graphics object consisting of 1 graphics primitive


The legend can be colored:

sage: P = points([(0,0),(1,0)], pointsize=40, legend_label='origin', legend_color='red')
sage: P + plot(x^2,(x,0,1), legend_label='plot', legend_color='green')
Graphics object consisting of 2 graphics primitives


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)
Graphics object consisting of 1 graphics primitive
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent


For plotting data, we can use a logarithmic scale, as long as we are sure not to include any nonpositive points in the logarithmic direction:

sage: point([(1,2),(2,4),(3,4),(4,8),(4.5,32)],scale='semilogy',base=2)
Graphics object consisting of 1 graphics primitive


Since Sage Version 4.4 (trac ticket #8599), the size of a 2d point can be given by the argument size instead of pointsize. The argument pointsize is still supported:

sage: point((3,4), size=100)
Graphics object consisting of 1 graphics primitive

sage: point((3,4), pointsize=100)
Graphics object consisting of 1 graphics primitive


We can plot a single complex number:

sage: point(CC(1+I), pointsize=100)
Graphics object consisting of 1 graphics primitive


We can also plot a list of complex numbers:

sage: point([CC(I), CC(I+1), CC(2+2*I)], pointsize=100)
Graphics object consisting of 1 graphics primitive

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), a list of points, a single complex number, or a list of complex numbers.

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

EXAMPLES:

sage: point((1,2))
Graphics object consisting of 1 graphics primitive

sage: point((1,2,3))
Graphics3d Object

sage: point([(0,0), (1,1)])
Graphics object consisting of 1 graphics primitive

sage: point([(0,0,1), (1,1,1)])
Graphics3d Object


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)
Graphics object consisting of 1 graphics primitive
sage: point([(cos(theta), sin(theta)) for theta in srange(0, 2*pi, pi/8)]).show(frame=True) # These are equivalent


TESTS:

One can now use iterators (trac ticket #13890):

sage: point(iter([(1,1,1)]))
Graphics3d Object
sage: point(iter([(1,2),(3,5)]))
Graphics object consisting of 1 graphics primitive


Plotting fields

Polygons