Points¶

class
sage.plot.point.
Point
(xdata, ydata, options)¶ Bases:
sage.plot.primitive.GraphicPrimitive_xydata
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]

plot3d
(z=0, **kwds)¶ Plots a twodimensional point in 3D, 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

sage.plot.point.
point
(points, **kwds)¶ Returns either a 2dimensional or 3dimensional 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

sage.plot.point.
point2d
(points, alpha=1, aspect_ratio='automatic', faceted=False, legend_color=None, legend_label=None, marker='o', markeredgecolor=None, rgbcolor=(0, 0, 1), 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 textlegend_label
– The label for this item in the legend.marker
– the marker symbol for 2D plots only (see documentation ofplot()
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 3space 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 ofpointsize
. The argumentpointsize
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 2dimensional or 3dimensional 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