Polygons¶
- class sage.plot.polygon.Polygon(xdata, ydata, options)¶
Bases:
sage.plot.primitive.GraphicPrimitive_xydata
Primitive class for the Polygon graphics type. For information on actual plotting, please see
polygon()
,polygon2d()
, orpolygon3d()
.INPUT:
xdata – list of \(x\)-coordinates of points defining Polygon
ydata – list of \(y\)-coordinates of points defining Polygon
options – dict of valid plot options to pass to constructor
EXAMPLES:
Note this should normally be used indirectly via
polygon()
:sage: from sage.plot.polygon import Polygon sage: P = Polygon([1,2,3],[2,3,2],{'alpha':.5}) sage: P Polygon defined by 3 points sage: P.options()['alpha'] 0.500000000000000 sage: P.ydata [2, 3, 2]
- plot3d(z=0, **kwds)¶
Plots a 2D polygon in 3D, with default height zero.
INPUT:
z
- optional 3D height above \(xy\)-plane, or a list of heights corresponding to the list of 2D polygon points.
EXAMPLES:
A pentagon:
sage: polygon([(cos(t), sin(t)) for t in srange(0, 2*pi, 2*pi/5)]).plot3d() Graphics3d Object
Showing behavior of the optional parameter z:
sage: P = polygon([(0,0), (1,2), (0,1), (-1,2)]) sage: p = P[0]; p Polygon defined by 4 points sage: q = p.plot3d() sage: q.obj_repr(q.testing_render_params())[2] ['v 0 0 0', 'v 1 2 0', 'v 0 1 0', 'v -1 2 0'] sage: r = p.plot3d(z=3) sage: r.obj_repr(r.testing_render_params())[2] ['v 0 0 3', 'v 1 2 3', 'v 0 1 3', 'v -1 2 3'] sage: s = p.plot3d(z=[0,1,2,3]) sage: s.obj_repr(s.testing_render_params())[2] ['v 0 0 0', 'v 1 2 1', 'v 0 1 2', 'v -1 2 3']
- sage.plot.polygon.polygon(points, **options)¶
Return either a 2-dimensional or 3-dimensional polygon depending on value of points.
For information regarding additional arguments, see either
polygon2d()
orpolygon3d()
. Options may be found and set using the dictionariespolygon2d.options
andpolygon3d.options
.EXAMPLES:
sage: polygon([(0,0), (1,1), (0,1)]) Graphics object consisting of 1 graphics primitive
sage: polygon([(0,0,1), (1,1,1), (2,0,1)]) Graphics3d Object
Extra options will get passed on to show(), as long as they are valid:
sage: polygon([(0,0), (1,1), (0,1)], axes=False) Graphics object consisting of 1 graphics primitive sage: polygon([(0,0), (1,1), (0,1)]).show(axes=False) # These are equivalent
- sage.plot.polygon.polygon2d(points, alpha=1, rgbcolor=(0, 0, 1), edgecolor=None, thickness=None, legend_label=None, legend_color=None, aspect_ratio=1.0, fill=True, **options)¶
Return a 2-dimensional polygon defined by
points
.Type
polygon2d.options
for a dictionary of the default options for polygons. You can change this to change the defaults for all future polygons. Usepolygon2d.reset()
to reset to the default options.EXAMPLES:
We create a purple-ish polygon:
sage: polygon2d([[1,2], [5,6], [5,0]], rgbcolor=(1,0,1)) Graphics object consisting of 1 graphics primitive
By default, polygons are filled in, but we can make them without a fill as well:
sage: polygon2d([[1,2], [5,6], [5,0]], fill=False) Graphics object consisting of 1 graphics primitive
In either case, the thickness of the border can be controlled:
sage: polygon2d([[1,2], [5,6], [5,0]], fill=False, thickness=4, color='orange') Graphics object consisting of 1 graphics primitive
For filled polygons, one can use different colors for the border and the interior as follows:
sage: L = [[0,0]]+[[i/100, 1.1+cos(i/20)] for i in range(100)]+[[1,0]] sage: polygon2d(L, color="limegreen", edgecolor="black", axes=False) Graphics object consisting of 1 graphics primitive
Some modern art – a random polygon, with legend:
sage: v = [(randrange(-5,5), randrange(-5,5)) for _ in range(10)] sage: polygon2d(v, legend_label='some form') Graphics object consisting of 1 graphics primitive
A purple hexagon:
sage: L = [[cos(pi*i/3),sin(pi*i/3)] for i in range(6)] sage: polygon2d(L, rgbcolor=(1,0,1)) Graphics object consisting of 1 graphics primitive
A green deltoid:
sage: L = [[-1+cos(pi*i/100)*(1+cos(pi*i/100)),2*sin(pi*i/100)*(1-cos(pi*i/100))] for i in range(200)] sage: polygon2d(L, rgbcolor=(1/8,3/4,1/2)) Graphics object consisting of 1 graphics primitive
A blue hypotrochoid:
sage: L = [[6*cos(pi*i/100)+5*cos((6/2)*pi*i/100),6*sin(pi*i/100)-5*sin((6/2)*pi*i/100)] for i in range(200)] sage: polygon2d(L, rgbcolor=(1/8,1/4,1/2)) Graphics object consisting of 1 graphics primitive
Another one:
sage: n = 4; h = 5; b = 2 sage: L = [[n*cos(pi*i/100)+h*cos((n/b)*pi*i/100),n*sin(pi*i/100)-h*sin((n/b)*pi*i/100)] for i in range(200)] sage: polygon2d(L, rgbcolor=(1/8,1/4,3/4)) Graphics object consisting of 1 graphics primitive
A purple epicycloid:
sage: m = 9; b = 1 sage: L = [[m*cos(pi*i/100)+b*cos((m/b)*pi*i/100),m*sin(pi*i/100)-b*sin((m/b)*pi*i/100)] for i in range(200)] sage: polygon2d(L, rgbcolor=(7/8,1/4,3/4)) Graphics object consisting of 1 graphics primitive
A brown astroid:
sage: L = [[cos(pi*i/100)^3,sin(pi*i/100)^3] for i in range(200)] sage: polygon2d(L, rgbcolor=(3/4,1/4,1/4)) Graphics object consisting of 1 graphics primitive
And, my favorite, a greenish blob:
sage: L = [[cos(pi*i/100)*(1+cos(pi*i/50)), sin(pi*i/100)*(1+sin(pi*i/50))] for i in range(200)] sage: polygon2d(L, rgbcolor=(1/8,3/4,1/2)) Graphics object consisting of 1 graphics primitive
This one is for my wife:
sage: L = [[sin(pi*i/100)+sin(pi*i/50),-(1+cos(pi*i/100)+cos(pi*i/50))] for i in range(-100,100)] sage: polygon2d(L, rgbcolor=(1,1/4,1/2)) Graphics object consisting of 1 graphics primitive
One can do the same one with a colored legend label:
sage: polygon2d(L, color='red', legend_label='For you!', legend_color='red') Graphics object consisting of 1 graphics primitive
Polygons have a default aspect ratio of 1.0:
sage: polygon2d([[1,2], [5,6], [5,0]]).aspect_ratio() 1.0
AUTHORS:
David Joyner (2006-04-14): the long list of examples above.