def polygon3d(points, **options):
"""
Draw a polygon in 3d.
INPUT:
- ``points`` - the vertices of the polygon
Type ``polygon3d.options`` for a dictionary of the default
options for polygons. You can change this to change
the defaults for all future polygons. Use ``polygon3d.reset()``
to reset to the default options.
EXAMPLES:
A simple triangle::
sage: polygon3d([[0,0,0], [1,2,3], [3,0,0]])
Some modern art -- a random polygon::
sage: v = [(randrange(-5,5), randrange(-5,5), randrange(-5, 5)) for _ in range(10)]
sage: polygon3d(v)
A bent transparent green triangle::
sage: polygon3d([[1, 2, 3], [0,1,0], [1,0,1], [3,0,0]], color=(0,1,0), alpha=0.7)
"""
from sage.plot.plot3d.index_face_set import IndexFaceSet
return IndexFaceSet([range(len(points))], points, **options)
def plot3d(self, 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']
TESTS:
Heights passed as a list should have same length as
number of points::
sage: P = polygon([(0,0), (1,2), (0,1), (-1,2)])
sage: p = P[0]
sage: q = p.plot3d(z=[2,-2])
Traceback (most recent call last):
...
ValueError: Incorrect number of heights given
"""
from sage.plot.plot3d.index_face_set import IndexFaceSet
options = self._plot3d_options()
options.update(kwds)
zdata = []
if isinstance(z, list):
zdata = z
else:
zdata = [z] * len(self.xdata)
if len(zdata) == len(self.xdata):
return IndexFaceSet(
[[(x, y, z)
for x, y, z in zip(self.xdata, self.ydata, zdata)]],
**options)
else:
raise ValueError('Incorrect number of heights given')
def polygons3d(faces, points, **options):
"""
Draw the union of several polygons in 3d.
Useful to plot a polyhedron as just one ``IndexFaceSet``.
INPUT:
- ``faces`` -- list of faces, every face given by the list
of indices of its vertices
- ``points`` -- coordinates of the vertices in the union
EXAMPLES:
Two adjacent triangles::
sage: f = [[0,1,2],[1,2,3]]
sage: v = [(-1,0,0),(0,1,1),(0,-1,1),(1,0,0)]
sage: polygons3d(f, v, color='red')
Graphics3d Object
"""
from sage.plot.plot3d.index_face_set import IndexFaceSet
return IndexFaceSet(faces, points, **options)